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Anticipatory Understanding of Resilient
Agriculture to Climate
Dr. David E. Willmes Nick S. Krall Dr. James H. Tanis
Dr. Zachary Terner Dr. Fernando T. Tavares
Dr. Chris W. Miller Joe Haberlin III Matt Crichton
Dr. Alexander Schlichting
November 11, 2024
Abstract
With billions of people facing moderate or severe food insecurity, the
resilience of the global food supply will be of increasing concern due to
the effects of climate change and geopolitical events. In this paper we
describe a framework to better identify food security hotspots using a
combination of remote sensing, deep learning, crop yield modeling, and
causal modeling of the food distribution system. While we feel that the
methods are adaptable to other regions of the world, we focus our analysis
on the wheat breadbasket of northern India, which supplies a large per-
centage of the world’s population. We present a quantitative analysis of
deep learning domain adaptation methods for wheat farm identification
based on curated remote sensing data from France. We model climate
change impacts on crop yields using the existing crop yield modeling tool
WOFOST and we identify key drivers of crop simulation error using a
longitudinal penalized functional regression. A description of a system
dynamics model of the food distribution system in India is also presented,
along with results of food insecurity identification based on seeding this
model with the predicted crop yields.
1 Introduction
In 2022, approximately 2.4 billion people faced moderate or severe food insecu-
rity, representing almost 30 percent of the global population [1]. This problem
has been exacerbated recently due to the war in Ukraine as well as an increase in
heat and droughts in some of the breadbaskets around the world. In India, the
2022 heat wave severely curtailed the country’s wheat production, prompting
India’s Minister of Agriculture to publish a memo suggesting the need for an
end-to-end system to monitor crop production and the delivery of grain to their
citizens [2].
1
arXiv:2411.05219v1 [cs.CV] 7 Nov 2024
We are focusing this research on the wheat breadbasket of northern India,
which is responsible for sustaining not only the most populated nation on Earth,
but also has become a significant source of grain to the rest of the world after the
war in Ukraine curtailed Ukrainian exports. While there are about 140 million
farms in India, with about 40% growing wheat in a given year, prediction of the
amount of food available is difficult. Most of India’s wheat crops are grown on
small, family-owned farms, with an average size of about 3 acres according to
the India Agricultural Census, and many different strains of wheat are grown
in each of the wheat-producing states [3]. This creates an uncertainty in crop
yield that necessitates an automated approach to crop identification and yield.
In this paper, we will discuss the technical development of a framework to
identify wheat fields using satellite remote sensing and deep learning classifi-
cation, predict crop production under various climate scenarios using physics-
based crop yield simulations, model the distribution of grain to food insecure
populations using a system dynamics approach, and suggest potential courses
of action that can improve the resiliency of the food system. An interactive
dashboard in which a user can explore the implications of different courses of
action has been built, which shows the results of running the system dynamics
models for each region of interest.
While the focus of this research is on the wheat breadbasket of northern
India, there are similarities to other scholarly work where techniques were de-
veloped for combining AI with remote sensing for agriculture, for example the
recent work by Nakalembe and Kerner and their analysis of agriculture in sub-
Saharan Africa [4]. For instance, both regions suffer from a lack of ground truth
for agricultural production, which makes it difficult to validate performance of
the algorithms. In our case, concentrate our deep learning analysis on wheat
production in France, where curated remote sensing datasets exist, and use do-
main adaptation techniques to transfer results to ou region of interest. The
distribution and market dynamics portion of this research focuses on modeling
the unique aspects of the Indian economy and governance.
2 Remote Sensing-based Crop Identification
In order to accurately forecast yield trends, the total growth area for each crop
type must be assessed in an automated manner. While there are several op-
tions for obtaining georeferenced crop type labels at scale, remote sensing data
was chosen due to its potential for timely and scalable collection of rich spatial,
spectral, and temporal information necessary for accurate crop type identifi-
cation. With the recent growth of machine learning (ML) capabilities applied
to computer vision and remote sensing, we selected a common family of ML
architectures that have shown to perform well on the crop type mapping appli-
cations. These architectures include semantic segmentation convolutional neural
networks (CNNs) which can exploit spatial relationships in pixels, long short-
term memory recurrent neural networks (LSTMs) that can accurately capture
temporal patterns, and combinations of the two to jointly handle spatial, spec-
2
Table 1. Information on the 13 bands in Sentinel-2 satellite sensors.
Sentinel-2 Spectral Band Central Wavelength (µm) Resolution (m)
Band 1: Coastal aerosol 0.443 60
Band 2: Blue 0.490 10
Band 3: Green 0.560 10
Band 4: Red 0.665 10
Band 5: Red Edge 1 0.705 20
Band 6: Red Edge 2 0.740 20
Band 7: Red Edge 3 0.783 20
Band 8: NIR 0.842 10
Band 8A: Red Edge 4 0.865 20
Band 9: Water vapor 0.945 60
Band 10: SWIR 1 1.375 60
Band 11: SWIR 2 1.610 20
Band 12: SWIR 3 2.190 20
tral, and temporal information.
2.1 Data
Several satellite constellations were considered and the European Space Agency’s
(ESA) Sentinel-2 (S2) satellite was selected. The S2 constellation was selected
because of its mix of medium-high spatial resolution at multiple spectral bands
(shown in Table 1), medium-high revisit rate of five days, and availability of
free data. An automated data download system was created to pull S2 imagery
from an AWS hosting service and store on a local network attached storage
drive, then indexed in a geospatially enabled SQL database. Python was used
to implement all methods and processing.
One consideration for data preprocessing was whether to use bottom of at-
mosphere (BoA) or top of atmosphere (ToA) data. The BoA product benefits
from being atmospherically corrected, but as shown in a recent crop type clas-
sification method [5], ToA data can lead to equivalent accuracy. ToA data (S2
processing level of L1C) was used in our models due to ease of adoption of
methods to other regions where atmospherically corrected data is not possible.
Robust crop type classification across different climates and terrains ideally
involves labeled data from each unique bioclimate. In order to efficiently use
these unique datasets it is important to create globally consistent labels, but
datasets from each region have different formats, as shown in Figure 1.
