=Paper=
{{Paper
|id=Vol-3942/S_04_Hnatiienko
|storemode=property
|title=
Site-Specific Forecasting of Agricultural Crop Yield as a Technology and Service
|pdfUrl=https://ceur-ws.org/Vol-3942/S_04_Hnatiienko.pdf
|volume=Vol-3942
|authors=Vladyslav Hnatiienko,Vitaliy Snytyuk
}}
==
Site-Specific Forecasting of Agricultural Crop Yield as a Technology and Service
==
https://ceur-ws.org/Vol-3942/S_04_Hnatiienko.pdf
Site-Specific Forecasting of Agricultural Crop Yield as a
Technology and Service
Vladyslav Hnatiienko1, Vitaliy Snytyuk1
1
Taras Shevchenko National University of Kyiv, Volodymyrs'ka str. 64/13, Kyiv, 01601, Ukraine
Abstract
The aim of the research is to improve the accuracy of crop yield forecasting by developing and applying
data processing methods and neural network models. A yield forecasting technology is proposed that will
include pattern recognition models for analyzing satellite images, data processing methods, and deep neural
networks in combination with other artificial intelligence models. This technology is used to analyze the
effectiveness and feasibility of agrotechnical measures, thereby supporting rational decision-making in
agricultural production.
Keywords 1
Crops, yields, site-specific forecasting, forecasting models and methods.
1. Introduction
Digital agronomy is at the stage of active development, and farm owners are increasingly
incorporating digital farm management into their strategies, which allows them to remotely monitor
and control field work. Experts apply artificial intelligence and conduct research to deepen
knowledge and develop effective digital agronomy technologies. In modern studies of the
effectiveness of yield forecasting methods, a root mean square error (RMSE) of 10-15% of the average
yield is achieved. Most models are used to predict the total yield of a field, without the ability to
perform site-specific forecasting. The ones that allow to build detailed maps of predicted yields are
generally tested on small samples, which makes it impossible to reliably assess their effectiveness.
The current challenge is to develop a forecasting technology that provides predictions for
individual field areas. To solve this problem, it is necessary to analyze the data features, relationships,
and degrees of influence of various agronomic indicators on the yield. The scientific value of the
results lies in simplifying and optimizing future research by providing insights into which agronomic
data to use and why. Furthermore, detailing forecasts to individual plots will open up new avenues
for future research. From a practical point of view, forecasting will enable budget planning, risk
analysis, and appropriate agronomic measures.
The expected results of the study will offer open-access innovative solutions, contributing to the
development of digital agronomy.
2. Analysis of preliminary results
Numerous studies have been conducted to enhance the accuracy of crop yield forecasting. These
efforts leverage a diverse array of information sources, such as plant genetic data, environmental
data, and satellite imagery. To process and analyze this data, researchers employ a variety of models,
ranging from traditional statistical approaches to advanced deep neural networks.
8th International Scientific and Practical Conference Applied Information Systems and Technologies in the Digital Society
AISTDS’2024, October 01, 2024, Kyiv, Ukraine
∗
Corresponding author.
†
These authors contributed equally.
hnatiienko.vladyslav@knu.ua (V. Hnatiienko); snytyuk@knu.ua (V. Snytyuk)
0009-0000-2678-5158 (V. Hnatiienko); 0000-0002-9954-8767 (V. Snytyuk)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
In particular, in [1], data on plant genotype, weather conditions, and soil indicators were used to
predict the yield. A deep neural network was used for forecasting, achieving an RMSE of 11-12% of
the average yield. However, the study only considers forecasting the total yield of an entire field
without detailing its individual plots, which is a limitation for possible applications of this approach.
A similar drawback applies to the study [2], which used the Random forest model. The RMSE values
were 11.9% for wheat, 16.7% for corn across the United States, 13.9% for potatoes, and 5.8% for corn
in the Northeast coastal region of the United States. The authors note that the chosen model is often
overfitted, which can lead to difficulties in generalization. Another problem is low reliability: the
model is effective on average, which allows analyzing the general features of big data, but there is a
high probability of significant errors in individual forecasts.
