Long-term drought prediction using deep neural networks based on
  geospatial weather data
The problem of high-quality drought forecasting up to a year in advance is
critical for agriculture planning and insurance. Yet, it is still unsolved with
reasonable accuracy due to data complexity and aridity stochasticity. We tackle
drought data by introducing an end-to-end approach that adopts a
spatio-temporal neural network model with accessible open monthly climate data
as the input.
  Our systematic research employs diverse proposed models and five distinct
environmental regions as a testbed to evaluate the efficacy of the Palmer
Drought Severity Index (PDSI) prediction. Key aggregated findings are the
exceptional performance of a Transformer model, EarthFormer, in making accurate
short-term (up to six months) forecasts. At the same time, the Convolutional
LSTM excels in longer-term forecasting.
Alexander Marusov, Vsevolod Grabar, Yury Maximov, Nazar Sotiriadi, Alexander Bulkin, Alexey Zaytsev
# Long Term Drought Prediction using Deep Neural Networks based on Geospatial Weather Data

###### Abstract

The accurate prediction of drought probability in specific regions is crucial for informed decision-making in agricultural practices. In particular, for long-term decisions it is important to make predictions for one year ahead. However, forecasting this probability presents challenges due to the complex interplay of various factors within the region of interest and neighboring areas. In this study, we propose an end-to-end solution based on various spatio-temporal neural networks to address this issue. Considered models focus on predicting the drought intensity based on Palmer Drought Severity Index (PDSI) for subregions of interest, leveraging intrinsic factors and insights from climate models to enhance drought predictions.

Comparative evaluations demonstrate the superior accuracy of Convolutional LSTM and Transformer models compared to baseline Gradient Boosting and Logistic Regression solutions. The two former models achieved impressive \(ROC\ AUC\) scores from 0.90 to 0.70 for forecast horizons from 1 to 6 months, outperforming baseline models. The transformer showed superiority for shorter horizons, while ConvLSTM took the lead for longer horizons. Thus, we recommend selecting the model in this way for long-term drought forecasting.

To ensure the broad applicability of considered models, we conduct extensive validation across regions worldwide, considering different environmental conditions. Moreover, we also run several ablation and sensitivity studies to challenge our findings and provide additional information on an appropriate way to solve the problem at hand.
keywords: weather, climate, drought forecasting, deep learning, long-term forecasting +
Footnote †: journal: Journal of Forecasting and Forecasting

## 1 Introduction

Drought forecasting is one of the crucial problems nowadays [1]. Indeed, monitoring and forecasting droughts hold significant importance due to their high occurrence across diverse terrains [2]. These natural climate events are costly and have far-reaching impacts on populations and various economic sectors [3]. Additionally, it is worth noting that global climate change will likely increase the probability of droughts [4]. So, drought forecasting is an essential but complicated task since the drought's beginning, ending, and duration are often hard to predict [5].

A quantitative measure of the drought is needed to solve the task described above. However, it is well-known that drought depends on many other climatic factors such as temperature and precipitation [6]. Hence, the drought measure (indices) can be calculated in many ways. Ones of the most fundamental and mostly known indices [7] are the Standardized Precipitation Index (SPI) [8] and Palmer Drought Severity Index (PDSI) [9]. In our studies, we use monthly PDSI for several reasons. First of all, our forecasting horizon is quite long - 12 months. According to recent work [10], PDSI is a good choice for long-term forecasting. Also, PDSI has a long recording history and allows us to consider the effect of global warming, which is quite a significant problem in our days [11].

More and more machine learning algorithms are involved in solving drought forecasting tasks. Regarding classic approaches, in [5] prominent stochastic models, AutoRegressive Integrated Moving Average (ARIMA) and multiplicative Seasonal AutoRegressive Integrated Moving Average (SARIMA), were exploited to predict drought via SPI index. Multivariate regression having a history of PDSI and some other global climate indexes on input was used to predict the PDSI index in South-Central Oklahoma [10]. Gradient boosting algorithm shown effectiveness for geospatial data [12; 13] and can handle imbalanced problems [14] encountered in drought prediction. Besides, this algorithm has proved its power in drought classification in Turkish regions [15]. Authors [16] used a logistic regression model for binary drought classification task via SPI index.

