Published as a conference paper at ICLR 2022

A WEAKLY SUPERVISED FRAMEWORK FOR
HIGH - RESOLUTION CROP YIELD FORECASTS
Dilli R. Paudel, Diego M. Gonzalez, Allard de Wit, Hendrik Boogaard & Ioannis N. Athanasiadis
Wageningen University and Research
PO Box 47, 6700 AA Wageningen, The Netherlands.
{dilli.paudel,diego.marcos,allard.dewit,
hendrik.boogaard,ioannis.athanasiadis}@wur.nl

A BSTRACT
Predictor inputs and label data for crop yield forecasting are not always available
at the same spatial resolution. We propose a deep learning framework that uses
high resolution inputs and low resolution labels to produce crop yield forecasts
for both spatial levels. The forecasting model is calibrated by weak supervisionfrom low resolution crop area and yield statistics. We evaluated the framework
by disaggregating regional yields in Europe from parent statistical regions to subregions for five countries (Germany, Spain, France, Hungary, Italy) and two crops(soft wheat and potatoes). Performance of weakly supervised models was compared with linear trend models and Gradient-Boosted Decision Trees (GBDT).
Higher resolution crop yield forecasts are useful to policymakers and other stakeholders. Weakly supervised deep learning methods provide a way to produce suchforecasts even in the absence of high resolution yield data.

1

I NTRODUCTION

Predictor inputs and label data for crop yield forecasting are often not available at the same spatial
resolution. Label data, such as yield statistics, are published at regional and national level. Weather
inputs are available at grid-level (EC-JRC, 2022; Thornton et al., 2020) and soil and remote sensing data at sub-kilometer resolutions (ESDAC, 2021; Poggio et al., 2021; Copernicus-ESA, 2022).
Common statistical and machine learning methods require both inputs and labels at the same spatial
level. Therefore, predictor inputs are usually aggregated to the level of yield data. Deep learning
methods can handle input and label data at two spatial levels, limiting the spatial aggregation required for input data. Neural network architectures can be trained using high resolution inputs andlow resolution yield data to produce crop yield forecasts for both spatial levels.
Many studies have used deep learning for crop yield forecasting (Fan et al., 2021; Shahhosseini
et al., 2021; Wolanin et al., 2020; Khaki et al., 2020), but they do not disaggregate yields to highresolutions. Other methods of disaggregating crop yields exist, for example, area-to-point kriging(Brus et al., 2018; Steinbuch et al., 2020) and spatial allocation based on cross-entropy method (Youet al., 2014) or remote sensing indicators (Shirsath et al., 2020). We draw inspiration from Jacobs
et al. (2018), who trained a convolutional neural network and an aggregation layer to predict pixellevel population density from high resolution satellite images and low resolution density statistics.
To our knowledge, weakly supervised methods have not been used to disaggregate crop yields tohigh resolutions.
We propose a weakly supervised deep learning framework that uses high resolution inputs and low
resolution labels to produce crop yield forecasts for both spatial resolutions. Predictor inputs comefrom NUTS3 regional level and yield and crop area statistics from NUTS2 level, with NUTS2 and
NUTS3 regions representing the low and high spatial resolutions. NUTS (Nomenclature of Territorial Units for Statistics) is a hierarchical system of dividing the territory of the European Union
for statistics and policy (Eurostat, 2016). Our approach is weakly supervised because models to
produce NUTS3 forecasts are trained using low resolution NUTS2 labels. Our objective is to buildand evaluate crop yield forecasting models that can produce high resolution forecasts even whenhigh resolution yield data are not available. This objective can be viewed from two perspectives.
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Published as a conference paper at ICLR 2022

First, we assess the performance of weak supervised models in disaggregating crop yields from low
to high resolution. Second, we evaluate the quality of low resolution yield forecasts produced using
high resolution inputs. Our analysis includes two crops (soft wheat and potatoes) and five countries:
Germany (DE), Spain (ES), France (FR), Hungary (HU) and Italy (IT).
The rest of the paper is structured as follows: Section 2 describes data and methods; Section 3
presents the results; and Section 4 discusses our findings and outlines directions for future work.