3
Figure 1. Crop type classification datasets are spread across many domains and
formats, requiring specialized preprocessing to homogenize data for consistent
usage.
Although the primary focus area for evaluating the overall food security
approach is the northern India region, (Figure 2), no known sufficient ground
truth exists for crop type classification in these regions, as concluded from a
significant literature review. Since modern deep learning methods require large
scale datasets, we train and validate our models on label-rich areas and then
test the models in northern India. This training strategy introduces challenges
due to domain transfer which will be addressed in a later section.
Figure 2. The three focus states in Northern India encompass several different
geographies.
Following [5], we first train and evaluate our models in France. As shown
in Figure 3, we use the associated ground truth parcels provided by the French
4
National Institute of Forest and Geography Information as part of the EU’s
Common Agricultural Policy. This dataset is known as the Agricultural Land
Parcel Information System (Registre Parcellaire Graphique or RPG) and con-
sists of 328 unique crop labels grouped into 23 groups [6]. The crop class “winter
wheat” is the primary focus of our study.
Figure 3. France’s RPG dataset provides parcel-level crop type annotations for
the full country.
We investigate growing periods in years 2017, 2018, and 2019. Unique RPG
layers exist for each year. Since many farmers grow different crops throughout
a period of several years, as shown in Figure 4, it is necessary to use temporally
appropriate labels. We also study the effect of using several different time
periods and scales, and all methods incorporate multiple time steps to account
for the full growth cycle of crops.
5
Figure 4. Wheat parcels rotate across years, deeming it necessary to use specific
inidividual year’s imagery and labels.
2.1.1 Data Preprocessing
Once all data is downloaded for the desired locations and time periods, all
bands are upsampled to the highest spatial resolution of 10 m to ensure uniform
inputs to the model. Although ESA provides cloud masks associated with each
collect, we determined the masks were not suitable for training applications due
to missing some significant cloud groupings, circled in red in Figure 5. As an
alternative, we used a separate package called S2Cloudless [7] and qualitatively
tuned it on several different cloud types and regions within France. The resulting
cloud mask is more complete than the ESA mask, with the correct masking
highlighted in green in the figure.
6
Figure 5. The tuned S2Cloudless model can capture most or all cloud instances
and cloud types in its per-pixel mask, where the default Sentinel-2 vector cloud
mask fails. The green ovals in S2Cloudless highlight the clouds that are suc-
cessfully masked that are incorrectly missed in the red ovals of ESA.
2.2 Crop Classification Models
We investigate several methods that collectively use combinations of spatial,
spectral, and temporal data. In selecting models to use, there are two major
considerations. The first is model complexity, which includes the number of
parameters, training stability, and computation time. Model complexity informs
the amount and types of data that are required to obtain accurate results. The
second consideration is model generalizability, or the ability of the model to
perform similarly across multiple geographic, temporal, spectral, and cultural
(economic, farming practices, etc.) domains.
The first model considered is spatial-spectral, which consists of a CNN
encoder-decoder architecture (UNet [8] architecture and a ResNet50 [9] encoder
backbone) with a separate temporal merging step outside of the training pro-
cess. Multispectral images from the entire growth cycle are randomized and
provided to the model during training, with the idea of generalizing the spatial
and spectral factors to detect specific crop types at any time during the growth
cycle.
The spatial-spectral model has been heavily researched in the broader com-
puter vision community and has mature, successful architectures for various
applications [10]. However, because this model type does not directly incorpo-
rate multiple time steps in training, it does not explicitly learn temporal growth
characteristics, which aid in the crop type classification task. Figure 6 shows
the three model types investigated.
7
Figure 6. Left: Spatial-Spectral (SS) model. Center : Spectral-Temporal (ST)
model. Right: Spatial-Spectral-Temporal (SST) model.
The second model type is spectral-temporal, which uses an LSTM recurrent
neural network to explicitly learn temporal growth characteristics during train-
ing. Each pixel is independently processed as a separate sample, so these are
typically the slowest in inference of a large image. However, because each pixel
is a separate sample, it is also the most easily extensible to all ground truth
vector formats including point, polygon, rectangular, and more. One major
drawback is that no contextual information is considered during training, so
neighboring pixels do not explicitly inform the current pixel.
As an improvement over both spatial-spectral and spectral-temporal, the
spatial-spectral-temporal [11] model jointly optimizes over all available input
features, allowing the model to incorporate neighboring pixel information, learn
temporal growth characteristics, and account for spectral relationships. How-
ever, this model comes at a cost of vastly increasing model size and complexity,
requiring more training data and making it harder to successfully train. Because
the input requires a temporal component in addition to the spatial and spectral
components, the satellite image time series input must be temporally interpo-
lated on a regular grid to ensure uniform time steps across all input samples.
As shown on the left side of Figure 7, each pixel of each spectral band (only 4
of the 12 bands are shown) must be separately interpolated across space and
time to account for clouds. The right side of Figure 7 shows the variability of
time steps across all spatial-spectral-temporal samples, which requires introduc-
ing another hand-tuned parameter of minimum allowable number of time steps.
For these reasons, the spatial-spectral-temporal model will not be shown in any
evaluations as it had poor training performance on our data. This remains a
promising approach but requires more work to yield valuable results.
8
Figure 7. Left: Spectral values for selected spectral bands over the course of the
year, taking into account cloud presence. Right: The gridded spatial subpatches
(chips) have a minimum of 20 and maximum of 80 time steps.
2.3 Evaluation in France
The first experiment was constrained to the region of Brittany, France, following
the spatial area and crop classes used in [5]. The train and test regions are shown
in Figure 8, also following the subregion splits used in [5].
Figure 8. Three subregions are used for training, and one held out subregion is
used for testing.
Four spatial-spectral models were trained to investigate spectral importance
and how the number of classes affects model performance. The two class model
consists of ”wheat” and ”background” only, while the eight class model includes
9
additional crop types such as ”barley” and ”vegetables”. As shown in Figure 9,
the 2 class/12 band model showed the most promise. For all future spatial-
spectral experiments, we use this combination of classes (wheat, background)
and number of spectral bands. Figure 8 shows examples of predictions for four
random patches from this model.