Moving on to deep learning methods, the authors in [17] proposed to use a recursive multistep neural network and direct multistep neural network for
drought forecasting via the SPI index. One of the most prominent approaches for time series data is Recurrent Neural Network (RNN) [18]. It is known that RNNs are often better than classical approaches [19]. Indeed, research [20] shows that Long Short-Term Memory (LSTM) [21] outperforms ARIMA for long-term forecasting of SPI index, but in short-term prediction, ARIMA has quite well results. To exploit the advantages of ARIMA and LSTM, authors of [22] proposed to use a hybrid ARIMA-LSTM model. The approaches described above used only historical (temporal) information about the data. Nevertheless, besides temporal information, the data has spatial dependencies. One of the most famous methods to account for both temporal and spatial information is ConvLSTM [23]. This method applies to many tasks, such as earthquake prediction [24]. Authors of [7] used ConvLSTM for short-term drought forecasting (8 days) of satellite-based drought indices - Scaled Drought Condition Index (SDCI) and SPI. Another idea is to use Transformer architectures. Initially developed for Natural Language Processing (NLP) tasks [25] now these models are widely used in a wide variety of domains, e.g., processing video frames in Computer Vision (CV) [26]. Consequently, adopting attention-based architectures to spatio-temporal modeling is a natural idea. One of the most known and modern weather transformers are EarthFormer [27] and FourCastNet [28]. These models solve different regression tasks (e.g., precipitation nowcasting) and show superior performance for various spatio-temporal problems. We adopted these architectures to our task.

The applications of deep learning models in conjunction with geospatial data extend beyond drought forecasting and can be effectively employed in diverse weather scenarios. Unlike computationally intensive numerical weather prediction methods based on solving partial differential equations, recent research by [29] demonstrates the enhanced capabilities of transformer-based models in delivering accurate medium-range predictions for various upper-air and surface variables. Furthermore, [30] successfully combined multiple deep-learning models to rectify short-term wind predictions derived from conventional numerical algorithms. In the realm of meteorological forecasting complexity, [31] harnessed the power of Generative Adversarial Networks (GANs) and Variational Autoencoder GANs (VAE-GANs) to generate spatial forecasts of precipitation in the UK. Similarly, in the context of the contiguous United States, [32] showcased the superior performance of a 3D convolutional network in short-term precipitation predictions. The existing literature highlights the strengths of deep learning models for generating short-term and
medium-term forecasts, spanning from durations of several hours to several days or even weeks. This diverse range of applications underscores the adaptability and potential of deep learning in enhancing meteorological prediction methodologies.

Besides weather forecasting problems, deep learning models for geospatial data have found many applications. To begin with, this type of data could be transformed into images and then used to forecast traffic with CNNs, as in [33]. Naturally, one would exploit spatial dependencies to predict epidemic propagation, as in the case of the Madrid region and COVID-19 in the paper [34]. More recently, [35] reviewed various machine learning methods for forecasting dengue risk, including CNNs and RNNs. Next, in the paper by [36], geospatial LSTMs were exploited to predict invasive species outbreaks. Finally, various convolutional and recurrent neural network architectures were successfully exploited in crop yield forecasts, thus immediately providing economic value for the agricultural sector.

Our paper considers different classic (Gradient boosting, logistic regression) and deep-learning (ConvLSTM, EarthFormer, and FourCastNet) methods for long-term drought forecasting using PDSI values. The main contribution of our research are:

1. Deep learning models solve the problem of medium (up to 12 months) drought forecasting. We formulate the problem as the prediction of the probability of a drought.
2. _Medium-term_ forecasting (up to 6 months ahead) is better to provide via **EarthFormer** meanwhile _Long-term_ forecasting is quite suitable for **ConvLSTM**. So, we recommend to use them accordingly.
3. Surprisingly, we observed pretty good performance of Logistic regression and Gradient Boosting models, especially in _Short-term_ forecasting, if correct features are used.