Methods that use satellite images for forecasting are effective. For example, the authors of [3]
predict potato yields based on identifying the relationship between the values of vegetation indices
and yields with deviations of 5-9% from the average, but the elements of the training and test sets
belonged to the same field, which makes it difficult to assess the generalizability of this approach. In
[4], 5 fields form the training set, and the other 5 fields are used to test the model. The results indicate
that the most effective model is Random forest, operating with RMSE values from 0.284 to 0.473 t/ha,
or about 9-14% of the average sunflower yield. However, due to the small size of the test sample, it
is difficult to assert the reliability of these results. According to the authors, the study had a good
period for collecting information: 16 satellite images were collected on sunny days during the
ripening period, providing favorable conditions for model training. Usually, due to the constant
presence of clouds, only 3 to 7 images can be collected, which greatly complicates forecasting using
such models.
Thus, we argue that the primary disadvantages of modern forecasting technologies are their
insufficient accuracy and the significant dependence of results on weather conditions. Moreover,
most studies focus on predicting total yield, while those that attempt site-specific forecasting often
rely on highly limited samples during experimental validation, making it impossible to reliably
evaluate the effectiveness of the proposed methods [5]. Additional challenges stem from the
uncertainty regarding the feasibility of using different data sources: it remains unclear which factors
exert the greatest influence on plant yields. Consequently, studies incorporate a wide variety of data,
including plant genotypes, weather conditions, terrain variations, nitrogen and phosphorus soil
content, and satellite imagery—data that originate from diverse sources and vary greatly in
complexity and acquisition cost.
Agronomic experts and farm owners frequently encounter the challenge of insufficient accuracy
and reliability in modern forecasting services. Forecast deviations from actual values range from 3–
5% to as high as 30–40%, highlighting the inefficiency of current methods [6]. As a result, many
abandon forecasting altogether, which hinders the advancement of agricultural production. This
abandonment deprives developers of data analysis and decision-making technologies of adequate
funding for further development and prevents farm owners from realizing the potential profits these
technologies could have delivered.
3. Analysis of data sources and processing methods
3.1. Satellite images
Most of the data on plants and their maturation conditions are a set of constant values that are
known at the beginning of the maturation period: genotype, sowing density, sowing date, field
coordinates, etc. Such data are static, reflecting only the initial conditions, and forecasting based on
them often leads to significant deviations from actual values.
For refined site-specific forecasting, satellite images are the most important source of data, as they
are accumulated throughout the entire ripening period and allow tracking the dynamics of plant
development, recording any deviations in time. When applying machine learning in yield prediction
tasks, the parameters whose values are obtained from satellite images are assigned the highest
weighting coefficients [7, 8]. Table 1 presents the list of parameters and their feature importance
scores for the LightGBM model. The importance scores are calculated during training: the parameters
are used to build decision trees, and those that contribute to a greater reduction in error receive a
higher importance score.
Table 1
Estimates of the importance of parameters for yield forecasting
Number Feature Importance score
1 GLI_mean 286
2 GLI_max 259
3 CLr_mean 254
4 NDVI_max 223
5 NDVI_mean 217
6 GLI_min 211
7 CLr_max 195
8 NDWI_max 189
9 CLg_max 174
10 CLr_min 156
11 NDVI_min 154
12 CLg_mean 147
13 NDWI_mean 146
14 NDWI_min 127
15 CLg_min 122
16 mid 61
17 Density 29
18 CAPE_180-0_mb_above_gnd_max 17
19 fungicide_58 12
20 mid_early 7
21 Temperature_2_m_elevation_corrected_max 5
... ... ...
Table 1 indicates:
● GLI, CLr, NDVI, CLg, NDWI are vegetation indices, the values of which are calculated for
each field area based on satellite data;
● mid, mid_early are parts of the categorical variable hybrid, which indicates the plant hybrid
of a given plot; the value 1 is set for the corresponding hybrid, and 0 for all others;
● Density is the density of planting on the field;
● CAPE_180-0_mb_above_gnd_max, Temperature_2_m_elevation_corrected_max, fungicide_58 -
other parameters from the sets of meteorological data and data on plant characteristics in the
field.