Figure 9. In both precision and recall, training with 12 bands and 2 classes
performs the best.
Figure 10. Predictions of wheat in various growth stages and regions closely
follow ground truth.
Following [5], we use an LSTM spectral-temporal model and train on the
same region, train/test splits, and classes. Here we use the metrics of preci-
sion, or the proportion of positive classifications actually correct, and recall, the
10
Table 2. Comparison of spatial-spectral and spectral-temporal validation re-
sults.
Model Type Model Classes Precision Recall
Spatial-Spectral All classes 0.69 0.40
Spatial-Spectral Wheat only 0.84 0.68
Spectral-Temporal All classes 0.83 0.83
Spectral-Temporal Wheat only 0.98 0.94
proportion of all positives correctly classified. As shown in Table 2, the spectral-
temporal model outperforms the spatial-spectral model in both precision and
recall.
Because the spectral-temporal model outperformed the spatial-spectral in
this first set of experiments, it was important to understand its limitations
before expanding its use to the northern India area of interest. We study the
importance of time period and number of time steps in the spectral-temporal
model by limiting the time points during training and plotting the validation
F1 score in Figure 11. The F1 score is the harmonic mean of precision and
recall, allowing a single combined metric. While the focus of this paper is the
wheat crop, we use all classes in this experiment to understand how the model
represents different types of vegetation in the temporal domain. As shown in
the plot, the spectral-temporal model can maintain comparable performance
even when reducing temporal range by 33% from 45 to 30 time points.
Figure 11. The spectral-temporal model maintains decent performance even
with limited number of input time steps during training.
2.4 Evaluation in India
Now with an understanding of performance in data rich areas, we apply these
trained models to northern India, which lacks any significant accurate parcel-
11
level ground truth in the formats and scales required to understand model per-
formance. As a workaround, we evaluate using several approximate, pseudo-
ground truth approaches.
2.4.1 MapSPAM
MapSPAM 2010 [12] is a global crop type estimation method and data source
developed using a variety of information sources. It provides an approximate
10x10 km per pixel estimate, with each pixel value representing the percentage
of each crop type in the pixel area. The latest global model was produced for
2010 data, as the process is manually intensive and relies on collecting vast
amounts of disparate data. An overview is shown in Figure 12. The potentially
stale information and relatively low spatial resolution qualify this as a pseudo-
ground truth, but we use this and several other approaches to quantify crop
type mapping performance in northern India.
Figure 12. MapSPAM system overview. Text and graphic from
https://www.mapspam.info/
12
To better understand MapSPAM’s limitations, we first evaluate the spatial-
spectral (SS), spectral-temporal (ST), and the actual RPG ground truth in
France against MapSPAM’s predictions. As shown in Figure 13, the real ground
truth is about 10% off from MapSPAM’s estimation in the French region eval-
uated. In Figure 13, we vary the threshold at which we classify a prediction
as wheat or not wheat. The SS model has a sharp peak around a classification
threshold of 0.2, and otherwise vastly underestimates the area of wheat growth
compared to MapSPAM. The ST model’s estimation is much smoother across a
wide range of prediction confidence thresholds and remains close to the actual,
indicating a more stable feature representation within the model.
Figure 13. The spectral-temporal model is more accurate in total wheat area
estimate than MapSPAM for a wide range of classification thresholds.
However, when applied to the northern India state of Punjab, both models
accurately estimate the MapSPAM area at relatively low classification thresh-
olds and have a large range of predictions sensitive to the classification thresh-
old, indicating a performance drop across regions. In the Punjab case, the SS
model outperforms ST as evidenced from a higher confidence threshold at the
MapSPAM’s estimation amount, as shown in Figure 14.
13
Figure 14. The MapSPAM area prediction intersects the 0% area difference
dashed line at low classification thresholds. This indicates a performance drop
relative to the performance on the training data in Fig 13.
2.4.2 NDVI as Upper Bound
Another pseudo-ground truth source is Normalized Difference Vegetation In-
dex (NDVI) as an upper bound. NDVI is defined as (NIR – Red) / (NIR +
Red). A high value indicates strong vegetation presence (via spectral response
of chlorophyll) in the pixel. We filter NDVI to the range of values expected of
wheat corresponding to a certain growth stage and time period. These rough
NDVI predictions should cover all of the wheat pixels, so our model should not
estimate more area than the NDVI prediction. We compare SS and ST models
trained with a single wheat species and multiple wheat species (considered to-
gether as a single class) in Figure 15 using the precision metric averaged across
all images. Precision was chosen since it compares only the model wheat predic-
tions and does not consider recall as there are many more non-wheat vegetation
pixels present in a region.
14
Figure 15. Using the NDVI map as pseudo-groundtruth, the model that treats
all wheat species as a single class performs best across all Indian states studied.
Given the model behavior of predicting wheat in a few non-vegetation areas,
we also consider using NDVI to filter the model predictions by removing any
predictions not in the NDVI filtered mask. We show one of the worst prediction
areas from India in Figure 16, and qualitatively demonstrate that using NDVI
to filter some non-vegetation areas is a useful technique.
Figure 16. Qualitatively, the NDVI layer can help filter wheat prediction in
obviously non-vegetation areas, as shown by barren land (light brown) in the
imagery.
2.4.3 State-level Area
Finally, as a third pseudo-ground truth source we use state-level reports from
the Indian Directorate of Wheat Development from 2019. We process the wheat
growing period of 2018-2019 and create final predictions for the same single
species and multi-species SS and ST models and show results in Figure 17.
Overall, Punjab has the smallest difference from the state-level reports by area,
as it is the most similar to the training regions in France. This similarity will be
further examined in a following section. We also include the MapSPAM 2010
predictions for Punjab, and they are off by about 50% from the state reports. It
15
is important to consider error in the state-level reports as not all of the grown
wheat is directly reported, but this error is much harder to quantify.