Detailed explanations and intuition on achieved results are in 4.1 section. The list of key novelties of our work is the following:

1. We adopted and explored traditional spatio-temporal methods (ConvLSTM, gradient boosting, logistic regression) as modern approaches (EarthFormer, FourCastNet). According to our knowledge, we are the first to use these models for long-term forecasting of PDSI values.
2. Unlike many previous works, which tried to predict PDSI value directly (regression task), we treated the drought forecasting task as a binary
classification task. We chose \(-2\) as threshold according to [10]. All PDSI values below \(-2\) are interpreted as a drought. So, now a model report a probability of a drought, making it more suitable for estimation of financial risk for particular
3. We provided extensive experiments using freely accessible data from diverse regions and continents.

## 2 Data

We have used publicly available geospatial data from Google Earth Engine [37]. Specifically, for obtaining the PDSI data, we employed the Terra-Climate Monthly dataset [38]. Our PDSI data encompasses a comprehensive range of climatic values spanning from 1958 to 2022, covering the entirety of Earth. To test the consistency of considered models, we look at regions across continents and various climate zones - from the state of Missouri and Eastern Europe to India. The considered regions are depicted in Figure 1. Their characteristics are given in Table 1.

The input data is downloaded as a tif file and later restructured as a 3D tensor, with one dimension representing the time scale (monthly intervals). In contrast, the other two dimensions correspond to spatial coordinates (x and y) of the grid. The resolution of the regional dataset varies, where grid

Figure 1: Regions chosen for PDSI forecast
dimensions range from 30 by 60 up to 128 by 192 (spatial resolution of a single cell of TerraClimate data is roughly 5 km), accommodating different levels of granularity and spatial detail.

## 3 Methods

We compare deep learning approaches, including Convolutional LSTM and novel transformer models, such as FourCastNet from Nvidia and Earth-Former from Amazon, with classic methods, including baseline model, gradient boosting, and logistic regression.

### Baseline

As a global baseline and a coherence check, we took the most prevalent class from train data and compared it with actual targets from the test subset. We also checked a rolling baseline - i.e., the most frequent class from recent history (from 6 to 24 months), but the results were almost indistinguishable from the global baseline, so we kept them out of our tables and graphs.

### Basic methods: Logistic regression and Gradient boosting

Both logistic regression and gradient boosting cannot work with raw data itself as it is. Hence, we created a data module that treated each grid cell as an individual value and transformed our task into a typical time series forecasting problem. To benefit from spatial correlations, we incorporate values from neighboring cells. For example, if we consider a 3x3 neighborhood, this includes eight additional time series. It is important to note that for "edge" cells, some of the neighboring cells may contain all zeros due to data limitations.

\begin{table}
\begin{tabular}{l c c c c} \hline Region & Span, & \% of normal & \% of drought & Spatial \\  & months & PDSI \(\geq-2\) & PDSI \(\leq-2\) & dimensions, km \\ \hline Missouri, USA & 754 & 74.91 & 25.09 & 416x544 \\ Madhya Pradesh, India & 754 & 70.66 & 29.34 & 512x768 \\ Goias, Brazil & 754 & 68.97 & 31.03 & 640x640 \\ Northern Kazakhstan & 742 & 68.70 & 31.30 & 256x480 \\ Eastern Europe & 742 & 66.28 & 33.72 & 352x672 \\ \hline \end{tabular}
\end{table}
Table 1: Regions’ summary statistics
Logistic RegressionLogistic regression is usually the natural choice for tasks with linear dependence or as a baseline model. The novel research [39] shows that time series linear models are a good choice.

Gradient boostingWe adopted the gradient boosting of decision trees, implemented using the well-established library XGBoost [40]. XGBoost, renowned for its speed and efficiency across a wide range of predictive modeling tasks, has consistently been favored by data science competition winners. It operates as an ensemble of decision trees, with new trees aimed at rectifying errors made by existing trees in the model. Trees are successively added until no further improvements can be made.

