# Challenges in data-based geospatial modeling for environmental research and
practice

Diana Koldasbayeva  Skolkovo Institute of Science and Technology, Bolshoy
Boulevard 30, bld. 1, 121205 Moscow, Russia  Polina Tregubova  Skolkovo
Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, 121205
Moscow, Russia  Mikhail Gasanov  Skolkovo Institute of Science and Technology,
Bolshoy Boulevard 30, bld. 1, 121205 Moscow, Russia  Alexey Zaytsev  Skolkovo
Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, 121205
Moscow, Russia  Yanqi Lake Beijing Institute of Mathematical Sciences and
Applications (BIMSA), No. 544, Hefangkou Village, Huaibei Town, Huairou
District, Beijing 101408  Anna Petrovskaia  Skolkovo Institute of Science and
Technology, Bolshoy Boulevard 30, bld. 1, 121205 Moscow, Russia  Evgeny
Burnaev  Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30,
bld. 1, 121205 Moscow, Russia  Autonomous Non-Profit Organization Artificial
Intelligence Research Institute (AIRI), 105064 Moscow, Russia

###### Abstract

With the rise of electronic data, particularly Earth observation data, data-
based geospatial modelling using machine learning (ML) has gained popularity
in environmental research. Accurate geospatial predictions are vital for
domain research based on ecosystem monitoring and quality assessment and for
policy-making and action planning, considering effective management of natural
resources. The accuracy and computation speed of ML has generally proved
efficient. However, many questions have yet to be addressed to obtain precise
and reproducible results suitable for further use in both research and
practice. A better understanding of the ML concepts applicable to geospatial
problems enhances the development of data science tools providing transparent
information crucial for making decisions on global challenges such as
biosphere degradation and climate change. This survey reviews common nuances
in geospatial modelling, such as imbalanced data, spatial autocorrelation,
prediction errors, model generalisation, domain specificity, and uncertainty
estimation. We provide an overview of techniques and popular programming tools
to overcome or account for the challenges. We also discuss prospects for
geospatial Artificial Intelligence in environmental applications.

To date, obtaining spatial predictions is an essential step in the monitoring,
assessment, and prognosis tasks applicable to all kinds of Earth systems on
both local and global scales (Figure 1). Regional spatial analysis for areas
of interest now plays a crucial role in risk-sensitive land use and
vulnerability assessment facing environmental sustainability threats, climate
change urgency, and disasters occurrences such as fires[1, 2, 3], floods[4, 5,
6], and droughts [7, 8], in biodiversity conservation prioritisation and
actions planning [9, 10, 11], natural resources inventorying [12, 13, 14],
land cover inventorying and change detection [15, 16], ecosystems functioning
assessment [17, 18], and other environment-related tasks.

Figure 1: Examples of geospatial mapping performed for different tasks of
environmental monitoring and assessment a) maps of forest disturbance regimes
of Europe [19]; b) land cover and mapping of losses for different types of
forest in Indonesia [20]; c) maps of soil organic carbon (SOC) fractions
contribution to SOC for selected depths of 0–5, 5–15, and 15–30 cm obtained
for Australia [21]; d) maps of chlorophyll-A estimation derived from
Sentinel-2 data in the Barents Sea [22].

Spatial modelling results could be not only the final expected outcome but an
intermediate step and required base for the following system analysis. For
instance, forest maps can be used to estimate how vulnerable vegetation is to
events contributing to climate change, such as cycles of forest damage and
forest succession after fires [23, 24], and to assess the long-term
sustainability of forest carbon sinks [25]. Another example is a prediction of
the quality of resources such as soil [26] based on environmental predictor
maps. One of the most common use cases is applying land use and land cover
(LULC) map products for a wide range of research and practical issues. Land
cover maps can be used to estimate environment-related phenomena, such as
ecosystem services [17, 18], assess spatiotemporal resource changes, and
distinguish influencing factors [26, 27]. Apart from that, LULC products serve
to enhance prediction — for example, to stratify modelling solutions
(ensembling) in order to raise forecast precision [28]. The products can also
serve as label data to develop new prediction approaches—for example, to
classify single-date images in order to obtain large area cover maps [29].

The expectations about mapping usefulness for developing decision-making tools
have been quite high since at least the beginning of the century[30]. Being
not only a tool for purely increasing our knowledge about the environment,
geospatial predictions have already been included as an essential base for
policy and coordinated action support. For instance, fire mapping supports The
Monitoring Trends in Burn Severity (MTBS) program [31], catching burn severity
and extent of large fires for monitoring the effectiveness of the National
Fire Plan. Invasive species habitat suitability mapping informs decision-
making by identifying high-risk species and pathways, increasing information
exchange, action efficiency, and cost-savings within the U.S. Department of
the Interior Invasive Species Strategic Plan [32]. Another example is the
geospatial assessment and management of flood risks as an information tool to
plan and prioritise technical, financial, and political decisions regarding
flood risk management within Directive 2007/60/EC (2007) [33]. It is
highlighted that Earth observation global maps play a crucial role in
supporting the key aspects of the Paris Agreement, such as making nationally
determined contributions, enhancing the transparency of national GHG
(greenhouse gas) reporting, managing GHG sinks and reservoirs, and developing
market-based solutions [34].

On a global scale, spatial mapping results can serve as both inputs for
integrated assessment models (IAMs) and target output data to forecast and
understand postponed consequences of changing socioeconomic development and
climate change scenarios, which helps to plan climate change actions
considering other sustainable development goals[35]. Additionally, information
from global mapping products can fill the blind spots where domestic land
cover inventories are poorly organised and impede coordinating responses to
global challenges [34].

At the same time, the question of the quality of spatial predictions and
possible struggles to achieve trustworthy results has been drawing much
attention recently. One of the most important concerns lies in the very nature
of data-based modelling—that is, the belief that knowledge can be obtained
through observation [36]. Thus, proper techniques for managing data from
geospatial observations are of great question. Another issue related to
efficient and fair data handling is the existing gap between domain
specialists and applied data scientists, both underrepresented in each other’s
fields.

In recent work [37] it was emphasised that ignoring the spatial nature of the
data led to the misleading high predictive power of the model, while
appropriate spatial model validation methods revealed poor relationships
between the target characteristic—aboveground forest biomass—and selected
predictors. On the contrary, in [38] the idea of spatial validation is
critically discussed, while other approaches to overcome biases in the data
are proposed instead. The importance of spatial dependence between training
and test sets and its influence on the model generalisation capabilities in
the Earth observation data classification is addressed in [39]. Other examples
of issues in global environmental spatial mapping are the distribution shift,
data concentration, and predictions’ accuracy assessment, which are discussed
in the latest comment article [40]. Thus, given the confusion about the
modelling process and quality estimation of results and in light of the rising
demand for spatial predictions, an overview of common struggles in geospatial
modelling and relevant approaches and tools to address the issues are of both
scientific and practical use.

In addition to the existing literature background [41, 42, 43, 44, 45, 46, 47,
40], this review aims to comprehensively address the limitations of data-
driven geospatial mapping at each step of predicting the spatial distribution
of target features. Here we provide a practical guide, discussing the
challenges associated with using nonuniformly distributed real-world data from
various domains in environmental research, including those from open sources.
These challenges include dealing with limited observations and imbalanced and
autocorrelated data, maintaining the model training process, and assessing
prediction quality and uncertainty (Figure 2). Throughout the review, we
provide examples from recent environmental geospatial modelling research to
illustrate the identified problems, highlight the underlying theoretical
concepts, and present approaches to evaluating and overcoming each specific
limitation.