Figure 17. Qualitatively, the NDVI layer can help filter wheat prediction in
obviously non-vegetation areas.
2.5 Need for Domain Adaptation
As shown in the previous pseudo-ground truth approaches, the models typically
perform best on Indian states closest to the France training region, although
they too suffer from domain differences.
In order to create an operational food security model, crop classification
models need to work with different terrains, climates, and agricultural practices
for broad applicability. As previously explained, many regions of interest have
little to no ground truth with which to develop data-intensive approaches such
as neural networks. To this end, Unsupervised Domain Adaptation (UDA)
may be a promising approach to multi-domain crop classification. UDA entails
automated knowledge transfer from label-rich source domain to target domain
with no labels, with a notional example shown in Figure 18.
16
Figure 18. Agricultural features in data-rich areas such as France must be
adapted to work in other domains across the world, with Sentinel-2 imagery
from each location shown.
To quantify and investigate the regional differences in wheat classification,
we first compare sub regions in France due to its high fidelity ground truth. We
train an SS model in Brittany, and test on other areas in France to show drop
in performance, as shown in Figure 19.
Figure 19. Training region of Brittany and testing regions of Somme, Landes,
and Meuse.
We show that testing regions with a similar latitude to the training regions
17
have less performance drop in Figure 20. This result motivates a deeper dive
into domain differences.
Figure 20. Left: Results showing performance drop when testing in different
regions from training. Right: Map representation of precision-recall area under
curve (PR AUC).
2.6 Understanding Domain Differences
To better understand these domain differences we try visualizing the learned
features using a dimensionality reduction method called Uniform Manifold Ap-
proximation and Projection (UMAP) [13]. UMAP is similar to a common
dimemsionality reduction method called t-SNE in that it projects high dimen-
sional data into a low dimensional embedding, but it also preserves both local
and global distances between individual samples, making it a useful tool for
visualizing high dimensional data on a 2D surface.
We compare features extracted from 400 samples (105M pixels) from the
France training region and three Indian states of Punjab, Rajasthan, and Uttar
Pradesh during their respective wheat growing seasons.
As shown in Figure 21, there is a relatively smooth spectrum of samples,
but some points group together for each region. Clouds and other atmospheric
effects were not directly taken into account, so some clusters may be due to
cloud presence.
18
Figure 21. Learned features extracted from our CNN model cluster on a smooth
spectrum, showing some regional differences.
We also consider USGS Environmental Land Units (ELUs) [14], which is
a map of ecophysiographic stratification based on bioclimate, landcover, land-
form, and lithology. The ELU data can explain some domain differences, but
to quantify how these affect current model performance, we map F1 crop clas-
sification performance metric in different regions to ELU input variables. A
notional example is shown in Figure 22, with the application of determining
ELU variable importance for predicting future model performance in new areas.
We also plan to use a regression model to inform domain generalization design
choices in future work.
19
Figure 22. Notional graphic of using USGS ELUs to predict performance in
other regions of interest.
2.7 Generalization vs Adaptation
As the ideal application of this system is to unique and disparate global regions,
it is important for a crop identification model to accurately map wheat and
other crops across many different domains. There are two main perspectives
for achieving robust models in this context: domain generalization (DG) and
domain adaptation (DA). The aim of DG is to have a single model that can
be used in a variety of domains and achieve suitable performance in all. As a
contrast, DA aims to transfer knowledge from one domain to another, meaning
a new DA training is performed for each separate domain.
A common approach for pretraining a DG model is called contrastive learning
[15], which is a self-supervised visual representation learning method that learns
invariance by predicting the features of a transformed image. As it is self-
supervised, it requires no labels, making it effective at training on large scale
datasets. Contrastive learning pre-training outperforms supervised pre-training
on many downstream tasks and datasets, proving a suitable choice for DG tasks.
As previously explained, UDA can provide automated knowledge transfer
across a single source and multiple target domains without the need for large la-
belled datasets. We studied two UDA approaches using different regions within
the France RPG dataset. The UDA setting is created by withholding the la-
bels in training for the target dataset, and only using the labels in the final
evaluation.
A first approach is called ProDA [16]. ProDA defines classes in the target
dataset using pseudo labels, created by iteratively minimizing the distance from
a sample point and its prototype (centroid of feature clusters). By using the
distance from the prototype for each class, the pseudo-labels are corrected online
during training and account for noisy outliers typically present in UDA datasets.
An overview is shown in Figure 23.
20
Figure 23. ProDA can use prototypes of classes in source and target data sets
to align domains in feature-space.
A second approach is called ADVENT [17], which combines the well-practiced
adversarial training regime to maximize domain overlap with a simple entropy
minimization on the target predictions. Figure 24 shows an overview of the
approach, where the joint loss combines a soft segmentation loss of the pre-
dicted target image and performs either a direct entropy minimization, or an
entropy minimization via adversarial training. The latter option attempts to
align the entropy distributions of the source and target datasets computed on
the self-information maps. Overall, ADVENT is a useful approach as it is rela-
tively simple in reducing entropy of pixelwise predictions across train and test
domains, and adds no significant overhead to semantic segmentation training.
Figure 24. ADVENT attempts to align source and target domains in feature-
space via entropy minimzation, allowing for very little additional computational
overhead.
The area of domain adaptation/generalization for crop classification remains
challenging. While these approaches show promise in theory, both are active ar-
21
eas of research in applying to crop classification, and have yet to yield significant
improvements over baseline networks in our effort.
3 Crop Models
3.1 Simulation Details
While remote sensing and machine learning are appropriate techniques for iden-
tifying individual wheat fields, they do not provide the fidelity or the predictive
capability that are necessary for quantifying wheat yields. For this, we turn
to physics-based crop growth models, of which there are several in use by aca-
demic and industrial researchers. We considered three of the most popular
models available (DSSAT, APSIM, and WOFOST) and chose WOFOST pri-
marily due to the existence of a Python wrapper, PCSE, to make integration
into our software pipeline easier [18].