Monitoring services often provide data in the form of maps with vegetation index values, but the
primary source of information is the intensity of reflected solar radiation in different spectral ranges,
which is recorded for each field once a day. Most satellites have sensors that measure the reflected
radiation for ten standard wavelengths belonging to the visible, near-infrared, and mid-infrared
spectrums. These values are presented in Table 2.
A snapshot can be labeled 𝑋𝑋𝑏𝑏𝑑𝑑 = {𝑥𝑥1𝑏𝑏
𝑑𝑑 𝑑𝑑
, 𝑥𝑥2𝑏𝑏 𝑑𝑑
, … , 𝑥𝑥𝑛𝑛𝑛𝑛 }, where
● 𝑛𝑛 - the number of field areas, each of which is represented by a separate pixel in the image;
● 𝑏𝑏 ∈ {𝐵𝐵02, 𝐵𝐵03, … , 𝐵𝐵12} - is the wavelength for which the intensity value is recorded;
● 𝑑𝑑 ∈ {1,2, … , 𝑇𝑇} - the day on which the picture was taken, where 𝑇𝑇 - is the number of days,
which can vary depending on the conditions (usually 𝑇𝑇 = 100).
● 𝑋𝑋𝑏𝑏𝑑𝑑 - image for the wavelength 𝑏𝑏 and day of observation 𝑑𝑑;
𝑑𝑑
● 𝑥𝑥𝑖𝑖𝑖𝑖 - intensity value for the area 𝑖𝑖 for the wavelength 𝑏𝑏 and day 𝑑𝑑.
Table 2
Designation of standard wavelengths
Number Symbolic designation Wavelength, nanometers
1 B02 492.4
2 B03 559.8
3 B04 665.2
4 B05 704.1
5 B06 740.5
6 B07 782.8
7 B08 832.9
8 B8A 864.7
9 B11 1613.7
10 B12 2202.4
To select a set of images suitable for further processing, we denote the set of distorted elements
of the set 𝑋𝑋𝑏𝑏𝑑𝑑 as 𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
𝑑𝑑
(the correctness of these elements of each image is determined by an expert [5,
6]) and check the following criterion:
if the number of elements of the set of distorted values 𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑
exceeds 10% of the total number of
areas in the image: � 𝑋𝑋𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 � > 0.1 · 𝑛𝑛, then the image 𝑋𝑋𝑏𝑏 is considered unsuitable for further use.
𝑑𝑑 𝑑𝑑
Since during most observations a certain part of the field is covered by clouds, most images are
classified as unsuitable for analysis, even if a significant part of the data in these images is correct.
To solve this problem, cloud recognition can be applied with subsequent recovery of lost information
by interpolation methods. Cloud recognition can be performed using object recognition technology
based on multiprojection analysis [9].
Solving the problem of information loss will enable data representation in the form of time series
and the application of deep learning methods for forecasting. At the current stage of the study, due
to insufficient data, only minimum, average, and maximum values are utilized:
𝑑𝑑
min{𝑥𝑥𝑖𝑖𝑖𝑖 } , ∀𝑖𝑖, 𝑏𝑏, (1)
𝑑𝑑∈𝐷𝐷
𝑑𝑑 1 𝑑𝑑
𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚({𝑥𝑥𝑖𝑖𝑖𝑖 | 𝑑𝑑 ∈ 𝐷𝐷}) = � 𝑥𝑥𝑖𝑖𝑖𝑖 , ∀𝑖𝑖, 𝑏𝑏, (2)
|𝐷𝐷|
𝑑𝑑∈𝐷𝐷
𝑑𝑑
max{𝑥𝑥𝑖𝑖𝑖𝑖 } , ∀𝑖𝑖, 𝑏𝑏, (3)
𝑑𝑑∈𝐷𝐷
where D is the set of days for which the images are considered suitable.
This creates uncertainty that reduces the information content of the dataset. First, most of the
information about the sequence of values is lost 𝑥𝑥 by reducing it to only three general characteristics.