##  1 Data-driven approaches to forecasting spatial distribution of
environmental features

In this review, we analyse geospatial modelling based on data-driven
approaches, meaning that models are built with parameters learned from
observations’ data, thus simulating new data minimally different from the
“ground truth” under the same set of descriptive features. Among the standards
guiding the implementation of data-based model applications, CRISP-DM is the
most well-known. There are, however, other workflows with more nuanced
guidelines tailored to specific problems or more mature fields of data-based
modelling [48, 49]. Recently, guidelines and checklists have been proposed for
environmental modelling tasks to help address common problems and improve the
reliability of outputs [45, 50]. For instance, a checklist [45] for ecological
niche modelling suggests using a standardised format for reporting the
modelling procedure and results to ensure research reproducibility. It
emphasises the importance of disclosing details of each prediction-obtaining
step, from data collection to model application and result evaluation. In
general, the main steps to solve the applied problems using data-driven
algorithms can be the following [51]:

  1. 1.

Understanding the problem and the data. This step depends on the specific
domain, such as conservation biology and ecology, epidemiology, spatial
planning, natural resource management, climate monitoring, and predicting
hazardous events.

  2. 2.

Data collection and feature engineering. Pre-processing data from different
domains involves collecting ground-truth data from specific locations and
combining it with relevant environmental features such as, for instance, Earth
observation images, weather and climate patterns.

  3. 3.

Model selection. The choice of model depends on the characteristics of the
target feature, the specificity of the task, and available resources.

  4. 4.

Model training. Training the model involves optimizing hyperparameters to fit
the data type and shape.

  5. 5.

Accuracy evaluation. Appropriate accuracy scores are selected based on the
task, with a focus on controlling overfitting. The model’s performance is
better to be evaluated using "gold standard" data with expert annotations.

  6. 6.

Model deployment and inference. This involves building maps with spatial
predictions for the region of interest and determining the level of certainty
of the model’s estimations.

For data-based modelling tasks, including mapping, various classic machine
learning (ML) algorithms [52] and deep learning (DL) algorithms [53, 54, 15,
16] are used. The choice of algorithm depends on the type of target variable.
Classification algorithms are employed for predicting categorical target
variables, which could be land cover and land change mapping [15, 16],
cropland and crop type mapping [52, 55], identification of pollution sources
[56], mapping pollutant impact to distinguish free and affected lands [57],
the landslide [53] and wildfire [28] susceptibility mapping, and habitat
suitability mapping [58]. Regression algorithms are used to forecast the
distribution of continuous target variables – for instance, the prediction of
the geospatial distribution of important soil features, such as soil carbon
characteristics [27], groundwater potential, and quality assessment [59, 60],
and vegetation characteristics such as forest height [61] and biomass [62].
Handling data and interpreting results at each step of obtaining spatial
predictions can be complex, leading to low-quality predictions and misleading
interpretations. Therefore, careful control using adopted approaches and
metrics is necessary.

Figure 2: General workflow for the tasks including geospatial modelling
process and common issues relevant for each stage.

##  2 Imbalanced data

###  2.1 Problem statement

The problem of imbalanced data is one of the most relevant issues in
environment-related research with a focus on spatial capturing of target
events or features. Imbalance occurs when the number of samples belonging to
one class or classes (majority class[es]) significantly surpasses the number
of objects in another class or classes (minority class[es]) [63, 64].

Although being highly imbalanced is one of the basic properties of the real
world, most models assume uniform data distribution and complete input
information. Thus, a nonuniform input data distribution poses difficulties
when training models. The minority class occurrences are infrequent, and
classification rules that predict the small classes are usually rare,
overlooked, or ignored. As a result, test samples belonging to the minority
classes are misclassified more frequently compared with test samples from the
predominant classes.

In geospatial modelling, one of the most frequent challenges is dealing with
sparse or nonexistent data in certain regions or classes [65, 66, 67, 68, 69].
This issue arises from the high cost of data collection and storage,
methodological challenges, or the rarity of certain phenomena in specific
regions.

For instance, forecasting habitat suitability for species — species
distribution modelling (SDM) — is a common task in conservation biology, and
it relies on ML methods, often involving binary classification of species
abundance. Although well-known sources such as the GBIF (the Global
Biodiversity Information Facility) database [70] provide numerous species
occurrence records, absence records are few, while it is additionally
difficult to establish such locations from the methodological point of view
[71]. For instance, anomaly detection and mapping, particularly relevant for
ecosystem degradation monitoring, often involves the challenge of overcoming
imbalanced data—for example, in pollution cases, such as oil spills occurring
on both land and water surfaces. Accurate detection and segmentation of oil
spills with image analysis is vital for effective leak cleanup and
environmental protection. But, despite the regular collection of Earth surface
images by various satellite missions, there are significantly fewer scenes of
oil spills compared with images of clean water [72, 73]. Similarly, detection
and mapping of hazardous events, such as wildfires, struggles from the same
problem [66].

In classic research, Weiss and Provost [74] examined the relationship between
decision trees’ classification abilities and the class distribution of
training data and demonstrated that a relatively balanced distribution
generally yields better results compared with an imbalanced one. The sample
size plays a critical role in assessing the accuracy of a classification model
considering the class imbalance. When the imbalance degree remains constant,
the limited sample size raises concerns about discovering inherent patterns in
the minority class. Experimental findings suggest that the significant error
rate caused by imbalanced class distribution decreases as the training set
size increases [75]. This observation aligns logically, because having more
data provides the classification model with a better understanding of the
minority class, enabling differentiation between rare samples and the
majority. According to Japkowicz [75], if a sufficiently large dataset is
available and the training time for such a dataset is acceptable, the
imbalanced class distribution may not hinder the construction of an accurate
classification model [76].

###  2.2 Approaches to measuring the problem of imbalanced data

Various approaches quantify class imbalance. One method is to examine the
class distribution ratio directly, which can be as extreme as 1:100, 1:1000,
or even more in real-world scenarios. The minority class percentage (MCP)
calculates the percentage of instances in the minority class. Gini index (GI)
measures inequality or impurity among classes, indicating imbalance [77].
Shannon entropy (SE) is another way to measure non-uniformity or data
substance and can be linked to imbalance through the entropy of the class
distribution [77]. The Kullback-Leibler (KL) divergence measures the contrast
between probability distributions. Thus, it shows how close the observed class
distribution is to a hypothetical balanced distribution [78]. Higher values of
GI, SE, and KL indicate a higher imbalance.

In dealing with class imbalance, it is crucial to use appropriate quality
metrics to reflect model performance accurately. Standard accuracy may
mislead, especially when there is a significant class imbalance — for example,
a model that always predicts the major class yielding a high accuracy but
performs poorly for the minority class [79]. The F1 score, combining precision
and recall, is a better alternative and is commonly used for imbalanced data,
particularly for the minority class. Another useful metric is the G-mean,
which balances sensitivity and specificity and provides a more reliable
performance assessment, especially in imbalanced datasets [80, 75].