2

M ETHODS

Our weakly supervised deep learning framework uses high resolution predictor inputs and low resolution labels to produce crop area and yield forecasts for both spatial resolutions. To evaluate theseyield forecasts, we compared performance with linear trend models and Gradient-Boosted Decision
Trees. To assess their usefulness to policymakers and other stakeholders, we analyzed the spatial
variability of high resolution forecasts.
2.1

DATA

Data sources used in this paper are summarized in Table A.1. Most of our data came from the MARS
Crop Yield Forecasting System of the European Commission’s Joint Research Centre (MARSWiki,2021) and covered two crops and five countries: soft wheat (DE, ES, FR, IT) and potatoes (DE, FR,
HU, IT). Data from all countries was combined to build one prediction model per crop. Seasonal data
included outputs of the WOFOST crop model (Van Diepen et al., 1989; Supit et al., 1994; De Wit
et al., 2019), weather variables and remote sensing indicators aggregated to NUTS3. The yield trend
was captured using yield values of five previous years at NUTS2. Static differences among regions
were captured by soil water holding capacity and agro-environmental features, such as elevation,slope, field sizes, irrigated area (Paudel et al., 2022). In addition, agro-environmental zones andcountries were added as categorical variables to account for other agro-climatic and administrative
differences. Reported yield and crop area statistics at NUTS2 served as labels. In most cases, we haddata from 1999 to 2018. The most recent 30% of the years were allocated to the test set. From theremaining 70% training years, 5 most recent years were used for a sliding-window 5-fold validation(Figure A.1).
2.2

T HE W EAKLY S UPERVISED F RAMEWORK

Figure 1: Weakly supervised framework to produce high resolution crop yield forecasts.
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Published as a conference paper at ICLR 2022

We selected two neural network architectures, namely long short-term memory (LSTM) networks
and 1-dimensional convolutional neural networks (1DCNN), that can learn from seasonal time series of predictors. Both LSTMs and 1DCNNs have been used in literature to learn features fromsequential data (You et al., 2017; Khaki et al., 2020). Seasonal data at NUTS level 3, including
crop model outputs, weather and remote sensing indicators, was processed by LSTM or 1DCNN.
Features from the LSTM or 1DCNN layers, together with static agro-environmental data and yieldtrend features (based on NUTS2 yields), were passed to an output layer (Figure 1). An aggregation
layer computed crop area weights and aggregated the forecasts to low resolution (NUTS2). The
framework was supervised with NUTS2 yields and crop areas. Data from all NUTS3 regions within
a NUTS2 region formed a batch to enable aggregation of NUTS3 forecasts.
The weakly supervised model (WS model) produced NUTS3 yield forecasts and crop area fractions.
We believe remote sensing inputs can predict crop area fractions (crop area/land area), but not theabsolute crop areas. Predicted crop area fractions were multiplied with land areas to produce NUTS3
crop areas, which were used to calculate crop area weights for the aggregation layer.

2.3

E VALUATION

Figure 2: Evaluation framework.