Second, often the values (1) and (3) values often do not correspond to the actual values of the
minimum and maximum intensity of reflected radiation, which is due to the removal of images for
the days on which these key indicators could be recorded. In addition, the average value of (2) can
differ significantly for a complete sequence. Thus, recovering complete time series 𝑋𝑋𝑏𝑏𝑑𝑑 ,
𝑏𝑏 ∈ {𝐵𝐵02, 𝐵𝐵03, … , 𝐵𝐵12}, 𝑑𝑑 ∈ {1,2, … , 𝑇𝑇}, will allow us to track the dynamics of changes in
parameter values during the ripening period, which will significantly increase the amount of
information about the state of plants.
3.2. Features of data display and sample balancing
During training, the weights of the neural network are adjusted to identify the most informative
features and calculate the output values based on them. These features form vectors that can be used
to analyze and process data. For example, when analyzing such vector representations in natural
language processing tasks, it was found that for synonyms, antonyms, word pairs in singular and
plural forms, and other semantically related words, the cosine distance of the corresponding vector
representations is significantly smaller than for unrelated words [10]. A similar approach is used in
image classification: vector representations of images are calculated to select key features, and then
images are divided into classes. Often, this can be done even with a linear classifier due to the fact
that the vector representations of images of one class are at a small distance and far enough removed
from the images of other classes.
This approach can be applied to analyze data collected during the plant maturation period. For
instance, it can be used to detect anomalies: vector representations of field areas containing distorted
information (e.g., regions covered by clouds or parts of the field occupied by equipment instead of
plants) are expected to deviate significantly from the majority of the data. Clustering techniques can
identify typical patterns, and the centroids of these clusters can serve as reference points for
detecting outliers.
Another potential application is the detection of fields with atypical data. For instance, if a dataset
includes a field with plants of an uncommon hybrid or other distinct characteristics, its data points
should be significantly distant from the majority of the training set. This concept can serve as the
basis for developing a method to construct balanced and representative samples. To ensure
representativeness, the training dataset should include a wide variety of plant species grown under
diverse conditions, thereby reducing the likelihood that a field will appear atypical compared to the
training data when the technology is implemented.
In trained models, vector representations typically capture the key features of the input data. For
example, in image recognition, objects can still be identified even if parts are missing or deformed—
the recognition process relies on the most significant features, while disregarding distortions in less
critical ones [11, 12]. Therefore, it can be inferred that analyzing the sensitivity of vector
representations to variations in input data can help identify the most important parameters: higher
sensitivity indicates greater importance.
When constructing training sets with a sufficient amount of data, the sample is typically balanced
to ensure an even distribution of data. This often involves maintaining an equal number of
representatives from each original class, which, in the context of forecasting, translates to an equal
number of observations corresponding to low, medium, and high yields (divided into an arbitrary
number of ranges).
Additionally, balancing the input data is also crucial. For instance, if the training set is dominated
by plants of a single hybrid, this can lead to overfitting and reduced prediction accuracy for plants
of other hybrids. Such balancing can be achieved through the analysis of vector data representations,
enabling the identification and adjustment of class imbalances [13].
3.3. Use of additional sources of information
The current forecasting method utilizes input data that includes satellite images, meteorological
indicators, and supplementary information about the plants in the field, such as hybrid type, seeding
density, and dates of chemical application. Additionally, the potential effectiveness of incorporating
other parameters—such as the elevation of field sections above sea level, section coordinates, and
sowing dates—should be thoroughly analyzed to assess their contribution to improving forecasting
accuracy.
Studies on yield forecasting also use data on plant yields in previous years [14] and data on
patterns of climate change in previous years [15]. Incorporating information about predecessor
crops, along with meteorological data and satellite imagery from previous years, can enhance
forecasting accuracy.
4. Approaches to yield forecasting
4.1. Uniformity of ripening
An essential parameter for yield prediction is the uniformity of plant maturation within a field.
Harvesting combines are calibrated to collect plants at a specific maturity stage, typically targeting
the stage that represents the majority of plants. However, yield losses occur when plants that are
either over-mature or under-mature are not harvested under optimal conditions. Since combines are
generally adjusted according to predefined standards, incorporating the distribution of plant
maturity across the field into the input data could improve prediction accuracy. Agronomic experts
often rely on the NDVI vegetation index to evaluate plant maturity [16]. Consequently, the formation
of this parameter can be achieved using the following algorithm:
1. Dividing NDVI values into ranges with the help of expert opinion;
2. Determining the distribution of the area of the field parts in these ranges;
3. A categorical variable is created based on the distribution, assigning a value of 1 to the
category with the largest area and 0 to all others.