###  2.3 Solutions to improve geospatial modelling for imbalanced data

Various reviews address imbalanced data in ML, in general, [76, 77, 81, 64],
while approaches relevant to geospatial modelling are also worth to be
discussed. Approaches to tackling imbalanced data problems in geospatial
prediction tasks can be divided into data-level, model-level and combined
techniques.

####  2.3.1 Data-level approaches

##### Numerical data

In terms of working with the data itself, the class imbalance problem can be
addressed by modifying the training data through resampling techniques. There
are two main ideas: oversampling the minority class and undersampling the
majority class [78, 82, 83, 76]. These techniques can be applied randomly or
in an informative way. For instance, in SDM, random oversampling is often a
choice to create new minority class samples (e.g., species absence) [84],
while random undersampling is used to balance the class distribution,
particularly for species occurrence [85]. Informative oversampling may involve
generating artificial minority samples based on geographic distance. For
instance, in SDM, pseudoabsence generation can be performed using the biomod2
R package [84] with a ’disk’ option based on geographic distance. Informative
undersampling can involve thinning the majority class by deleting
geographically close points, which can be done with spThin R package [85]. In
Figure 3, we illustrate the issue of imbalanced data and present solutions,
including oversampling and undersampling techniques.

More complex methods for handling imbalanced data involve adding artificial
objects to the minority class or modifying samples in a meaningful way. One
popular approach is the synthetic minority oversampling technique (SMOTE)
[78], which combines both oversampling of the minority class and undersampling
of the majority class. SMOTE creates new samples by linearly interpolating
between minority class samples and their K-nearest neighbour minority class
samples.

Figure 3: Handling imbalance data for artificially species distribution
generated data. A) Data generation using virtualspecies [86] R package based
on annual mean temperature and annual precipitation, obtained from WordlClim
[87] database. B) Oversampling the minority class by smote method with
smotefamily [88] R package. C) Achieving a balanced dataset through random
undersampling of the prevalent class.

Various has recently seen various modifications [89, 90]. Since there are more
than 100 SMOTE variants in total [91], here we focus on those relevant to
geospatial modelling. One widely used method for oversampling the minority
class is the Adaptive synthetic sampling approach for imbalanced learning
(ADASYN) [92, 93, 94, 95]. ADASYN uses a weighted distribution that considers
the learning difficulties of distinct instances within the minority class,
generating more synthetic data for challenging instances and fewer for less
challenging ones [96].To address potential overgeneralization in SMOTE [77,
89], Borderline-SMOTE is proposed. It concentrates on minority samples that
are close to the decision boundary between classes. These samples are
considered to be more informative for improving the performance of the
classification model on the minority class. Two techniques, Borderline-SMOTE1
and Borderline-SMOTE2, have been proposed, outperforming SMOTE in terms of
suitable model performance metrics, such as the true-positive rate and an
F-value [97]. Another approach is the Majority Weighted Minority Oversampling
Technique (MWMOTE), which assigns weights to hard-to-learn minority class
samples based on their Euclidean distance from the nearest majority class
samples [98]. The algorithm involves three steps: selecting informative
minority samples, assigning selection weights, and generating synthetic
samples using clustering. MWMOTE consistently outperformed other techniques
such as SMOTE, ADASYN, and RAMO in various performance metrics, including
accuracy, precision, F-score, G-mean, and the Area Under the Receiver
Operating Characteristic (ROC) Curve (AUC) [98].

As for the limitations of discussed data-level approaches, oversampling and
undersampling may, given that they are widely used, lead to overfitting and
introduce bias in the data [77, 91]. Additionally, these techniques do not
address the root cause of class imbalance and may not generalise well to
unseen data [99, 76].

##### Image data

Computer vision techniques applied to Earth observation tasks have gained
their popularity and now play a pivotal role in the analysis of remote sensing
data[100, 101, 102, 15]. Thus, it is worth examining approaches to overcoming
data imbalance problems on the image level.

Data augmentation is a fundamental technique for expanding limited image
datasets [103]. It revolves around enriching training data by applying various
transformations, such as geometric alterations, colour adjustments, image
blending, kernel filters, and random erasing. These transformations enhance
both model performance and generalization. Geospatial modelling frequently
uses data augmentation strategies to address specific challenges. For example,
experts employ a cropping-based augmentation approach in mineral prospective
mapping. This technique generates additional training samples while preserving
the spatial distribution of geological data [104]. DL-based oversampling
techniques such as adversarial training, Neural Style Transfer, Generative
Adversarial Networks (GANs) and meta-learning approaches offer intelligent
alternatives for oversampling [105]. Neural Style Transfer stands out as a
captivating method for generating novel images. It achieves this by
extrapolating styles from external sources or blending styles among dataset
instances [106]. For instance, researchers have harnessed the power of Neural
Style Transfer alongside ship simulation samples in remote sensing ship image
classification. This dynamic combination enhances training data diversity,
resulting in substantial improvements in classification performance [107].
GANs, on the other hand, specialise in crafting artificial samples that
closely mimic the characteristics of the original dataset. For instance, GANs
have been used for data augmentation in specific domains, such as roof damage
detection and partial discharge pattern recognition in Geographic Information
Systems [108, 109]. In the context of landslide susceptibility mapping, a
notable research study introduces a GAN-based approach to tackle imbalanced
data challenges, comparing its effectiveness with traditional methods such as
SMOTE [110].

Taking it a step further, researchers have unveiled a deeply supervised
Generative Adversarial Network (D-sGAN) tailored for high-quality data
augmentation of remote sensing images. This innovative approach proves
particularly beneficial for semantic interpretation tasks. It not only
exhibits faster image generation speed but also enhances segmentation accuracy
when contrasted with other GAN models like CoGAN, SimGAN, and CycleGAN [111].

However, it’s worth noting that these advanced oversampling techniques come
with their own set of challenges. One notable concern is the potential for
overfitting the oversampled minority class. This risk primarily arises from
the biases that can persist in the data even after applying these oversampling
techniques [112].

####  2.3.2 Model-level approaches

Cost-sensitive learning
Cost-sensitive learning involves considering the different costs associated
with classifying data points into various categories. Instead of treating all
misclassifications equally, it takes into account the consequences of
different types of errors. For example, it recognises that misclassifying a
rare positive instance as negative (more prevalent) is generally more costly
than the reverse scenario. In cost-sensitive learning, the goal is to minimise
both the total cost resulting from incorrect classifications and the number of
expensive errors. This approach helps prioritise the accurate identification
of important cases, such as rare positive instances, in situations where the
class imbalance is a concern [113].

Cost-sensitive learning finds application in spatial modelling, scenarios
involving imbalanced datasets, or situations where the impact of
misclassification varies among different classes or regions. Several studies
have shown it is effective in this context [114, 115, 116].

Boosting

Boosting algorithms are commonly used in geospatial modelling because they are
superior in handling tabular spatial data and addressing imbalanced data [117,
118, 119, 115, 120]. They effectively manage both bias and variance in
ensemble models.