Forecasts from the WS model were evaluated at both spatial resolutions. The quality of disaggregated NUTS3 yields was assessed by comparing with two sets of models. The first set was anaive trend model that acted as our baseline for disaggregation. The naive trend model predicted
the NUTS2 yield trend as NUTS3 forecasts for all NUTS3 sub-regions. The second set included
the NUTS3 trend model and Gradient-Boosted Decision Trees (GBDT) model (Figure 2). Unlike
the naive trend and WS models, the NUTS3 trend and GBDT models had access to NUTS3 yielddata. The NUTS3 GBDT and WS models used the same predictor inputs, except yield trend features: GBDT had access to NUTS3 trend; WS only had NUTS2 trend. Forecasts were made 60 days
before harvest. At NUTS2, WS model forecasts were compared with the NUTS2 trend model and
NUTS2 GBDT model. All trend models were calibrated with yield values of five previous years.
Models were compared based on box plots of prediction residuals (i.e., predicted yield - reported
yield) and normalized root mean squared errors (NRMSE), normalized by average yield of the test
set. The significance of model performance was evaluated by running Wilcoxon signed-rank test on
the prediction residuals of different models.
In addition to error comparisons, we also analyzed the spatial variability of NUTS3 yield forecasts
from disaggregation models (naive trend and WS model). A significant part of yield variability is
explained using the yield trend attributed to factors such as technological improvements (see Lecerf
et al. (2019)). We expected the NUTS2 trend features to make the model more accurate, but suppress
spatial variability among NUTS3 regions. Therefore, we ran a version of the WS model without
NUTS2 trend to learn spatial differences. Spatial variability of NUTS3 yield forecasts was analyzed
for soft wheat (FR). We selected regions based on maximum acreage and years (2016 and 2017)
based on significant yield losses reported in the north of FR in 2016 (see Ben-Ari et al. (2018)).
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3

R ESULTS

In this section, we report results from the LSTM version of the WS model because of its superior
validation set performance over the 1DCNN one (Figure A.2).
3.1

E VALUATION OF HIGH RESOLUTION YIELD FORECASTS

The WS models were statistically similar to NUTS3 GBDT models (p-values: 0.67 for soft wheat
and 0.265 for potatoes) (Table A.2), and significantly better than the naive trend models (p-values
near zero). For soft wheat, the WS model was also better than the NUTS3 trend model (p-value nearzero). For soft wheat, interquartile range was smaller and per-country NRMSEs were mostly lower
compared to both trend models (Figure 3). Disaggregation worked less well for potatoes, but theperformance was still better than the naive trend model (Table A.2, Figure A.3).

Figure 3: Left: Boxplots of NUTS3 prediction residuals. Right: NRMSEs for soft wheat.
3.2

E VALUATION OF LOW RESOLUTION YIELD FORECASTS

The WS models produced NUTS2 forecasts that were similar compared to NUTS2 GBDT models(p-values: 0.083 for soft wheat and 0.455 for potatoes) (Table A.3), and better than the NUTS2 trendmodels (p-values: 0.00095 for soft wheat and 0.000002 for potatoes). Box plots and per-country
NRMSEs again showed that residuals and errors were smaller for soft wheat than for potatoes (Figure 4, A.3). The WS models had smaller median residuals compared to GBDT models for both
crops (Table A.3), indicating some value in using NUTS3 inputs to forecast at NUTS2.

Figure 4: Left: Boxplots of NUTS2 prediction residuals. Right: NRMSEs for soft wheat.
3.3

S PATIAL VARIABILITY OF HIGH RESOLUTION FORECASTS

As mentioned before, the north of France had significant yield losses for soft wheat in 2016. The
naive trend model predicted higher yields, with an average prediction residual of 2.865. The WS
model predicted slightly lower (average residual: 2.21) but still higher than the reported yields(Figure 5, top). In 2017, the naive trend model was heavily influenced by the 2016 yields (especiallyin the middle: FRI3, FRB0, FRC1), while the WS model predicted values similar to the reported
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yields (Figure 5, bottom). As expected, the WS model with trend did not capture yield variability
within NUTS2 regions. The WS No Trend model captured such differences better, but generally
underestimated the yields: the average prediction residual was -0.57 compared to -0.028 for the WS
model using trend. Combining information from both versions of the WS model provided moreaccurate estimates of yields as well as spatial differences among NUTS3 regions.

