Potential of Deep Learning in drought assessment by extracting information from hydrometeorological precursors

This study explores the potential of the Deep Learning (DL) approach to develop a model for basin-scale drought assessment using information from a set of primary hydrometeorological precursors, namely air temperature, surface pressure, wind speed, relative humidity, evaporation, soil moisture and geopotential height. The novelty of the study lies in extracting the information from the hydrometeorological precursors through the efficacy of the DL algorithm, based on a one-dimensional convolutional neural network. Drought-prone regions, from where our study basins are selected, often suffer from the vagaries of rainfall that leads to drought-like situations. It is established that the proposed DL-based model is able to capture the underlying complex relationship between rainfall and the set of aforementioned hydrometeorological variables and, subsequently, shows its promise for the basin-scale meteorological drought assessment as revealed through different performance metrics and skill scores. The accuracy of simulating the correct drought category, among the seven categories, is also high (>70%). Moreover, in general, the skill of any climate model is much higher for the primary meteorological variables as compared with other secondary or tertiary variables/phenomena, like droughts. Thus, the novelty of the proposed DL-based model also lies in the improved assessment of ensuing basin-scale meteorological droughts using the projected meteorological precursors and may lead to new research directions.

However, the development of these models primarily requires multiple trials to determine weights and biases, run into restrictions while handling large data and consider the drought-causing factors to be limited. Moreover, these ML-based models suffer from overfitting in calibration, underfitting in validation and trapping at local minima, especially in the case of ANN and support vector machine (Khan et al. ). These lead to a pressing need for more advanced methods for the hydrometeorological analysis of complex processes like extreme events including droughts.
Although in some studies, ANN is used for complex timeseries modeling with a sufficient number of hidden layers and a specified number of units (Zhang et al. ), yet the complex hydrometeorological phenomena, such as droughts, summon more hidden layers leading to the problem of non-convex optimization. The issue can be dealt with Deep Learning (DL) algorithms with an unsupervised greedy layer-wise training for Deep Neural Networks (DNNs) (Hinton & Salakhutdinov ), which perform better than conventional ML approaches by avoiding getting stuck in the wrong local solutions (Lecun et al. ). The DL approach is able to extract the data features from raw data using multiple hierarchical layers (Khan & Maity ). The ability to learn from exposure to data without any human expertise enables it to effectively study the nonlinear, complex and hidden information involved in hydroclimatological processes and thus helps to develop the models at various spatiotemporal scales (Khan & Maity  The objective of the study is to develop a DL-based model for drought assessment utilizing a set of hydrometeorological precursors. We picked out two medium-sized, rainfed river basins that are located in the central belt of India and frequently stricken by droughts due to the vagaries of precipitation. Further details about the study basins are provided in the 'Study area and data' section. Following that, the 'Methodology' section provides details on the methodology including drought characterization, data preparation and the proposed DL approach. Results and related discussions are presented in the 'Results and discussion' section along with more specific details of the DL model. The performance of the DL-based model is also compared with another popular ML-based approach, i.e., SVR, to explore the additional benefits against an existing approach keeping all other conditions the same. Finally, the major findings and conclusions are drawn in the 'Conclusions' section.  As the rainfall in India is strongly seasonal due to its monsoon-dominated climatology, the SPAI is used as the drought characterization index. For a monthly scale

STUDY AREA AND DATA
where y i,j is the precipitation anomaly for the ith year and jth time step of the year, x i,j is the precipitation value for the ith year and jth time step of the year and x j is the long-term mean precipitation for the jth time step of the year. Next, a probability distribution (parametric or nonparametric) is fitted across the monthly anomaly series to obtain the probability quantiles. If a nonparametric distribution is considered, then the empirical Cumulative Distribution Function (CDF) may be obtained by using the Weibull plotting position formula as follows: where p is the cumulative probability, m is the rank of the dataset arranged in descending order and N is the sample size. Finally, the quantiles obtained in the previous step are transformed to standard normal variates (z-score), which give the SPAI. Thus, the SPAI is obtained as follows: where F À1 (p) represents the inverse of the standard normal distribution for a CDF value of p. Wet (W0)' conditions for À1.5 SPAI < À1 and 1 < SPAI 1.5, respectively. Likewise, for À2 SPAI < À1.5 and 1.5 < SPAI 2, it is categorized as 'Severe Drought (D1)' and 'Severely Wet (W1)' conditions, respectively. Finally, 'Extreme Drought (D2)' and 'Extremely Wet (W2)' conditions are denoted by SPAI < À2 and SPAI > 2, respectively.