Ensemble methods such as Bagging or Random Forest reduce variance by
constructing independent decision trees, thus reducing the error that emerges
from the uncertainty of a single model. In contrast, AdaBoost and gradient
boosting train models consecutively and aim to reduce errors in existing
ensembles. AdaBoost gives each sample a weight based on its significance and,
therefore, assigns higher weights to samples that tend to be misclassified,
effectively resembling resampling techniques.

In cost-sensitive boosting, the AdaBoost approach is modified to account for
varying costs associated with different types of errors. Rather than solely
aiming to minimise errors, the focus shifts to minimising a weighted
combination of these costs. Each type of error is assigned a specific weight,
reflecting its importance in the context of the problem. By assigning higher
weights to errors that are more costly, the boosting algorithm is guided to
prioritise reducing those particular errors, resulting in a model that is more
sensitive to the associated costs [76].

This modification results in three cost-sensitive boosting algorithms: AdaC1,
AdaC2, and AdaC3. After each round of boosting, the weight update parameter is
recalculated, incorporating the cost items into the process [121, 122]. In
cost-sensitive AdaBoost techniques, the weight of False Negative is increased
more than that of False Positive. AdaC2 and AdaCost methods can, however,
decrease the weight of True Positive more than that of True Negative. Among
these methods, AdaC2 was found to be superior for its sensitivity to cost
settings and better generalisation performance with respect to the minor class
[76].

####  2.3.3 Combining model-level and data-level approaches

Modifications of the discussed techniques could be used as well. For instance,
several techniques combine boosting, and SMOTE approaches to address
imbalanced data. One such method is SMOTEBoost, which synthesises samples from
the underrepresented class using SMOTE and integrates it with boosting. By
increasing the representation of the minority class, SMOTEBoost helps the
classifier learn better decision boundaries and boosting emphasises the
significance of minority class samples for correct classification [78, 123,
120]. As for limitations, SMOTE is a complex and time-consuming data sampling
method. Therefore, SMOTEBoost exacerbates this issue as boosting involves
training an ensemble of models, resulting in extended training times for
multiple models. Another approach is RUSBoost, which combines RUS (Random
Under-Sampling) with boosting. It reduces the time needed to build a model,
which is crucial when ensembling is the case, and mitigates the information
loss issue associated with RUS [124]. Thus, the data that might be lost during
one boosting iteration will probably be present when training models in the
following iterations.

Despite being a common practice to address the class imbalance, creating ad-
hoc synthetic instances of the minority class has some drawbacks. For
instance, in high-dimensional feature spaces with complex class boundaries,
calculating distances to find nearest neighbours and performing interpolation
can be challenging [78, 77]. To tackle data imbalances in classification,
generative algorithms can be beneficial. For instance, a framework combining
generative adversarial networks and domain-specific fine-tuning of CNN-based
models has been proposed for categorising disasters using a series of
synthesised, heterogeneous disaster images [125]. SA-CGAN (Synthetic
Augmentation with Conditional Generative Adversarial Networks) employs
conditional generative adversarial networks (CGANs) with self-attention
techniques to create high-quality synthetic samples [126]. By training a CGAN
with self-attention modules, SA-CGAN creates synthetic samples that closely
resemble the distribution of the minority class, successfully capturing long-
range interactions. Another variation of GANs, EID-GANs (Extremely Imbalanced
Data Augmentation Generative Adversarial Nets), focus on severely imbalanced
data augmentation and employ conditional Wasserstein GANs with an auxiliary
classifier loss [127].

##  3 Autocorrelation

###  3.1 Problem statement

Autocorrelation is a statistical phenomenon where the value at a data point is
influenced by the values at its neighbouring data points. In the context of
environmental research, autocorrelation is frequently observed resulting from
the spatial continuity of natural phenomena, such as temperature,
precipitation, or species occurrence patterns. However, the data-driven
approaches applied for the tasks of spatial predictions assume independence
among observations. If spatial autocorrelation (SAC) is not properly
addressed, the geospatial analysis may result in misleading conclusions and
erroneous inferences. Consequently, the significance of research findings may
be overestimated, potentially affecting the validity and reliability of
predictions [128, 129].

On the contrary, there could be environment-related tasks where
autocorrelation is explored as the interdependence pattern between spatially
distributed data not to be mitigated. For instance, based on an assessment of
SAC catching regional spatial patterns in the LULC changes, a decision-support
framework considering both land protection schemes, adapted financial
investment and greenway construction projects supporting habitats was
developed [130]. Other examples are the enhancement of a landslide early
warning system introducing susceptibility-related areas based on catching
autocorrelation of landslide locations with rainfall variables [131], and an
approach to assessing the spatiotemporal variations of vegetation productivity
based on the SAC indices valuable for integrated ecosystem management [132].

##### Spatial autocorrelation

While the definition of SAC varies, in general it integrates the principle
that geographic elements are interlinked according to how close they are to
one another, with the degree of connectivity fluctuating as a function of
proximity, echoing the fundamental law of geography [133, 134]. Essentially,
SAC outlines the extent of similarity among values of a characteristic at
diverse spatial locations, providing a foundation for recognising and
interpreting patterns and connections throughout different geographic areas 4.

Spatial processes exhibit characteristics of spatial dependence and spatial
heterogeneity, each bearing significant implications for spatial analysis:

  * •

Spatial dependence. This phenomenon denotes the autocorrelation amidst
observations, which contradicts the conventional assumption of residual
independence seen in methods such as linear regression. One approach to
circumvent this is through spatial regression.

  * •

Spatial heterogeneity. Arising from non-stationarity in the processes
generating the observed variable, spatial heterogeneity undermines the
effectiveness of constant linear regression coefficients. Geographically
weighted regression offers a solution to this issue [135, 136].

Numerous studies have ventured into exploring SAC and its mitigation
strategies in spatial modelling. There exists a consensus that spatially
explicit models supersede non-spatial counterparts in most scenarios by
considering spatial dependence [137]. However, the mechanisms driving these
disparities in model performance and the conditions that exacerbate them
warrant further exploration [138, 139, 140, 141]. A segment of the academic
community contests the incorporation of autocorrelation in mapping,
attributing potential positive bias in estimates as a consequence and
advocating its application only for significantly clustered data [38].

Residual spatial autocorrelation (rSAC) manifests itself not only in original
data but also in the residuals of a model. Residuals quantify the deviation
between observed and predicted values within the modelling spectrum.
Consequently, rSAC evaluates the spatial autocorrelation present in the
variance that the explanatory variables fail to account for. Grasping the
distribution of residuals is vital in regression modelling, given that it
underpins assumptions such as linearity, normality, equal variance
(homoscedasticity), and independence, all of which hinge on error behavior
[137].

Figure 4: The difference in spatial autocorrelation in Geochemical maps from
USGS Open-File Report[142]. A) There appears to be a strong positive spatial
autocorrelation with high concentrations (in red) and low concentrations (in
blue) clustered together. B) The Bismuth map shows more scattered and less
distinct clustering, indicating weaker spatial autocorrelation. The central
and eastern regions show interspersed high and low values, suggesting a
negative or weaker spatial autocorrelation.

###  3.2 Approaches to measuring the problem of spatial autocorrelation

Logically, the first step is to determine whether SAC is likely to affect the
planned analysis — that is, if the model residuals display SAC, before
considering modelling techniques that account for geographical
autocorrelation. Checking for SAC has become commonplace in geography and
ecology [43, 143]. Among the methods used are 1) Moran’s correlogram, 2)
Geary’s correlogram, and 3) variogram (semi-variogram) [144]. The main idea of
checking SAC underlies the investigation and tests whether nearby locations
tend to be more clustered than randomness alone [145].