The World Food Studies (WOFOST) crop model, from Wagneningen Univer-
sity & Research, Netherlands, has been in use for over 25 years and is currently
a key component of the MARS Crop Forecasting System for Europe [19]. It
provides potential yields, which are limited only by environmental conditions
and plant characteristics, as well as attainable yields, which are also limited by
water and soil nutrition conditions. The model uses daily time series weather
data, soil data, and crop parameters to provide crop yields in kg/ha.
We collected and mapped soil data from the Harmonized World Soil Database’s
[20, 21] Texture field to one of WOFOST’s three built-in soil classes. Our test-
ing focused on the winter wheat crop. We chose winter wheat 104 as the wheat
strain to use after testing different strains across the country. We identified
October 1st as an optimal planting date by testing each potential day, 9/16
through 11/30, against our ground truth data in France.
For validation efforts, PCSE provided a built-in API linked to the NASA
POWER database (https://power.larc.nasa.gov). This provided good historical
weather data for all parameters used by PCSE that we compared to ground
truth data. However, for future climatic conditions, we employed MarkSim,
which can provide weather projections for any year on a daily basis [22]. This
allowed us to run models for future crop yield output.
Although MarkSim provided most of the requisite data, it did not provide top
of atmosphere radiation, dew point, wind speed, and average daily temperature.
Top of atmosphere radiation was assumed to be relatively constant and was
mapped to the previous year’s values. Ground level radiation was provided by
MarkSim. Dew point, wind speed, and average temperature were calculated
using a probability distribution based on historical NASA POWER weather
data for each site.
We compared crop projections from PCSE to 20 years of harvest data from
France, spanning 2000-2019. The data were obtained from the French Ministry
of Agriculture and Food (https://agreste.agriculture.gouv.fr.)
22
3.2 Crop Yield Modeling Analysis Details
We wanted to determine if WOFOST could be used to project crop production
trends one or two decades into the future. Therefore, we sought to identify
which weather patterns in France were associated with increased error from
the WOFOST simulation. We computed simulation error by comparing the
predicted crop yield output for each department in France, for every year from
2000 through 2019, to the true crop yield in France in those regions. The year
2016 was omitted from the analysis due to the severe loss in wheat yield that
year [23, 24, 25]. France weather data were collected via the NASA Power API.
With absolute percent error as the response variable, we built a longitudinal
penalized functional regression model using the lpfr function from the refund
package in R [26]. The predictors included a fixed effect for time, which was
coded as a categorical variable; a random intercept for geographic department or
region; and up to three functional variables: weekly average max temperature;
monthly total precipitation; and weekly average irradiance. These data were
aggregated to their respective timescales to allow the functions to be somewhat
smooth and aid in constructing the regression model. Another example of using
functional data analysis for crop yield predictions can be found in [27].
The analysis was done once at the department-level, using data aggregated
and averaged by each of the 93 departments, and once at the level of the 13
regions. At the region-level, we removed three regions, which are all in the south-
eastern portion of France, from the analysis: Corse, Auvergne-Rhˆone-Alpes and
Provence Alpes Cˆote d’Azur. Each of these regions are low producers of wheat,
and they also tend to be regions of low soil depth, as shown in Figure 25. There-
fore, since we focused on the bread-basket regions of France, we omitted these
regions.
The region-level analysis identified that the categorical variable of time was
critical to the model, affirming that each year can be quite different in terms
of weather and crop production. However, after including time in the model –
and therefore adjusting for its effects – rain and irradiance were identified to be
significant predictors in the model as well. Removing rain or irradiance from
the model worsened model fit; additionally, temperature was not found to be a
significant variable in the region-level analysis. The adjusted R2of .68 indicated
that the model with time, rain, and irradiance explained 68% of the variation
in absolute percent error at the regional level.
Additionally, coefficient plots (Figure 28) help explain when and how these
weather factors may be associated with absolute percent error. An increase in
rain is associated with more error throughout the year, whereas temperature
is associated with error from Week 16 to Week 40, or from May to the end of
September. The coefficient plots can be interpreted following the rules in [28].
The analysis at the department-level required several additional steps. First,
all departments within the low soil-depth regions above were similarly omitted
from this analysis. Next, Haute-Garonne was removed since its average percent
error across the 19 years was over 10000%. We then built a model which included
the remaining 73 departments and examined the model for departments which
23
contained at least one outlier-year. This process of identifying outliers was
conducted until we obtained a model without any notable outlier-years that
hampered the model fit.
In total, 62 departments were included in the final department-level model,
as shown in Figure 27. The conclusions here resemble those in the regional-level
model: rain and irradiance are again included in this model, along with temper-
ature. The adjusted R2value of .78 indicates that the model with time, rain,
irradiance, and temperature explained 78% of the variation in absolute percent
error at the department-level. We can examine coefficient plots in Figure 26 to
learn when and how the weather factors are associated with changes in error. An
increase in rain is associated with more error throughout the year; temperature
is associated with changes in error prior to Week 30 (August); and irradiance
appears important all year round.
By simulating crop yield output with PCSE and comparing crop yield errors
to local weather data, we have built a roadmap for this type of crop production
modeling. Given a reliable simulator, a representative crop strain, weather data,
and a map of soil depth, one can identify the impact of changes in weather on
crop production in different geographic regions. This kind of work can be used
in anticipation of climate change – identifying weather patterns which hinder
food production can allow for measures to be taken to prevent food shortages.