Data preparation
Entire data preparation and handling are carried out in the scientific python development environment (Spyder) notebook. It starts with spatially averaging the gridded datasets across the basins following the area weightage method and converting to a monthly scale honoring their units (Table 1).
In the proposed DL model, the values of the seven hydro- In this study, two regularization parameters, Gamma (γ) and cost function (C ) X P , then CC, RMSE and NSE may be determined as follows: The simulation skill is determined through k-fold (here,

RESULTS AND DISCUSSION
At the outset, the SPAI values obtained from the spatially averaged ERA5 reanalysis precipitation data are compared with that of the observed precipitation data (Pai et al. ) over the two study basins. The scatter plots are shown in Figure 4 for both the study basins. The CC is found to be 0.71 for TRB and 0.68 for WRB. Given the limitations of any reanalysis product, such correspondence with the observed data can be considered as good. The proposed DL-based model is trained and tested based on its efficacy to capture the rainfall variation using the hydrometeorological precursors. It was targeted to consider as many months as possible simultaneously so as to avoid running the model for each month separately and at the same time not to be burdened by an increased computational effort. We found that the model is able to consider three consecutive months with comparable accuracy for all the months and at a reasonable computational effort. Henceforth, in general, these 3 months are designated as 1st, 2nd and 3rd months in the following discussion.

Model performance in capturing the drought status
To assess the potential of the proposed DL-based model to capture the drought status in terms of SPAI, the observed and simulated rainfall values are converted to SPAI indices. Moreover, the performances are comparable for all three consecutive months that indicate the ability of the model to simulate drought status for all 3 months simultaneously.
As mentioned before, the DL-based model performance is also compared against another popularly used ML approach, i.e., SVR, keeping all other conditions the same.
The results are presented in the same tables and figure, i.e., Tables 2 and 3 and Figure 7, for an easy side-by-side comparison. The higher potential of the DL-based model is clearly established for all the cases. It is true for both the study basins. However, one point is to be mentioned   here. SVR needs to be trained for each month separately, while the DL-based model is able to provide the output for all three consecutive months simultaneously. Thus, computational effort is less in the case of the DL-based approach.
The effectiveness of the DL-based approach in analyzing and capturing the upcoming drought status with higher efficacy may be attributed to the convolutional feature of Conv1D, i.e., each layer contains a set of filters whose parameters need to be learned and the neurons are connected to the local region instead of being connected to all the neurons of the previous layer (Haidar & Verma ).

Model performance in drought category identification
While the overall prediction performance reflects the model ability over the entire range, it will be interesting to inspect the performances for different drought categories. Thus, the potential of the proposed DL model is also assessed by examining its skill to accurately simulate the category.
Toward this, two-way (here, 7 × 7) contingency tables are prepared between observed and simulated drought categories. Referring to Figure   As a first observation, the results indicate that the performance of both the models (DL and SVR) is much better than an unskilled random performance. In fact, the performances are very good, considering that the accuracy is almost always greater than 0.7 and KSS/HSS is much higher than random performance (≫0). The performances are more or less uniform across different folds and across two study basins. A graphical presentation of performances, summarizing all the folds, along with the range is shown in Next, all the testing period performances are considered to prepare the contingency tables. This helps to assess the model testing performance for the assessment of drought categories throughout the time period of analysis as a testing period only. However, this exercise is carried out only for the DL-based model, as the performance of SVR is already proved to be inferior. Secondly, the performance during the training period is kept aside while preparing the contingency tables, which will anyway be better than that during the testing period. Thus, the contingency tables only for the DL-based model and only for the performance during the testing period are shown in Tables 5 and 6

CONCLUSIONS
This study explores the potential of the DL-based model The potential of the DL-based model is used to extract the information from a set of hydrometeorological precursors, namely air temperature, surface pressure, wind speed, relative humidity, evaporation, soil moisture and geopotential height for the assessment of drought status, characterized through SPAI. The following conclusions are drawn from the study: • DL has the potential to successfully capture the complex relationship between different hydrometeorological precursors and rainfall variation. Simultaneous modeling of 3 months is possible with a suitable model architecture that can be run with standard computing facility yielding reasonable accuracy.
• Findings of this study emphasize that the potential of the DL-based approach to extract the hidden complex  Findings of this study also lead to a possible scope for future research to utilize the potential of climate models in simulating/predicting the primary hydrometeorological variables and, thereafter, to utilize the potential of DL to assess the status of secondary/tertiary hydrometeorological variables. In general, a proper training of such models needs a large amount of data, which is a shortcoming. To utilize the potential of such models in data-scarce regions, the spatial transferability of aforementioned models needs to be explored. This is kept as a future scope of this study.

DATA AVAILABILITY STATEMENT
The data used in this study are available from online reposi-