### Transformer-based methods

FourCastNetFourCastNet (short for Fourier ForeCasting Neural Network) is a weather forecasting model developed by authors from Nvidia [28]. It constitutes part of their Modulus Sym deep learning framework for solving various applied physics tasks. It combines Adaptive Fourier Neural Operator (AFNO) from [41] with Vision Transformer, and the model is both computationally, reducing spatial mixing complexity to \(O(N\log N)\), and memory efficient, where \(N\) is the sequence length. In the original papers, authors produced high-resolution short-term forecasts of wind speed and precipitation. We modified the last layer of the model to switch it from regression to classification task and evaluate it for the long-term forecasting problem.

EarthFormerVanilla transformers have \(O(N^{2})\) complexity, and consequently, it is hard to apply them to weather spatio-temporal data because of their large dimensionality. Authors [27] propose to use the "divide and conquer" method: they divide original data into non-intersecting parts (called cuboids) and use a self-attention mechanism on each cuboid separately in parallel. Such an approach allows significantly reduced complexity. The authors introduced EarthFormer for regression tasks, so we adopted it for a classification problem.

### ConvLSTM

This model draws inspiration from the work presented in the paper by Kail et al. (2021) [24], and it represents a modified version of the Convolutional LSTM architecture proposed by Shi et al. (2015) [23]. To capture temporal dependencies, we adopt Recurrent Neural Networks (RNNs).
Specifically, we employ Long Short-Term Memory (LSTM), a type of RNN that utilizes an additional state cell to facilitate long-term memory retention. We extend the traditional one-dimensional hidden states of LSTM to two-dimensional feature maps, enabling grid-to-grid transformations, which are crucial for our task. We process grids of PDSI values with various dimensions, ranging from 9x16 to 40x200.

To exploit spatial dependencies among drought severity values, we incorporate Convolutional Neural Networks (CNNs), well-suited for image and two-dimensional signal processing, including geospatial data. This approach combines the strengths of both RNN and CNN architectures by passing information through the RNN component as a feature map obtained using CNN operations. This integration allows us to capture and utilize temporal and spatial information within the following architecture.

Details of architectureConvolutional LSTM follows the pipeline:

1. We represent data as a sequence of grids: for each cell, we specify a value of PDSI for a particular month; the input grid at each time moment has dimension \(grid_{h}\times grid_{w}\) (varying from 50x50 to 200x200 for different regions of interest).
2. We pass the input grid through a convolutional network to create an embedding of grid dimensionality size with 16 channels. As an output of LSTM at each time moment, we have a hidden representation (short-term memory) of size \(h\times grid_{h}\times grid_{w}\), cell (long-term memory) representation of a similar size, and the output of size \(h\times grid_{h}\times grid_{w}\).
3. We transform the output to the size \(1\times grid_{h}\times grid_{w}\) using convolution \(1\times 1\) to receive probabilities of the drought for each cell as a final prediction (or to \(k\times grid_{h}\times grid_{w}\), where \(k>2\) is a number of classes of drought conditions that we are trying to predict). As an additional hyperparameter, we vary the forecasting horizon - i.e., we can forecast PDSI for the next month or \(k\)-th month.

## 4 Results

Description of experimentFor a binary classification problem, we arbitrarily set a drought threshold as \(-2\), which can be justified by PDSI bins from Table 2 and later adjusted for further experiments. For each cell in a considered region, the problem to solve is a binary classification problem with
the true value is the indicator that PDSI exceeds \(-2\). By construction, the model outputs the probability of a serious drought from the model output.

For validation purposes, we have divided our dataset into the train (\(70\%\)) and test (\(30\%\)) subsets for all of the five world regions (Missouri, Northern Kazakhstan, Madhya Pradesh, Eastern Europe, and Goias). The model is trained via a train subset of the data, the quality metrics are calculated via an independent test subset. The validation is out-of-time: the test subset follows the training subset in time.