Figure 5: Spatial variability of soft wheat yields and forecasts. Top: FR 2016. Bottom: FR 2017

4

D ISCUSSION

Data on crop yield predictors will be increasingly available at higher resolutions. Yield data may
not be available due to many reasons, including privacy concerns. When there is an imbalance
between spatial resolutions of inputs and yields, weak supervised methods provide a solution. Our
results showed that weakly supervised models were able to produce reliable NUTS3 yield forecasts,
especially for soft wheat, without using NUTS3 yields. The no-trend version of the model also
captured some of NUTS3-level yield variability. Our approach will continue to work when yielddata is available at low resolution for some regions and at high resolution for others. Similarly, highresolution crop areas, when available, will further improve the quality of yield forecasts.
In this paper, we have scratched the surface of high resolution crop yield forecasting without strongsupervision. We see three areas that need further research to gauge the ability of weak supervision to
produce reliable forecasts. First, the scale differences that can be handled by weak supervision needs
investigation. For example, weak supervision from NUTS3 yields may produce good quality forecasts for 25km grids, but not 1km grids. Second, predictor inputs must be suitable to capture yield
variability at selected resolutions. Weather variables may influence NUTS2 and NUTS3 yields, but
become less relevant at farm level. Third, we experimented with standard neural network architectures. Future work could investigate other architectures that are more suitable for weak supervision.
Data size and quality will always play a role due to the data-driven nature of neural networks.
High resolution crop yield forecasts provide useful information to policymakers and other stakeholders for local analysis and monitoring. We have shown that weakly supervised methods can produce
such forecasts in the absence of high resolution labels.

5

ACKNOWLEDGMENTS

This work was partially supported by the European Union’s Horizon 2020 research and innovation
programme under grant agreement No. 825355 (CYBELE). We would like to thank S. Niemeyerfrom the European Commission’s Joint Research Centre (JRC) for permission to use MARS Crop
Yield Forecasting System data. We also would like to thank M. van der Velde, L. Nisini and I.
Cerrani from JRC for sharing the Eurostat regional yield statistics and crop areas.
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A PPENDIX

A.1

DATA S OURCES

Most of our data comes from the MARS Crop Yield Forecasting System (MCYFS) of European
Commission’s Joint Research Centre (MARSWiki, 2021). Other sources are indicated in Table A.1.
Table A.1: Data sources summaryDATAWOFOSTcrop
model outputs

Meteo

Remote Sensing
Crop Areas
Irrigated area
Elevation, slope
Soil
Field Size
Yield

A.2

INDICATORS, SOURCES
Water-limited dry weight biomass (kg ha−1 ), Water-limited dryweight storage organs (kg ha−1 ), Water-limited leaf area divided bysurface area (m2 m−2 ), Development stage (0 − 200), root-zone soil
moisture as % of soil water holding capacity, sum of water limited
transpiration (cm). Source: MCYFS. See Lecerf et al. (2019).
Maximum, minimum, average daily air temperature (°C), sum of daily
precipitation (PREC) (mm), sum of daily evapotranspiration of shortvegetation (ET0) (Penman-Monteith, Allen et al. (1998)) (mm), climate water balance = (PREC - ET0). Source: MCYFS. See Lecerf
et al. (2019).
Fraction of Absorbed Photosynthetically Active Radiation(Smoothed) (FAPAR). Source: MCYFS. See Copernicus GLS(2020).
Absolute crop areas (ha). Fraction of parent regions’s crop area.
Source: Eurostat (Eurostat, 2021) and MCYFS (EC-JRC, 2022).
Irrigated total area and irrigated crop-specific area. Source: EC-JRC(2022).
Average and standard deviation. Source: USGS-EROS (2021).
SM WHC (water holding capacity). Source: MCYFS. See Lecerf
et al. (2019).
Average and standard deviation. Source: Lesiv et al. (2019).
Yield at NUTS3 level.
Source: FR-Agreste (2020); DERegionalStatistiks (2020); Eurostat (2021); EC-JRC (2022).