Instead of using a categorical variable with possible values {0, 1}, a set of variables can be
employed to represent the full distribution—specifically, the percentage of the field area falling
within each range of NDVI values.
While NDVI is primarily used during the final stages of ripening, it can also be utilized for early-
stage forecasting by predicting future NDVI values based on the dynamics of its changes over time.
This approach enables more accurate predictions of plant maturity and yield at earlier stages.
4.2. Using deep learning models for time series forecasting
When data is presented as time series, the most effective artificial intelligence methods for
forecasting are recurrent neural networks (RNNs) and transformers.
Recurrent neural networks, including architectures such as Long Short-Term Memory (LSTM)
and Gated Recurrent Unit (GRU), are widely used for efficiently processing sequential data while
preserving the context of previous observations. These models are particularly effective for
forecasting based on sequences of observations collected over multiple years [17, 18].
Transformers, a more recent development in time-series forecasting, are gaining traction due to
their flexibility and ability to process sequences in parallel. While their application in yield
forecasting remains an emerging field, transformers have been increasingly utilized in recent
research [19, 20].
4.3. Using separate models for different sources of information
In previous studies, high accuracy was achieved by combining models, specifically the computer
vision model U-Net and the ensemble model LightGBM. U-Net was employed to forecast yield based
on satellite images by segmenting fields into nine performance categories, ranging from the lowest
to the highest. LightGBM was then used to refine these predictions by incorporating additional data,
such as meteorological indicators and field-specific plant characteristics. This approach effectively
distributed tasks, leveraging the strengths of each model for their most suitable functions.
The effectiveness of this approach warrants further investigation with alternative models and
different methods of dataset construction. For segmentation tasks, modern models like YOLO [21]
and SAM [22] could potentially outperform U-Net, offering improved accuracy and efficiency.
Currently, each forecasting iteration processes approximately 1 hectare of a field. The U-Net
model is designed to perform predictions separately for each segment of the data, after which the
results are aggregated. While this approach allows for dataset augmentation and facilitates model
training even with limited data, it restricts insights into the overall field condition.
Given that weather conditions and plant maturation data are already incorporated in the
LightGBM forecasting stage, a new model is required to analyze satellite images of the entire field
and extract key features. This could involve developing a dedicated artificial intelligence model to
either transform the data into usable formats or independently derive general characteristics deemed
important by agronomic experts, such as the average NDVI value across the entire image, the range
(difference between maximum and minimum values) of specific vegetation indices, and similar
metrics.
One limitation of this approach is that the models are trained separately. After training they are
simply combined: using the first model, 𝑀𝑀1 (U-Net), the yield is predicted 𝑌𝑌1 based on satellite images.
𝑋𝑋1 :
𝑌𝑌1 = 𝑀𝑀1 (𝑋𝑋1 ) (4)
and when forecasting with the second model 𝑀𝑀2 (LightGBM), the output values of the first model
are used together with additional data 𝑋𝑋2 to generate the final yield forecast:
𝑌𝑌 = 𝑀𝑀2 (𝑌𝑌1 , 𝑋𝑋2 ) (5)
Each model is trained independently. The process is shown schematically in Fig. 1.
Figure 1: Schematic of the independent model learning process
Since LightGBM does not allow specifying a differentiated loss function, an alternative model,
such as a multilayer perceptron (MLP), can be used instead. This substitution enables the use of a
customized loss function tailored to the specific requirements of the task.
The learning process can also be adapted to allow simultaneous error propagation for both
models. This means that the training pipeline can be designed to integrate the outputs of both models,
ensuring that updates to the parameters of one model account for the influence of the other, thereby
improving overall synergy and performance 𝑀𝑀1 and 𝑀𝑀2 and facilitate their simultaneous learning
and effective interaction. For this purpose, a common loss function is calculated:
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 = 𝐿𝐿(𝑌𝑌, 𝑌𝑌𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 ) = 𝐿𝐿(𝑀𝑀2 (𝑀𝑀1 (𝑋𝑋1 ), 𝑋𝑋2 ), 𝑌𝑌𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 ), (6)
where 𝐿𝐿 - is a loss function (e.g., root mean square error), 𝑌𝑌 - is the final forecast, and 𝑌𝑌𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 - is
the set of actual values.