Figure 25. Regions of France overlaid with wheat production and soil depth
24
2 4 6 8 10 12
−6 −4 −2 0 2 4 6
Precipitation function using 10 regions in France from 2000−2015, 2017−2019
Month of year
BetaHat
0 10 20 30 40 50
−0.6 −0.2 0.0 0.2 0.4 0.6 0.8
Irradiance function using 10 regions in France from 2000−2015, 2017−2019
Week of year
BetaHat
Figure 26. Coefficient plots for precipitation and irradiance using 10 regions in
France
25
Figure 27. Regions of France overlaid with wheat production and soil depth
26
2 4 6 8 10 12
0.0 0.5 1.0 1.5
Precipitation function using 62 departments in France from 2000−2015, 2017−2019
Month of year
BetaHat
0 10 20 30 40 50
−0.4 −0.2 0.0 0.2 0.4 0.6
Temperature function using 62 departments in France from 2000−2015, 2017−2019
Week of year
BetaHat
0 10 20 30 40 50
0.0 0.2 0.4 0.6
Irradiance function using 62 departments in France from 2000−2015, 2017−2019
Week of year
BetaHat
Figure 28. Coefficient plots for precipitation and irradiance using 62 depart-
ments in France
27
4 The System Dynamics of India’s Public Dis-
tribution System
The dissemination of food to the vulnerable population is just as important
for food security as predicting food production. This dissemination is done by
a government program called Public Distribution System (PDS). The Public
Distribution System was established in the middle of the 20th century by the
government of India to deliver grain to its food insecure citizens [29]. Over the
following decades, the Indian government expanded and formalized the program
to improve food security. Today, roughly two thirds of the country’s population
of more than 1.4 billion is entitled to a grain subsidy under the National Food
Security Act (NFSA) [30]. Then in addition to the intention of the PDS to
provide for the food insecure, the PDS also has a large impact on the food
economy of India.
Hence, we model it to estimate food insecurity trends of India’s citizens.
The country of India is a collection of 28 states and eight union territories which
have their own governments. These states and territories are further partitioned
into administrative divisions called districts. Because states can be large and
demographically diverse, we model the PDS at the local level of districts, which
should be more helpful government officials.
The model may also be able to suggest prescriptive policies that a govern-
ment can apply. For this purpose, we’ve developed system dynamics models to
identify potential levers for policymakers and to show effects of these decisions
on food security. Our approach is to build individual modules to model different
aspects of food distribution. This allows modelers to swap out modules as new
complexities are identified, or to enable new scenarios, such as modeling new
geographic regions or expanding the model to include livestock or other crops.
India’s crop production and dissemination requires an understanding of the
market dynamics as well as the dissemination policies of the government. The
Indian federal government provides a Minimum Support Price, or MSP, to the
farmers to encourage them to produce certain crops. Without the MSP, it is
likely that many farmers would forgo growing staples such as wheat and focus
on cash crops instead. Figure 29 shows our four modules – Farm Production,
Market Dynamics, Storage and Transportation, and Food Insecure Consumer
Behavior – as well as the overall dissemination pipeline into which these modules
feed. The MSP policy lever can be modified to assess how changing the MSP
affects the availability of wheat for the food insecure.
28
Figure 29. Modules for the overall system dynamics model that describe the
production and distribution of wheat in northern India
Building such a model has two main challenges. First, grain consumption
trends inform how grain should be distributed within each state, but publicly
available data on this is scarce at the district level. Therefore, we estimate
food consumption trends using related data, which comes from a variety of data
sources and varying spatial scales. Second, the transportation system of grain
from farms to consumers is complex. Grain produced in one state may need to
be transported to a different one, which could depend on many factors includ-
ing grain production in neighboring states, the weather, and current economic
and infrastructural conditions. To make the problem more tractable, we focus
only on the wheat crop and the state of Uttar Pradesh. Uttar Pradesh has
a large, economically diverse population that produces and consumes wheat,
which makes it a good test case for modeling the PDS for the rest of India [31].
Section 4.1 outlines how we estimate grain consumption data that is missing
from public sources at the district level. This is done by aggregating informa-
tion from multiple spatial scales: district, state, and regional level, as listed in
Table 3. Section 4.2 discusses our model for the flow of wheat through Uttar
Pradesh, where we model only the essential features. A stock and flow diagram
describes the within district behavior and a fully connected graph describes the
transportation between districts. The final section, Section 4.3, presents the
results. Our model predicts the percent undernourished for the year 2019 using
input data from previous years.
29
Table 3. Spatial-level description of input data for our model of food insecurity
risks in Uttar Pradesh.
District State Regional
Purchasing power [32] Ration cards [33, 34] Ration cards [35]
Population [36] Annual wheat yield Income estimates [35]
Wheat storage [33, 34]
Average family size [33, 34]
Drive time distances
4.1 Ration Card Estimates at the District Level
The government of India issues ration cards to its citizens who are eligible
to purchase subsidized grain. There are two types of ration cards under the
NFSA: Antyodaya Anna Yojana (AAY) cards, which are intended for India’s
poorest citizens, and Priority Household cards, which are more common [37].
Each ration card type allows different amounts of grain to be purchased at the
subsidized rates. Specifically, AAY households can purchase 35 kg per month,
while members of Priority households may buy 5 kg per month per person. To
our knowledge, the AAY and Priority cardholder populations are not publicly
available at the district level, so we estimate them.
To make these population estimates, we assume that the ratio of the propor-
tion of AAY and Priority households within each district of Uttar Pradesh at
the time of the 2010-2011 Census is roughly the same as today. Then Figure 30
is obtained by the following steps:
1. Estimate the fraction of rural (respectively urban) AAY households at a
district level based on per-capita income.1
2. Use district level rural (respectively urban) population estimates to ap-
proximate the population of such AAY cardholders at a district level.2
3. Repeat the above steps for Priority cardholders.3
4. Fill in missing rural (respectively urban) Priority and AAY cardholder
population estimates at the district level by averaging the respective values
from the district’s neighbors.
5. Sum the estimated Priority and AAY cardholders for the rural (respec-
tively urban) regions. This gives an estimate for the total cardholders in
the rural and urban regions of each district.
1See Table A6 and A7 of [35].
2See [36].
3Note: at the time of the 2010-2011 Census, the landmark National Food Security Act
(2013) had not yet been passed. So Tables A6 and A7 of [35] provide Below Poverty Line and
Above Poverty Line columns from the system at the type, the Targeted Public Distribution
System. We use Below Poverty Line numbers for our Priority estimates.
30
6. Scale the district level populations so that their aggregate matches the
state level estimates for rural regions provided by the Food Grain Bulletin
[33]. This yields an improved estimate for the rural and urban cardholders
at the district level.
7. Now sum the rural and urban AAY (resp. Priority) cardholder population
estimates, which produces an estimate of the AAY and Priority popula-
tions at the district level.