Evaluation procedureWe use \(ROC\,AUC\), \(PR\,AUC\) and \(F1\) score to evaluate the model. During validation for early stopping and hyperparameter optimization, we chose \(ROC\,AUC\) score. All these scores are the medians - i.e., concatenating spatial prediction, we receive a temporal vector at every cell of spatial prediction. Next, we receive a single score for each cell, so we end up with a grid full of metrics, and finally, we compute a median. Higher values of all scores correspond to better models. \(ROC\,AUC\) scores has the perfect value being \(1\) and the value for a random prediction being \(0.5\).

Compared methodsFor our main experiments, we have exploited the performance of baseline (most frequent class from historical data), XGBoost (gradient boosting of random forests), LogReg (logistic regression), Convolutional LSTM (ConvLSTM), FourCastNet (transformer model from Nvidia) and Eartformer (transformer model from Amazon).

XGBoost and LogReg are two basic algorithms often used as strong baselines. The last three are variants of neural networks that showed strong performance in various geospatial problems. They represent two dominating architectures in geospatial modeling: ConvLSTM is a combination of recurrent and convolutional neural networks, FourCastNet and Eartformer

### Main results

Analysis of resultsOur findings indicate that ConvLSTM model outperformed the competitors, including the gradient boosting tree algorithm, achieving an impressive \(ROC\,AUC\) score of \(0.9\) for a one-month prediction. Notably, ConvLSTM exhibits a gradual decline in performance, reaching \(0.6-0.65\) for longer forecasting horizons (ranging from \(1\) month to \(12\) months). The standard gradient boosting approach initially yielded a similar \(ROCAUC\) score of \(0.9\) but sharply dropped to \(0.5\) as the forecasting horizon extended. EarthFormer outperforms other approaches for shorter horizons and falling
short of ConvLSTM at longer horizons of 9-12 months. These results are visually depicted in Figure 2. Additionally, we present the results for six-month prediction by regions in Figure 4, where the variation in scores for different geographies across models is visible.

_Why does transformer fail in long-term prediction?_ Our assumption of such behavior is the permutation-invariance of the attention mechanism. Despite positional encoding, transformers can't effectively extract temporal information from long input sequences. Since a long input sequence is essential for long-term forecasting, transformers don't show good results. Similar results for different time-series tasks were observed in [39]. ConvLSTM naturally extracts temporal information via LSTM.

_Why is logistic regression impressive?_ Since Gradient boosting results are almost identical to Logistic regression, we want to discuss only Logistic regression performance. First of all, the power of linear models was already shown in [39], where they beat modern Transformer architectures on almost all datasets. In our experiments, linear models are worse than other models on _Long-term_ prediction, but on _Short-term_ scale, we can see quite comparable results. We tried different history lengths, but our results show that it is enough to take only the nearest to the future horizons element. Our intuition is that the nearest future predictor variables are closely (particularly linearly) related to the history element. For example, PDSI in July is close to PDSI in August but far away from December. Hence, linear models are good at _Short-term_ predictions but poor at _Long-term_ forecasting.