Moran’s I and Geary’s C are measures used to analyze spatial autocorrelation
in data[146]. Moran’s I, ranging from -1 to +1, identifies general patterns
within the entire dataset: values near +1 indicate clusters of similar values,
-1 suggests adjacent dissimilar values, and 0 represents a random pattern. In
contrast, Geary’s C, ranging from 0 to +2, is sensitive to local variations,
with 0 indicating positive, 2 showing negative autocorrelation, and 1 denoting
a random pattern. While Moran’s I is preferred for analyzing global patterns,
Geary’s C is useful for detecting local patterns [147].

Correlograms based on Moran’s I typically exhibit a decline from a certain
level of SAC to a value of 0 or even lower, signifying an absence of SAC at
specific distances between locations. Essentially, a value of 0 or below
suggests no observable SAC or a random spatial distribution of the variable
under consideration. Similarly, for Geary’s C, a value near 0 indicates an
absence of SAC or spatial randomness, suggesting that the spatial distribution
of the variable is akin to what might be expected if it were randomly
distributed. On the other hand, higher values of Geary’s C, especially those
greater than 1, suggest positive SAC. This means that the variable’s
distribution shows similarity or clustering at different locations,
highlighting a distinct spatial pattern in the data [143].

One of the crucial mathematical tools to assess the spatial variability and
dependence of a stochastic variable is a variogram. Its primary purpose is to
measure how the values of a variable alter as the spatial separation between
sampled locations increases.

The variogram is mathematically defined as one-half of the variance of the
dissimilarities observed between pairs of random variables at distinct
locations, expressed as a function of the spatial separation between those
locations. In precise terms, the variogram represents the variance of the
difference between the values of the spatial variable at two points, which are
separated by the vector. In simpler terms, it quantifies the extent of
dissimilarity or variation between pairs of observations at different spatial
distances. The shape of the variogram cloud brings valuable insights into the
spatial structure of the studied variable. Commonly employed variogram models,
such as spherical, exponential, or Gaussian models, can be fitted to the
scatter plot to estimate the parameters that characterize the spatial
dependence. The variogram holds significant importance in geostatistics and
finds diverse applications, including spatial interpolation, prediction, and
mapping of environmental variables such as soil properties, pollutant
concentrations, and geological features. By comprehending the spatial
structure through variogram analysis, researchers and practitioners can make
more informed decisions and accurate predictions in fields such as geology,
hydrology, environmental science, and related disciplines.

###  3.3 Solutions to overcome SAC and rSAC

The most common ways to eliminate the influence of SAC in the data on the
prediction quality are the following:

  1. 1.

proper sampling design

  2. 2.

careful feature selection method

  3. 3.

model selection

  4. 4.

spatial cross-validation

####  3.3.1 Sampling design

SAC influences occur in its capacity to delineate significance levels,
demarcate discernible disparities in attribute measures across diverse
populations, and elucidate attribute variability [148]. An amplified presence
of SAC in georeferenced datasets invariably leads to an augmentation in
redundant or duplicate information [149]. This redundancy stems from two
primary sources: geographic patterns informed by shared variables or the
consequences of spatial interactions, typically characterised as geographic
diffusion.

Exploring the details of sampling in relation to SAC reveals many layers of
understanding:

  * •

The employment of diverse stratification criteria elicits heterogeneous
impacts upon the amplitude of SAC [150].

  * •

The soil sampling density and SAC critically influence the veracity of
interpolation methodologies [151].

  * •

Empirical findings suggest that sampling paradigms characterised by
heterogeneous sampling intervals — notably random and systematic-cluster
designs — demonstrate enhanced efficacy in discerning spatial structures,
compared with purely systematic approaches [152].

The size of the sample also plays a key role in spatial modeling. In
quantitative studies, it affects how broadly the results can be applied and
how the data can be handled. In qualitative studies, it’s crucial to establish
that results can be applied in other contexts and for discovering new insights
[153]. The relationship between SAC and the best sample size in quantitative
research has been a popular topic, leading to many studies and discussions
[154, 149, 155].

In remote sensing, the main goal is often to use spectral data to guess
attributes of places that have not been sampled. Regular sampling methods are
usually best for this. Using close pairs of points in a regular design may
make our predictions more accurate. But these designs do not work as well in
different situations. Spatially detailed models are good for places with clear
spatial patterns. They do not adapt well, however, to places with different
patterns. Importantly, if our sampling design creates distances that match the
natural spacing in the area, our predictions might be less certain [156].

####  3.3.2 Variable selection

Spatial autocorrelation can be influenced significantly by selecting and
treating variables within a dataset. Several traditional methodologies,
encompassing feature engineering, mitigation of multicollinearity, and spatial
data preprocessing, present viable avenues to address SAC-related challenges.

One notable complication arises from multicollinearity amongst the selected
variables, which can potentiate SAC [157]. Indications of multicollinearity
are discernable through various diagnostic tools such as correlation matrices
and variance inflation factors. To counteract multicollinearity, strategies
encompassing the elimination of variables with high correlations and the
application of dimensionality reduction techniques such as principal component
analysis (PCA) can be employed. A judicious selection of pertinent variables,
complemented by the development of novel variables hinged on domain expertise
and exploratory data analysis, may further attenuate the manifestation of SAC.
Another approach for addressing this challenge is the consideration of rSAC
across diverse variable subsets, followed by the deployment of classical model
selection criteria like the Akaike information criterion [158]. It is,
however, imperative to recognise that the Akaike information criterion retains
its efficacy in the context of rSAC when the independent variables do not
exhibit spatial autocorrelation [159].

In ML and DL, emerging methodologies have embraced spatial autocorrelation as
an integral component. For instance, while curating datasets for training Long
Short-Term Memory (LSTM) networks, an optimal SAC variable was identified and
integrated into the dataset [160]. Furthermore, spatial features, namely
spatial lag and eigenvector spatial filtering (ESF), have been introduced to
the models to account for spatial autocorrelation [161].

A novel set of features, termed the Euclidean distance field (EDF), has been
innovatively designed based on the spatial distance between query points and
observed boreholes. This design aims to seamlessly weave spatial
autocorrelation into the fabric of ML models, further underscoring the
significance of variable selection in spatial studies [162].