For example, learning by gradient descent will work like this:
1. For model 𝑀𝑀2 the gradient with respect to its weights 𝜃𝜃2 :
𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕
𝛻𝛻𝜃𝜃2 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 = · (7)
𝜕𝜕𝜕𝜕 𝜕𝜕𝜃𝜃2
2. For model 𝑀𝑀1 the gradient with respect to its weights 𝜃𝜃1 :
𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝑌𝑌1
𝛻𝛻𝜃𝜃1 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 = · · (8)
𝜕𝜕𝜕𝜕 𝜕𝜕𝑌𝑌1 𝜕𝜕𝜃𝜃1
3. Updating the weighting coefficients 𝑀𝑀1 and 𝑀𝑀2 :
𝜃𝜃1 ← 𝜃𝜃1 − 𝜂𝜂𝛻𝛻𝜃𝜃1 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿
(9)
𝜃𝜃2 ← 𝜃𝜃2 − 𝜂𝜂𝛻𝛻𝜃𝜃2 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿
where 𝜂𝜂 - is the learning rate.
Thus, model 𝑀𝑀1 is trained to generate intermediate outputs 𝑌𝑌1 that maximize the accuracy of
model 𝑀𝑀2 's predictions. In turn, model 𝑀𝑀2 is trained to optimally utilize the intermediate outputs 𝑌𝑌
to minimize the deviation of the final forecast 𝑌𝑌 from the actual values 𝑌𝑌𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 . The backward
propagation of errors affects the weights of both models, enabling joint learning where each model
is optimized to improve the final forecast 𝑌𝑌. This process is illustrated schematically in Fig. 2.
Figure 2: Diagram of the simultaneous model training process
Alternatively, a unified model capable of analyzing all types of information simultaneously might
prove even more effective. For instance, study [23] introduced a transformer-based model designed
to integrate various information sources, including both static and dynamic indicators. This approach
enabled the model to outperform commonly used methods, such as Random Forest and XGBoost, in
terms of forecasting accuracy, making it a promising direction for further research and application
in yield prediction.
5. Application prospects
5.1. Differentiated application of chemicals
One of the primary methods for preparing plants for harvest is desiccation, an artificial drying
process that equalizes moisture levels in the field and accelerates ripening. This practice addresses
the problem of uneven ripening, which can otherwise lead to significant harvest losses. However,
desiccation is not always economically justified, as the costs of the substances and their application
may exceed the value of the yield saved. Forecasting technology can play a key role in evaluating
the feasibility of desiccation [24].
Assume the existence of a highly accurate yield prediction model. This model can be retrained by
incorporating a binary variable, 𝑑𝑑𝑑𝑑𝑑𝑑, into the training set, where 1 indicates that desiccation was
performed, and 0 indicates it was not.
The impact of desiccation varies depending on the conditions: in some cases, it results in a
substantial yield increase, while in others, the improvement is negligible. With a sufficiently large
dataset, these effects will be reflected in the data. Once trained, the model can be used to predict the
potential benefits of desiccation, enabling informed decision-making for its application:
1. Yield forecast without desiccation: 𝑌𝑌𝑛𝑛𝑛𝑛_𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑀𝑀(𝑋𝑋, 𝑑𝑑𝑑𝑑𝑑𝑑 = 0)
2. Yield forecast with desiccation: 𝑌𝑌𝑤𝑤𝑤𝑤𝑤𝑤ℎ_𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑀𝑀(𝑋𝑋, 𝑑𝑑𝑑𝑑𝑑𝑑 = 1)
3. Increase in yields: 𝛥𝛥𝛥𝛥 = 𝑌𝑌𝑤𝑤𝑤𝑤𝑤𝑤ℎ_𝑑𝑑𝑑𝑑𝑑𝑑 − 𝑌𝑌𝑛𝑛𝑛𝑛_𝑑𝑑𝑑𝑑𝑑𝑑
The value of the crop and the cost of purchasing desiccants and spraying may vary, but agronomic
experts can get accurate information about them. The only uncertainty is the potential yield of the
field. Thus, if forecasting accuracy is high, the potential benefit of desiccation can be calculated with
high accuracy:
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = �𝛥𝛥𝛥𝛥 · 𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 � − 𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 , (10)
where 𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 - is the cost per unit of harvest, 𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡𝑑𝑑𝑑𝑑𝑑𝑑 - cost of desiccants and their application.