\begin{table}
\begin{tabular}{l l} \hline PDSI value & Drought severity class \\ \hline
4.00 and above & Extreme wet spell \\
3.00-3.99 & Severe wet spell \\
2.00-2.99 & Moderate wet spell \\
1.00-1.99 & Mild wet spell \\ -1.00 to 0.99 & Normal \\ -1.00 to -1.99 & Mild dry spell \\ -2.00 to -2.99 & Moderate dry spell \\ -3.00 to -3.99 & Severe dry spell \\ -4.00 and below & Extreme dry spell \\ \hline \end{tabular}
\end{table}
Table 2: Classification of various PDSI values, source [42]
\begin{table}
\begin{tabular}{r r r r r r} \hline \hline Horizon, months & 1 & 3 & 6 & 9 & 12 \\ \hline \multicolumn{5}{l}{Median ROC AUC:} \\ \hline Baseline & 0.5 & 0.5 & 0.5 & 0.5 & 0.5 \\ LogReg & 0.886 & 0.774 & 0.640 & 0.546 & 0.518 \\ XGBoost & 0.878 & 0.754 & 0.628 & 0.568 & 0.542 \\ FourCastNet & 0.881 & 0.711 & 0.624 & 0.561 & 0.536 \\ EarthFormer & **0.948** & **0.840** & 0.690 & 0.556 & 0.480 \\ ConvLSTM & 0.887 & 0.802 & **0.693** & **0.650** & **0.617** \\ \hline \multicolumn{5}{l}{Median PR AUC:} \\ \hline Baseline & 0.355 & 0.354 & 0.354 & 0.355 & 0.356 \\ LogReg & 0.766 & 0.598 & 0.470 & 0.394 & 0.360 \\ XGBoost & 0.752 & 0.574 & 0.44 & 0.39 & 0.372 \\ FourCastNet & 0.776 & 0.546 & 0.455 & 0.402 & 0.382 \\ EarthFormer & **0.880** & 0.650 & 0.514 & 0.438 & 0.362 \\ ConvLSTM & 0.772 & **0.689** & **0.565** & **0.505** & **0.452** \\ \hline \multicolumn{5}{l}{Median F1:} \\ \hline Baseline & 0.645 & 0.646 & **0.646** & **0.645** & **0.644** \\ LogReg & **0.846** & **0.698** & 0.480 & 0.226 & 0.094 \\ XGBoost & 0.836 & 0.674 & 0.480 & 0.366 & 0.292 \\ FourCastNet & 0.831 & 0.603 & 0.460 & 0.366 & 0.314 \\ EarthFormer & 0.816 & 0.604 & 0.448 & 0.226 & 0.178 \\ ConvLSTM & 0.784 & **0.698** & 0.600 & 0.558 & 0.543 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Median Metrics vs Forecast Horizon, binary classification; best values are in bold, second best are underlined

Figure 2: Median metrics: ROC-AUC, PR-AUC, F1 from left to right for different forecast horizons averaged over five considered regions, binary drought classification
### Predictions and errors for a particular region

To assess the performance of the Convolutional LSTM algorithm (which proved to be the most stable and promising for drought forecasting), we focused on the region of Missouri state, where we will run several ablation studies. As an illustration, the spatial distribution of \(ROCAUC\) scores is depicted in Figure 3. Notably, we observed a non-uniform distribution of \(ROCAUC\) values across the cells within the region. The standard deviation of the scores is substantial, and individual values range from those close to random predictors (\(ROC\ AUC=0.6\)) to near-perfect scores approaching 1.0. This variability highlights the diverse predictive capabilities of our algorithm across different spatial locations within Missouri.

\begin{table}
\begin{tabular}{r c c c c c} \hline \hline Region & Northern & Eastern & Madhya & Goias & Missouri \\  & Kazakhstan & Europe & Pradesh & & \\ \hline median ROC AUC: & & & & & \\ \hline Baseline & 0.5 & 0.5 & 0.5 & 0.5 & 0.5 \\ LogReg & 0.60 & 0.63 & 0.61 & 0.61 & **0.75** \\ XGBoost & 0.59 & 0.64 & 0.59 & 0.61 & 0.71 \\ FourCastNet & 0.60 & 0.55 & 0.65 & 0.61 & 0.69 \\ EarthFormer & 0.54 & **0.69** & **0.84** & **0.65** & 0.73 \\ ConvLSTM & **0.71** & 0.68 & 0.71 & 0.60 & **0.75** \\ \hline median PR AUC: & & & & & \\ \hline Baseline & 0.37 & 0.43 & 0.35 & 0.39 & 0.23 \\ LogReg & 0.46 & **0.67** & 0.24 & **0.55** & 0.43 \\ XGBoost & 0.46 & 0.63 & 0.20 & 0.54 & 0.37 \\ FourCastNet & 0.46 & 0.55 & 0.36 & 0.54 & 0.37 \\ EarthFormer & 0.47 & 0.22 & **0.77** & 0.52 & **0.59** \\ ConvLSTM & **0.55** & 0.65 & 0.57 & 0.54 & 0.50 \\ \hline median F1: & & & & & \\ \hline Baseline & 0.63 & 0.57 & 0.65 & **0.61** & **0.77** \\ LogReg & 0.42 & 0.62 & 0.35 & 0.41 & 0.60 \\ XGBoost & 0.45 & 0.58 & 0.30 & 0.54 & 0.53 \\ FourCastNet & 0.42 & 0.39 & 0.46 & 0.51 & 0.52 \\ EarthFormer & 0.03 & 0.18 & **0.80** & 0.55 & 0.65 \\ ConvLSTM & **0.65** & **0.64** & 0.64 & 0.52 & 0.56 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Median Metrics vs Region, binary classification, 6 months horizon; best values are in bold, second best are underlined
#### 4.2.1 Performance Evaluation for Cropped Region