####  3.3.3 Model selection

Selecting or enhancing models to mitigate SAC impact is crucial. Spatial
autoregressive models (SAR), especially simultaneous autoregressive models,
are effective in this regard [163]. SAR may stand for either spatial
autoregressive or simultaneous autoregressive models. Regardless of
terminology, SAR models allow spatial lags of the dependent variable, spatial
lags of the independent variables, and spatial autoregressive errors. Spatial
errors model (SEM), incorporate spatial dependence either directly or through
error terms. SEMs handle SAC with geographically correlated errors. Other
approaches include auto-Gaussian models for fine-scale SAC consideration
[164]. Spatial Durbin models further improve upon these by considering both
direct and indirect spatial effects on dependent variables [165].
Additionally, Geographically Weighted Regression (GWR) offers localised
regression, estimating coefficients at each location based on nearby data
[166]. In the context of SDM, six statistical methodologies were described to
account for SAC in model residuals for both presence/absence (binary response)
and species abundance data (Poisson or normally distributed response) [143].
These methodologies include autocovariate regression, spatial eigenvector
mapping, generalised least squares (GLS), (conditional and simultaneous)
autoregressive models, and generalised estimating equations. Spatial
eigenvector mapping creates spatially correlated eigenvectors to capture and
adjust for spatial autocorrelation effects [167]. GLS extends ordinary least
squares by considering a variance-covariance matrix to address spatial
dependence [168]. The use of spatial Bayesian methods has grown in favour of
overcoming SAC. Bayesian Spatial Autoregressive (BSAR) models and Bayesian
Spatial Error (BSEM) models explicitly account for SAC by incorporating a
spatial dependency term and a spatially structured error term, respectively,
to capture indirect spatial effects and unexplained spatial variation [169].
In recent years, the popularity of autoregressive models for spatial modelling
as a core method has slightly decreased, while classical ML and DL methods
have been extensively employed for spatial modelling tasks. Consequently,
various techniques have been developed to leverage SAC’s influence
effectively. The common approach is to incorporate SAC with the usage of
autoregressive models during the stages of dataset preparation and variable
selection. This approach is presented in greater detail in the previous
subsection 3.3.2. On the other hand, combining geostatistical methods with ML
is gaining popularity. For example, the usage of an artificial neural network
(ANN) and the subsequent modelling of the residuals by geostatistical methods
to simulate a nonlinear large-scale trend [170].

####  3.3.4 Spatial cross-validation

Spatial cross-validation is a widely-used technique to account for SAC in
various research studies [171, 128, 172, 173]. Neglecting the consideration of
SAC for spatial data can introduce an optimistic bias in the results. This
issue has been highlighted in the research, emphasising the importance of
accounting for spatial dependence to obtain more accurate and unbiased
assessments of model performance [174, 175, 145, 176]. For instance, it was
shown [171] that random cross-validation could yield estimates up to 40
percent more optimistic than spatial cross-validation.

The main idea of spatial cross-validation is to split the data into blocks
around central points of the dependence structure in space in space [175].
This ensures that the validation folds are statistically independent of the
training data used to build a model. By geographically separating validation
locations from calibration points, spatial cross-validation techniques
effectively achieve this independence [177].

Various methods are commonly employed in spatial cross-validation, including
buffering, spatial partitioning, environmental blocking, or combinations
thereof [175, 37]. These techniques aim to strike a balance between minimising
SAC and avoiding excessive extrapolation, which can significantly impact model
performance [175]. Buffering involves defining a distance-based radius around
each validation point, excluding observations within this radius from model
calibration. Environmental blocking groups data into sets with similar
environmental conditions or clusters spatial coordinates based on input
covariates [178]. Spatial partitioning, known as spatial K-fold cross-
validation, divides the geographic space into K spatially distinct subsets
through spatial clustering or using a coarse grid with K cells [175].

However, it’s worth mentioning an alternative discussion [38] showing that
both standard and spatial cross-validation procedures may not be considered
unbiased solutions for estimating the accuracy of mapping results, while the
very concept of spatial cross-validation is heavily criticised. According to
the results, neither standard nor spatial cross-validation provided satisfying
results: map accuracy was overestimated for clustered data in the case of
standard cross-validation or severely underestimated in the case of chosen
spatial cross-validation strategies. Instead, probability sampling and design-
based inference are suggested to obtain unbiased estimates of map accuracy in
large-scale studies. Another concern is the request for better articulation of
the meaning of validating a mapping model while examples of model validation
and validation of the map are discussed.

In summary, spatial cross-validation techniques could be suitable to address
SAC in data-based spatial modelling tasks while providing a transparent and
precise description of the methodology of the model accuracy assessment and
inference obtaining in a step-by-step manner is of high importance. Selecting
the most suitable technique and its corresponding parameters should result
from thoughtful consideration of the specificity of the research problem and
the corresponding dataset.

##  4 Uncertainty quantification

###  4.1 Problem statement

Figure 5: Example of uncertainty quantification (UQ) for spatial mapping
provided within the project SoilGrids [179] a) maps of one of the target
variables – soil pH(water) in the topsoil layer; b) maps of associated
uncertainty estimated using prediction interval coverage probability (PICP)
index for the same territory.

Geospatial predictions using machine learning have become convenient for
routine decision-making workflows. To ensure these predictions are reliable
and sufficient, assessing the uncertainty associated with the model’s
forecasts is crucial. Uncertainty quantifies the level of confidence the model
has in its predictions (Figure 5). Two primary types of uncertainty exist:
aleatory uncertainty, which arises from data uncertainty, and epistemological
uncertainty, which originates from knowledge limitations [180].

Sources of uncertainty may stem from incomplete or inaccurate data,
inaccurately specified models, inherent stochasticity in the simulated system,
or gaps in our understanding of the underlying processes. Assessing aleatoric
uncertainty caused by noise, low spatial or temporal resolution, or other
factors which cannot be taken into account can be challenging. For that
reason, the most of research is focused on epistemic uncertainty. Reducing
uncertainty in ML models is essential for improving their reliability and
accuracy.

###  4.2 Solutions for uncertainty quantification

####  4.2.1 Classical ML approaches

One of the common approaches for uncertainty quantification (UQ) in geospatial
modelling is quantile regression [181]. It allows one to understand not only
the average relationship between variables but also how different quantiles
(percentiles) of the dependent variable change with the independent variables.
In other words, it helps to analyze how the data is distributed across the
entire range, rather than just focusing on the central tendency. Quantile
regression is particularly useful when dealing with data that may not follow a
normal distribution or when there are outliers in the data that could heavily
influence the results.

For instance, to quantify the uncertainty of models for nitrate pollution of
groundwater, quantile regression and uncertainty estimation based on local
errors and clustering (UNEEC) [182] were used [183]. Quantile regression was
also used for the UQ of four conventional ML models for digital soil mapping:
to estimate UQ the authors analysed mean prediction intervals (MPI) and
prediction interval coverage probability (PICP) [184]. Another widely used
technique for UQ is bootstrap, which is a statistical resampling technique
that involves creating multiple samples from the original data to estimate the
uncertainty of a statistical measure [185, 186]. One more metric is mean-
variance estimation (MVE), which is used to simultaneously estimate both the
mean (average) and variance (spread) of a dataset. It helps to describe the
central tendency and variability of the data [187].

####  4.2.2 Gaussian process regression

Gaussian Process Regression, also known as kriging, is commonly used for UQ in
geospatial applications, providing a natural way to estimate the uncertainty
associated with spatial predictions. In a study focused on spatiotemporal
modelling of soil moisture content using neural networks, the authors utilised
sequential Gaussian simulations to estimate uncertainty and reduced RMSE by
18% in comparison with the classical approach [188]. Another approach, known
as Lower Upper Bound Estimation, was applied to estimate sediment load
prediction intervals generated by neural networks [189]. For soil organic
mapping, researchers compared different methods, including sequential Gaussian
simulation (SGS), quantile regression forest (QRF), universal kriging, and
kriging coupled with random forest. They concluded that SGS and QRF provide
better uncertainty models based on accuracy plots and G-statistics [190].
However, Random Forest demonstrated better performance of prediction
uncertainty in comparison with kriging in soil mapping in another study [191],
although predictions of regression kriging were found to be more accurate,
that can be related to the architecture of these models.