8. Finally, due to the imprecise nature of the estimates, in a small number
of districts, the ration card population estimates from the previous step
exceeded the actual population of those districts, which is impossible. We
distribute the excess ration cards from these districts uniformly among the
remaining districts of the state. This yields the district level estimate of
the AAY and Priority populations in Figure 30, which agrees with ground
truth when aggregated up to the state level.
Figure 30. According to India’s National Food Security Act [38], the poorest
(AAY households) receive 35 kg of grain each month, and the less poor (Priority
households) receive 5 kg per person per month.
4.2 Model of the PDS
We model the PDS of grain in Uttar Pradesh as a fully connected, bidirectional
graph with districts as nodes and transportation routes as edges. See Figure 31.
4.2.1 Nodes
All nodes of Figure 31 are represented by the same model of the PDS at the
district level, which Figure 32 describes. This model is implemented in Vensim,
31
Figure 31. Our model for the PDS of Uttar Pradesh is given by a fully connected,
bidirectional directed temporal graph, where nodes are districts and edges are
transportation routes between those districts. The bi-directional dotted edges
are a short-hand way to depict that every node is connected to every other node.
The same differential equations given by a stock and flow diagram determine the
trajectory of wheat within all nodes, and import requests and surplus storage
among the districts determine the flow of wheat between edges.
see Figure 36.
32
Produced
Wheat
Farm
Storage
Farm
Waste
Market
Purchased
Wheat
Imported
Procured
Wheat
Procured
Storage
Surplus
Wheat
Consumer
Purchased
Wheat
Consumed
Wheat
Figure 32. When districts produce wheat, wheat flows from the Produced Wheat
stock to the Farm Storage stock. The market purchases some portion of that
wheat, which it collects in the Market Purchased Grain stock. Excess wheat
flows to Farm Waste and is no longer used in the model. The remaining wheat
flows to the Procured Storage stock, which holds wheat purchased by the state or
national government that the district can use over the coming weeks. Any excess
wheat flows to the Surplus Wheat stock, where it is available for transportation
to other districts within the state. Ration card population estimates together
with state-wide wheat consumption estimates determine each district’s weekly
wheat requirements. Then available wheat in the Procured Storage stock flows
to the Consumer Purchased Wheat stock and ultimately arrives in the Con-
sumed Wheat stock. Districts that do not have enough wheat in the Procured
Storage stock for the coming weeks request it from districts that have a surplus.
Any requested wheat arrives in the Imported Procured Wheat stock, where it
subsequently flows to the Procured Storage stock to be available to that dis-
trict’s consumers. We provide the complete system dynamics diagram in the
appendix, which has stocks, flows and information arrows.
The stock and flow diagram of Figure 32 begins at the Produced Wheat
stock. Starting from an initial district level distribution of produced wheat in
Uttar Pradesh, we scale those values so that the aggregate sum of all produced
wheat will match our ground truth value of 32.6 million metric tonnes of wheat
from 2018.
From the Farm Storage stock, wheat flows to either Procured Storage, Farm
Waste or the Market Purchased Wheat stock. We use the following expression
to describe how much wheat enters the Market Purchased Wheat stock.
(Last Year’s Non-Wasted Wheat Harvest −Last Year’s Procured Wheat) (1)
×MSP
Last Year’s MSP ×Last Year’s Market Price
Market Price .(2)
33
Observe that (1) is the amount of wheat that the market purchased last year.
Then this year’s estimate of market purchased wheat is positively correlated
with Equation (2). Notice that if MSP prices increase more than the market
price year-over-year, i.e.,
(2) >1,
then the model predicts less wheat will enter the Market Procured Wheat stock
this year, and therefore more will enter the Procured Storage stock. This agrees
with intuition, because farmers would be incentivized to sell more wheat to
state and national governments. The reverse occurs if the market price of wheat
increases more than the MSP.
From the Procured Storage stock, wheat flows to the Consumed Wheat stock
or the Surplus Storage stock depending on whether the district has enough wheat
for the coming weeks. The rate at which each district consumes wheat does not
seem to be publicly available, so we estimate it using our district level ration
card population estimates obtained in Section 4.1. We then scale these district
level estimates so that their aggregate matches the rate that wheat is depleted
from the Procured Storage levels at the state-level, for which we have ground
truth [33, 34]. This determines the rate that each district consumes wheat in
one week.
The model transports wheat from a district with positive Surplus Storage to
a district that requests it. Each district tries to maintain a four week supply of
wheat in their Procured Storage, so those without this reserve will request more
wheat. Districts receive grain through the Imported Procured Wheat stock.
4.2.2 Edges
Wheat transportation data between districts in Uttar Pradesh also do not seem
to be publicly available, so we assume that any district can transfer wheat to
any other district. See Figure 31. We also assume that districts transport wheat
to closer districts before farther districts, where distance was measured in terms
of a drive time estimate between the largest population center of each district.
4.3 Results
To model food insecurity risk, we first estimate typical undernourishment rates
among the districts of Uttar Pradesh. Our estimates come from two sources.
The first source is Table 2 of [39], which is a 2009 report that estimates the
percent undernourished in 17 states in India. The percent undernourished wasas
defined by the 2008 Global Hunger Index as consuming less than 1,632 kcal per
day.
The second source is the ratio of the AAY population to the Priority pop-
ulation among these states. Figure 33a shows these quantities are correlated,
which is intuitive, because a greater proportion of AAY residents in a population
should mean that a greater proportion of those residents need food assistance.
We assume that this relationship, given by the slope of the line in Figure 33a,
34
(a) (b)
Figure 33. There is ground truth of the percent of citizens who are undernour-
ished at the state level, but not at the district level. We need this information at
the district level for our model, so we estimate it. Figure 33a is a scatter plot of
the relationship between a state’s percent undernourished and its ratio of AAY
to Priority populations. The correlation of these two variables is strongly sta-
tistically significant. The line in Figure 33a is the best fit line by least squares
linear regression, which has a slope of 83.67 and a p-value of 3.67e−149. Fig-
ure 33b is the estimate of each district’s percent undernourished that results
from computing the ratio of the estimated AAY and Priority populations at
the district level (see Figure 30) and then using the linear regression line from
Figure 33a.
also holds for the districts of Uttar Pradesh. An estimate of the percent under-
nourished in Uttar Pradesh can then be derived using our district level estimates
of the AAY and Priority populations. See Figure 33b.