Description of experimentAs is typical with ROC AUC maps, the worst predictions are found on the edges and some corners. We have observed that this behavior is consistent regardless of the region being studied. Consequently, making predictions for a larger region and cropping the desired region of interest may be advantageous. We have conducted a study to test this hypothesis for the attached map, and the results are shown in Table 5.

Analysis of resultsBased on the findings of this specific experiment, we deduce that cropping approximately 40-50% of the initially selected region maximizes our score. In other words, choosing a region that is initially 1.6-2 times larger than our target region is advisable. However, the precise amount of zoom required for optimal results has to be determined through further experiments.

Next, we conducted several similar experiments to investigate how the model

Figure 3: Spatial distribution of ROC AUC for 6 month forecast, Missouri, ConvLSTM

\begin{table}
\begin{tabular}{l c c c c c} \hline \hline Percent of map cropped & 0 & 10 & 20 & 30 & 40 \\ median ROC AUC & 0.7525 & 0.7592 & 0.7665 & 0.7749 & 0.7834 \\ \hline Percent of map cropped & 50 & 60 & 70 & 80 & 90 \\ median ROC AUC & 0.7886 & 0.7899 & 0.7880 & 0.7838 & 0.7825 \\ \hline \hline \end{tabular}
\end{table}
Table 5: ROC AUC score vs crop percentage, 6 month forecast, ConvLSTM model for Missouri
predictions change with the decrease in the total squared area. For this, we took the same geographic region, Missouri, and examined various combinations of history length and forecast horizon. We trained a new checkpoint for each variant of history length, forecast horizon, and region area (varying from entire state to about a quarter of it).

The results are summarized in Table 6, and in more detail, they are presented in Tables 8, 9, 10, 11. We observed that predicting at a smaller area with pre-trained model from a larger area generally works better. However, the degree of improvement is marginal, usually not exceeding 0.5-1%. Figure 4 presents the evolution of spatial maps.
convex [44], and Gradient boosting is an ensemble per se [15]. Obtained ensembles can also be used to access the uncertainty of predictions by machine learning models improving the decision-making process [45].

## 5 Conclusion

Droughts have emerged as severe natural disasters that significantly impact the economy, influencing sectors such as agriculture and the well-being of populations. The frequency and intensity of droughts have been amplified worldwide due to climate change, as exemplified by the summer of 2022 in the Northern Hemisphere.

Accurate prediction of future drought occurrences and adequate preparation for their consequences is crucial in mitigating the adverse impacts of climate change. Our research study has shown substantial improvements in forecasting capabilities for PDSI indicator, including the Palmer Drought Severity Index (PDSI), by combining convolutional neural networks and recurrent neural networks. This Convolutional LSTM model surpasses the performance of standard algorithms, such as gradient boosting, and even more advanced transformer models for long-term predictions.

By enhancing our understanding and predictive abilities related to droughts, we can proactively address the challenges of climate change. We hope that the insights gained from this study will contribute to better preparedness and mitigation strategies to alleviate the adverse effects of droughts on the economy and society.