####  4.2.3 Bayesian techniques

Another approach to estimating uncertainty in ML models is through Bayesian
inference [192]. In Bayesian methods, model parameters are treated as random
variables with prior distributions, allowing for uncertainty modelling.
However, with its complex relationships and spatial dependencies, geospatial
modelling poses challenges in uncertainty quantification. To estimate
uncertainty in model predictions, the posterior distribution of parameters
given the data and priors is used.

Bayesian techniques have been applied to various models, including neural
networks, Gaussian processes, and spatial autoregressive models, to estimate
uncertainty in predictions of variables such as temperature, air quality, and
land use. Some main methods for uncertainty quantification using Bayesian
neural networks include Monte Carlo (MC) dropout [193], sampling via Markov
chain Monte Carlo (MCMC) [194], and Variational autoencoders [195]. However,
it should be noted that most of these methods are specifically used for
uncertainty quantification in DL and at the moment they are not widely
implemented in geospatial modeling [180].

For instance, Bayesian techniques have been used in weather modelling,
particularly wind speed prediction and hydrogeological calculations, to
analyse the risk of reservoir flooding [196]. Probabilistic modelling was
employed to assess the uncertainty of spatial-temporal wind speed forecasting,
with models based on spatial-temporal neural networks using convolutional GRU
and 3D CNN. Variational Bayesian inference was also utilised [197]. Similarly,
Bayesian inference has been applied to estimate uncertainty in soil moisture
modelling [198]. Another study used Bayesian inference to model the spread of
invasive species [199].

####  4.2.4 Ensemble techniques

Model ensembling is a powerful technique used in geospatial modelling to
address uncertainty. Geospatial models often deal with complex systems where
uncertainty arises from various sources, including input data,
parametrisation, and modelling assumptions. Ensembles can help both during the
reduction and estimation of uncertainty. The diversity of predictions from
different members of an ensemble serves as a natural way to estimate
uncertainty. On the other hand, more robust and reliable estimates can be
obtained by combining predictions from multiple models through ensembling
methods like weighted averaging, stacking, or Bayesian model averaging.
Ensembling helps mitigate uncertainties associated with individual models and
provides a way to estimate uncertainty by computing the variance of
predictions across the ensemble [200]. To solve the problems of spatial
mappings, such as equifinality, uncertainty and conditional bias, ensemble
modelling and bias correction framework were proposed. The method was
developed for mapping soils using the XGBoost model and environmental
covariances as predictors. It was shown that ensemble modelling helped solve
the equifinality problem in the data set while demonstrating better
performance [201]. Another example is the comparison of regional and global
ensemble models for soil mapping [202]. It was found that the performance of
an ensemble of regional models was the same as global models, but regional
model ensembles had less uncertainty than global models. Ensembling approaches
to UQ were also applied in the DL modelling tasks [203]. In another study,
authors proposed a system that combines ML models within a spatial ensemble
framework to reduce uncertainty and enhance the accuracy of site index
predictions [204]. For soil clay content mapping, authors estimated the
uncertainty of seven ML models and their ensembles [205]. Ensembling proves to
be a valuable technique in geospatial modelling, as it leverages the
collective knowledge of multiple models to improve predictions and provide
more comprehensive uncertainty estimates.

###  4.3 Solutions to address the uncertainty in spatial predictions

Several approaches can be used to reduce uncertainty, falling into two groups.
The first group is related to input data and involves increasing data quality,
using more data from different domains, and adding feature engineering to
select predictors highly relevant to the problem. This can help the model
focus on the most informative aspects of the data, reducing uncertainty caused
by irrelevant or redundant features. The second group is devoted to the
modelling step and includes spatial and temporal cross-validation, model
regularisation techniques to prevent overfitting, combining multiple models
through techniques such as bagging or boosting, and more complex approaches
such as Bayesian methods, Gaussian techniques, and transfer learning, which
are described above.

Visualisation methods for UQ in geospatial modelling hold a distinct place
compared to other areas of ML. Researchers emphasize the significance of
visually analyzing maps with uncertainty estimates, especially for
biodiversity and policy conversation tasks [206]. Visualisation techniques
such as bivariate choropleth maps, map pixelation, and glyph rotation to
represent spatial predictions with uncertainty can be used [207].

##  5 Practical tools

In summary, it is crucial to consider the specificity of environmental data
and its outcomes when selecting appropriate approaches for analysis. Table 1
presents various methods to address the challenges discussed, including
packages and libraries for geospatial analysis. Considering the dominant
spread of Python and R as programming environments for data-based geospatial
modelling, most of the tools to be implemented within these languages are
provided. It is worth mentioning that although discussing libraries and
packages are widely used in both academia and industry, common ML tools
available in Python and R cover most of their functionality, being a
replacement of these more specialized instruments with little change in
quality and utility if used by advanced data scientists.