W EAKLY S UPERVISED M ODELThe weakly supervised model was supervised using NUTS2 crop areas and yields. The combined
loss was the sum of the two losses (crop area loss and yield loss) normalized by the training set average of the corresponding labels. The hyperparameters learning rate and L2-penalty lambda were
optimized using custom sliding validation (Figure A.1; Paudel et al. (2022)). After optimizing hyperparameters, the model was trained on the entire validation set (no 5-fold) with early stopping:training stopped after validation error increased for two successive epochs. The optimized hyperparameters and early stopping epochs were used to evaluate the model on the test set.
A.2.1

1DCNN A RCHITECTURE

CNN Layer1 : Conv1d(11, 16, kernel size=(3,), stride=(1,), padding=(1,))
CNN Layer 2: Conv1d(16, 32, kernel size=(3,), stride=(2,), padding=(1,))
CNN Layer 3: Conv1d(32, 8, kernel size=(3,), stride=(2,), padding=(1,))
Batch Normalization, ReLU Activation and Dropout(p=0.1) were added after each CNN layer.
Output Layer: Linear(in features=100, out features=2, bias=True)
A.2.2

LSTM A RCHITECTURE

LSTM Layer : LSTM(11, 64, batch first=True)
Output Layer : Linear(in features=100, out features=2, bias=True)
Both LSTM and 1DCNN were implemented using pytorch (https://pytorch.org/).
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A.3

GBDT M ODEL

Input data and training, validation and test splits were identical between the GBDT model and theweakly supervised model, except for trend features (NUTS3 vs NUTS2). The GBDT model usedin this paper has some differences compared to Paudel et al. (2022). First, a combined model wasbuilt for four countries. Second, agro-environmental zones and countries were added as categoricalfeatures.
The GBDT model is based on GradientBoostingRegressor() from scikit-learn (Pedregosa et al.,2011). Hyperparameters including GBDT parameters, feature selector and number of features optimized using BayesSearchCV from scikit-optimize package (Scikit-optimize Contributors, 2021).
Feature selectors included a Random Forests model (SelectFromModel) and Recursive Feature
Elimination using a Lasso Regression model.
A.4

T RAINING , VALIDATION AND TEST SPLITS

Figure A.1: Training, validation and test splits. Reproduced from Paudel et al. (2022)
A.5

S OFTWARE IMPLEMENTATION

Software implementation of the weakly supervised framework can be accessed here:
https://github.com/BigDataWUR/MLforCropYieldForecasting/tree/weaksup
A.6

VALIDATION SET RESULTS FOR A RCHITECTURE S ELECTION

The decision to use combined data from four countries was based on validation set performance ofstrongly supervised NUTS3 models for soft wheat. Since NRMSEs were similar for both cases, wechose to use combined data because the larger data size would limit overfitting issues. CV comparisons for weak supervision using 1DCNN and LSTM showed that LSTM had lower NRMSEs on
the validation set (Figure A.2).
A.7

S UPPLEMENTARY R ESULTS

Wilcoxon signed rank test was run using prediction residuals (predicted yield - reported yield).

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Figure A.2: Validation NRMSEs of weakly supervised NUTS3 and NUTS2 forecasts.

Table A.2: Wilcoxon-signed rank test (NUTS3)MODEL
WS LSTM
Naive Trend
NUTS3 GBDTNUTS3 Trend

P-VALUE
Soft wheat
–
0
0.67
0

MEDIAN-0.1440-0.1930.01

WS LSTM
Naive Trend
NUTS3 GBDTNUTS3 Trend

Potatoes–
0.000020.265
0.078560.447-0.0920.397
0.039

Table A.3: Wilcoxon-signed rank test (NUTS2)MODEL
WS LSTMNUTS2 GBDTNUTS2 Trend

P-VALUE
Soft wheat–
0.083460.00095

MEDIAN-0.089-0.0942-0.005WS LSTMNUTS2 GBDTNUTS2 Trend

Potatoes–
0.455
0.000002

0.494
0.664
-0.1

Figure A.3: Per-country NRMSEs for potatoes. Left: NUTS3. Right: NUTS2.

10