To further enhance the training dataset, the model can be improved by incorporating detailed
information about desiccation application methods. This involves adding data on two key aspects:
1. Selective Spraying: Desiccation can be applied only to specific areas where it is necessary.
2. Variable Intensity: Different chemical application intensities can be used for different
areas, tailored to the needs of the plants in each plot.
With a sufficiently large dataset, a model can be trained to predict yield improvements based
on the method of application. To achieve this, the dataset should include an additional variable,
𝑑𝑑𝑑𝑑𝑠𝑠𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ∈ [0, 2], representing the intensity of substance application for each plot (e.g., 0 liters
for no application, and 2 liters for the standard maximum intensity).
Once the model is trained, the most effective desiccation strategy can be determined using the
following algorithm:
1. generation of application variants: since each field consists of numerous plots, and an
arbitrary amount of substance can be applied to each within the standard range, it is advisable
to limit the generated variants using heuristics based on accepted desiccation practices;
2. limitation of the generated options: even with the previous limitation, the set of options may
be too large, so some rules need to be applied, such as discarding similar options (which
options are considered similar should be determined separately) and search algorithms to
minimize computation;
3. forecasting yields for each of the application methods. Formally, for each variant 𝑉𝑉𝑖𝑖
containing information about the intensity of desiccation 𝑑𝑑𝑑𝑑𝑠𝑠𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 on each field plot;
4. selection of the best option: the option is selected 𝑉𝑉 ∗for which the predicted yield is
maximized: 𝑉𝑉 ∗ =𝑎𝑎𝑎𝑎𝑎𝑎 max 𝑌𝑌𝑖𝑖
Vi
This approach enables optimized desiccation by incorporating selective spraying and variable
application rates, thereby ensuring more efficient resource use.
This approach can be extended to apply to other agronomic procedures, such as the use of
pesticides and other chemicals.
5.2. Prediction in the early stages of maturation
If the forecasting technology is successfully developed, it can be extended to smaller, limited
datasets. By considering the input data as a time series 𝑋𝑋 𝑑𝑑 , 𝑑𝑑 ∈ {1,2, … , 𝑇𝑇}, the sample size can be
reduced by decreasing the value of 𝑇𝑇, thereby training the model on shorter time periods. Although
this may reduce accuracy, it enables yield predictions at earlier stages of plant development.
One key advantage of early-stage forecasting is the ability to promptly detect problems. For
example, a low predicted yield in a specific area may indicate the presence of diseases or pests,
allowing agronomic experts to address potential issues proactively and prevent significant yield
losses. This application can be further enhanced with remote monitoring and plant health analysis
techniques, such as automated lesion detection [25].
Overall, early problem detection and early planning capabilities can significantly improve
decision-making and optimize agricultural production processes.
6. Conclusions
The site-specific yield forecasting technology developed through these methods and approaches
has the potential to significantly enhance agricultural efficiency. The proposed data processing
techniques are designed to effectively leverage available data, even under challenging conditions
such as heavy cloud cover in satellite images, enabling accurate forecasts across diverse scenarios.
The method emphasizes the formation of balanced and representative samples, ensuring that
forecasting models can generalize effectively across varying conditions and plant types. By
integrating advanced deep learning models and their combination methods, the accuracy of forecasts
is expected to improve significantly.
Implementing this technology will enable better resource management by adapting field care to
specific conditions, thereby reducing the risks of yield losses due to uneven maturation, pests, or
diseases. Its successful application could facilitate innovations such as optimized, differentiated
fertilization and precise early-stage yield forecasting. Practical implementation is anticipated to
validate the effectiveness of these technologies, paving the way for broader applications across
different regions and crop types.
Declaration on Generative AI
The author(s) have not employed any Generative AI tools.
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