Because our estimates are based on incomplete data, our model does not
predict the exact percent of undernourished, but rather it predicts trends in
undernourishment. Figure 34a is the model’s prediction under normal circum-
stances. Figure 34b is the model’s prediction under a flooding event in Septem-
ber. In this scenario, there is a temporary spike in undernourishment in the
affected districts. The model predicts that wheat from neighboring districts
will re-establish normal food insecurity levels for those impacted by the flood.
The only ground truth input to the model that is not temporally sparse is
the amount of wheat in storage per month at the state level. Figure 35 compares
the ground truth wheat in storage at the state level against the aggregate over
all districts of the model’s predicted wheat in storage. The two curves should
trend together. Figure 35a calibrates the model by using 2019 inputs to predict
wheat storage in 2019. Overall, the model fits the ground truth well, but it
predicts too much grain enters the PDS after the spring harvest. This may be
improved with a more accurate model of the market dynamics that determine
whether wheat enters into the PDS or the public market (see Equation (2)).
35
(a) (b)
Figure 34. The 75 curves represent the predicted percent undernourished for
the 75 districts in Uttar Pradesh in 2019. Figure 34a is the predicted under-
nourishment for each district under normal conditions. Figure 34b includes a
September flooding event in northeast Uttar Pradesh, where 75% of the stored
wheat in 21 districts is destroyed. The model predicts a temporary spike in food
insecurity for those districts which is soon restored.
Figure 35b describes a realistic scenario where only data from previous years is
available. The model again predicts that too much wheat enters the PDS, but
this time it also predicts that wheat leaves the system too quickly. Regarding
the latter property, the model uses ground truth data on the rate the wheat
left the system in 2018 as the rate in 2019, which might be improved by instead
averaging rates over several previous years.
36
(a) (b)
Figure 35. These plots show the ground truth wheat storage per month in
Uttar Pradesh in 2019 as well as the model’s prediction after aggregating from
the district level up to the state level. Figure 35a uses 2019 data to predict the
rate that wheat leaves the system in 2019. Figure 35b uses 2018 data for 2019
predictions.
5 Conclusion
The global challenge of food insecurity, exacerbated by conflicts such as the war
in Ukraine and by climate change-induced events like heatwaves and droughts,
underscores the urgent need for innovative solutions to ensure food security
for all. Focusing our research on the wheat breadbasket of northern India, a
critical region responsible for sustaining not only India’s vast population but also
serving as a significant source of grain to the rest of the world, we have outlined
a comprehensive framework to address the complexities of crop production,
distribution, and resilience in the face of evolving environmental and socio-
economic factors.
Through the integration of satellite remote sensing, deep learning classifica-
tion, physics-based crop yield simulations, and system dynamics modeling, our
research offers a multifaceted approach to understanding and improving the dy-
namics of food production and distribution systems. By developing predictive
models for crop production under diverse climate scenarios and simulating the
distribution of grain to food-insecure populations, we aim to provide actionable
insights that can inform policy decisions and interventions aimed at enhancing
the resilience of food systems.
While our focus has been on the wheat production landscape of northern
India, we acknowledge the challenges posed by the lack of ground truth data
for validation purposes. Thus, we have leveraged curated datasets from regions
like France to validate our algorithms, while tailoring our distribution and mar-
ket dynamics models to the unique characteristics of the Indian economy and
governance structure.
37
In conclusion, this research represents a significant step towards harnessing
technology and data-driven approaches to address the complex and intercon-
nected challenges of food security. By fostering collaboration between stake-
holders, policymakers, and researchers, we can work towards building more
resilient and sustainable food systems that ensure equitable access to nutritious
food for all, even in the face of global disruptions.
6 Acknowledgments
NASA POWER data were obtained from the National Aeronautics and Space
Administration (NASA) Langley Research Center (LaRC) Prediction of World-
wide Energy Resource (POWER) Project funded through the NASA Earth
Science/Applied Science Program.
The authors would like to thank the following members of our team who con-
tributed to this research: Monica Barbu-McInnis, Anuraag Kaashyap, Heather
Phelps, Dan Mauer, Anneliese Braunegg, Meryl Flaherty, and Mark Zimmer-
mann. This work was funded by MITRE’s internal research and development
program.
7 Appendix
This is the detailed stock and flow diagram for each node of our model for the
PDS of Uttar Pradesh.
38
Grain Yield Procured Storage
Time Scale
Procurement Delay
Consumer Purchased
Grain
<Time Scale>
Consumer Delivery
Delay
Consumer
Delivery Rate
Food Security Metric
Imported Procured
Grain
Imported Procured
Storage Rate
Surplus Grain
Surplus Grain
Storage Rate
Initial Grain Yield
Initial Procured Storage
Initial Farm Storage
Initial Surplus Grain
Initial Consumer
Purchased Grain
Initial Imported
Procured Grain
Consumed Food Delay
<Time Scale>
food insecurity for
vulnerable
Consumed Grain
Consumed Grain Rate
Initial Consumed Grain
<Time Scale>
<Procured Storage>
Procured Storage
Request
Source Delivery Factor
Extra Weeks Supply
<Extra Weeks Supply>
<District Required
Grain>
<FINAL TIME>
<FINAL TIME>
<Available Procured
Storage>
Farm Waste
<Available Procured
Storage>
Farm Storage Capacity
Initial Farm Waste
Initial Market
Purchased Grain
Farm Storage
Market Purchased
Grain
Production Rate
Market Delivery Rate
Farm Waste Rate
Source Delivery Rate
<Market Delivery
Ratio>
<Production>
Consumer Delivery Delay
Correction Factor
Figure 36. This is an image of the main components of our stock and flow model
implemented in Vensim.
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