Table 1: Geospatial data science tools in selected programming environments Solutions | Environment | Package/library | Description
---|---|---|---
Geospatial data analysis: general tools | R | sp [208] |  Reading and writing spatial data represented by points, lines, polygons and grids, producing spatial objects, and performing spatial operations, e.g. plotting data as maps, spatial selection, retrieving coordinates, subsetting, print, summary.
R | Simple Features (sf) [209] |  Reading, writing and converting Simple Features. Provides a set of tools for working with geospatial geometries represented by points, lines, polygons.
R | raster [210] |  Creating, reading, manipulating, and writing raster data. The package can process very large datasets. Raster algebra functions and high-level methods such as cropping and resampling are implemented.
Python | geopandas[211] |  Extends the datatypes used by python pandas to allow spatial operations on geospatial vector data. Reading, writing files, making maps and plots, data analysis and manipulations, such as buffering, intersection, and spatial joins.
Python | rasterio[212] |  Reading and writing gridded raster datasets, raster values can be extracted at precise points, and raster data can be warped and reprojected.
Python | gdal[213] |  Geospatial Data Abstraction Library for raster and vector data reading, creating, writing, transformation and analysis
Python | pysal[214] |  A family of packages for spatial data science: a collection of tools to explore, visualise and estimate relationships in spatial data with a focus on vector data. Among the core functions are detection of spatial clusters, hot-spots, and outliers, exploratory spatiotemporal data analysis, spatial regression and statistical modeling supported with inference obtaining.
General oversampling methods of minority class | R | imbalance [215] |  Set of tools to work with imbalanced datasets: oversampling algorithm based on the extension of the original SMOTE algorithm, filtering of instances and evaluation of synthetic instances, imbalance ratio computation.
R | smotefamily[88] |  A collection of various oversampling techniques for the minority class developed from SMOTE, including ADASYN, Borderline-SMOTE, DBSMOTE.
General oversampling methods of minority class and undersampling of the majority class | R | themis[216] |  Collection of techniques for balancing the data, including variations of SMOTE, ADASYN, ROSE, balancing majority class in a distance-based manned.
Python | Imbalanced-learn[217] |  Over-sampling methods include SMOTE, SMOTENC, SMOTEN, ADASYN, BorderlineSMOTE, KMeansSMOTE, SVMSMOTE. Under-sampling techniques include random under-sampling, algorithms based on cluster centroid of a KMeans algorithm, instance hardness threshold, variations of the nearest neighbour method, etc.
Spatial oversampling methods of minority class | R | biomod2[218] |  Ensemble Platform for Species Distribution Modeling, allows sampling minority class in a random, disk (select the locations of minority class based on the distance to prevalent class) and condition-based (a condition that differs from a defined proportion of prevalent class, could lead to over-optimistic result) manners.
Spatial undersampling of the majority class | R | SpThin[85] |  SpThin provides spatial thinning of species occurrence records but can be applied for any other point-based spatial data. It is helpful for addressing problems associated with spatial sampling biases.
Measuring SAC | R | spdep[219] |  Conducting spatial autocorrelation analysis, constructing spatial weight matrices, and visualizing spatial dependence patterns. Includes global and local Morans I and Gearys C, Hubert/Mantel general cross product statistic, Empirical Bayes estimates.
R | ncf[220] |  Spatial analysis tool which is addressed to spatial autocorrelation, modelling semi-variograms, computing spatial covariance functions, and performing geostatistical interpolation.
Python | esda[214] |  Exploratory Spatial Data Analysis: Geary, Moran, Silhouette statistics are available.
Spatial cross-validation | R | blockCV[178] |  Toolbox for cross-validation in spatial modelling. Includes tools for generating train and test folds for k-fold and leave-one-out cross-validation, to measure spatial autocorrelation ranges in candidate covariates, interactive graphical capabilities for creating spatial blocks and exploring data folds.
Uncertainty estimation | R | inlabru[221] |  Spatial and general latent Gaussian modelling using integrated nested Laplace approximation. A prediction method based on fast Monte Carlo sampling allows posterior prediction of general expressions of the latent variables. Provide access to Bayesian inference from spatial point process, spatial count, gridded, and georeferenced data.
R | Vizumap[222] |  R package for visualising uncertainty in spatial data creating bivariate maps, pixel maps, glyph maps, and exceedance probability maps.
R | spup[223] |  The package for examining the uncertainty propagation for input data and model parameters via the environmental model onto model outputs. The functions include uncertainty model specification, stochastic simulation and uncertainty propagation using Monte Carlo techniques. Probability distributions describe uncertain variables.
Python | Uncertainty Toolbox[224] |  A python toolbox for predictive uncertainty quantification, calibration, metrics, and visualizations.
Spatial modelling | R | biomod2[218] |  Functions for modelling, calibration and evaluation, an ensemble of models, ensemble forecasting and visualization. Models include Random Forest, Boosted Regression Trees, Support Vector Machines, Artificial Neural Networks and others.
JavaScript/Python | Google Earth Engine[225] |  Catalog of satellite imagery and geospatial datasets and collection of tools for data retrieving, geospatial analysis and modelling.
R | sdmTMB[226] |  Implements spatial and spatiotemporal Generalized Linear Mixed Effect Models.
Python | verde[227] |  Provides classes and functions for processing spatial data, like bathymetry, GPS, temperature, gravity, or anything else that is measured along a surface. The main focus is on methods for gridding such data (interpolating on a regular grid).
Python | GSTools[228] |  Provides methods for generating random fields and performing simple, ordinary, universal and external drift kriging and variogram estimation.

##  6 Key areas for focus and growth

Geospatial modelling has grown rapidly, driven by data-based models and the
integration of ML and DL alongside traditional geospatial statistics. Previous
sections highlighted common implementation gaps and approaches to address
them. Additionally, it is worth exploring and discussing future developments
and key possibilities concerning challenges in data-driven geospatial
modelling. Below, we highlight the major points of growth that can lead to new
seminal works in this area.

##### New generation of datasets

It is crucial to enhance data quality, quantity, and diversity to ensure
reliable models. Establishing well-curated databases in environmental research
is of utmost importance as it drives scientific progress and industrial
innovation. When combined with modern tools, these databases can contribute to
developing powerful models.

A particular area of interest is the collection of cost-effective and
efficient semi-supervised data, which typically has limited labels. Although
currently underdeveloped, this data type holds significant potential for
expansion and improvement. In computer vision and natural language processing,
the superior quality of recently introduced models often comes from using more
extensive and better datasets. Internal Google dataset on semi-supervised data
JFT-3B with nearly three billion labelled images led to major improvements
[229, 230]. Another major computer vision dataset example is LVD-142M with
about 142 million images [231]. We note that the paper provides a pipeline
that can be used to extend the size of existing datasets to two orders of
magnitude. In natural language processing, a recent important example is
training large language models. [232]. It uses a preprocessed dataset with 2
trillion tokens. More closely related to geospatial modelling is the adoption
of climate data. It now also allows the application of DL models mainly due to
the increasing number of available measurements. For example, SEVIR dataset
[233] allowed better prediction via a variant of Transformer architecture
[234]. In [235], the authors developed a model for precipitation nowcasting.
To train the model, they employ radar measurements at a grid with cells of
$1\times 1$ kilometres, taking every $5$ minutes for $3$ years. In total,
around 1 TB of data were used.

Furthermore, integrating diverse data sources offers a promising path forward.
Combining datasets from various domains, such as satellite imagery,
meteorological and climatic data, and social data, such as social media posts
that provide real-time environmental information for specific locations, can
be beneficial. By developing multimodal models capable of processing these
diverse data sources, the community can enhance model robustness and
effectively address the challenges discussed in this study and the existing
literature. Most of the research combines image and natural language
modalities [236], while other options are possible.

##### New generation of models

The continuous advancement of technology has led to the emergence of more
sophisticated data sources, including higher-resolution remote sensing and
more accurate geolocation data. Additionally, human efforts contribute to
high-quality curated data. While this is beneficial, it presents challenges in
adapting existing geospatial models to handle such data. Traditional models
may need to be more suitable and efficient, necessitating the developing and
validation of new models and computational methods. Incorporating DL methods
is a potential solution, although they come with challenges related to
interpretability and computational efficiency, especially when dealing with
large volumes of data. We anticipate the emergence of self-supervised models
trained on large semi-curated datasets for geospatial mapping in environmental
research, similar to what we have seen in language modelling and computer
vision. Such modelling approaches have also been applied to satellite images
[237] including, for example, a problem of the state of plants estimation
[102] and assessment of damaged buildings in disaster-affected area [238].

##### Producing industry-quality solutions: deployment and maintenance.

After constructing a model, it needs to be deployed in a production
environment. Access to necessary data and supporting services is crucial to
ensure safe and continuous operation. Another challenge is the ageing of data-
based models caused by environmental factors like changing climate [239],
shifts in data sources, or transformations in output variables, e.g.,
alterations of land use and land cover [240]. Monitoring and considering such
changes is essential to either discontinue using an outdated model or retrain
it with new data [241]. The monitoring schedule can vary, guided by planned
validation checking or triggered by data corruption as well as new business
process implementations. Deployment and maintenance are often underestimated
despite requiring significant resources and additional steps for long-term
success [242]. Another area of possible growth is related to developing new
methods, including advanced DL methods. Incorporation of concept drift into
the maintenance process is also an option [243].

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