A parsimonious setup for streamflow forecasting using CNN-LSTM

Streamflow prediction is one of the most challenging tasks in water resources management and is vital for various sectors, e.g. agriculture, disaster mitigation, and planning and management of water resources (Le et al. 2021; Pokharel et al. 2023). It is an integrated practice involving complex nonlinear physical processes that operate at multiple temporal and spatial scales within a watershed (Girihagama et al. 2022; Dehghani et al. 2023). Accurate streamflow prediction allows for advanced warning of potential floods, giving people in flood-prone areas time to prepare and implement flood control measures. Due to the proliferation of high-resolution and remote sensing datasets at both high spatial and temporal resolutions, the use of deep learning (DL) algorithms has gained traction in the field of hydrology, especially in streamflow prediction (Kratzert et al. 2018, 2019; Yan et al. 2019; Ding et al. 2020; Xiang et al. 2020; Hunt et al. 2022; Dehghani et al. 2023; Pokharel et al. 2023; Vatanchi et al. 2023).

Streamflow is typically modeled in two different ways. The first method involves time-series modeling, where we incorporate both lagged predictors and lagged target values over a specific time period (look-back window) to make predictions. In contrast, the second method, i.e., rainfall-runoff modeling, focuses solely on the predictors up to a given time (t) without considering the lagged target values.

The long short-term memory (LSTM) (Hochreiter & Schmidhuber 1997) model has gained traction and is widely used in streamflow prediction due to its ability to store and regulate information over time. It is well-suited for time-series modeling because it can effectively remember long-term dependencies and handle sequential data (Bengio et al. 1994). In streamflow prediction, where the data often exhibit temporal patterns, LSTM can learn from historical information, including lagged predictors and target values, making them suitable for streamflow prediction (Khandelwal et al. 2020; Majeske et al. 2022).

Convolution neural networks (CNNs) are DL networks, which are widely used for image and video recognition tasks. They are well known for their ability to learn spatial patterns within gridded data, such as images/videos, which is why this DL network is suitable for processing gridded spatial data in water resources. CNNs are a feedforward network like artificial neural networks (ANN). However, CNNs are more advanced than ANN with convolution and pooling layers, which help automatically extract the essential features from the input layer (Shu et al. 2021). CNNs can be 1-D, 2-D, and 3-D depending on the shape of the input layer. In 1-D CNN, the inputs are vectors, whereas in 2-D CNN, the inputs are in gridded/matrix form. The majority of the studies in hydrology involving CNN utilized the 1-D version of it (Haidar & Verma 2018; Chong et al. 2020; Hussain et al. 2020), although a few studies applied 2-D CNN (Huang et al. 2020; Chen et al. 2021).

CNN-LSTM is a hybrid neural network that combines the strengths of both CNN and LSTM. It is a DL architecture designed for sequence prediction problems with spatial inputs like images or videos (Donahue et al. 2017). The CNN model is used for feature extraction, while the LSTM model is used for interpreting the features across timesteps. Only a few studies in hydrology have applied CNN–2-D-LSTM in comparison to the widely used LSTM model (Anderson & Radić 2022; Li et al. 2023; Ng et al. 2023). Anderson & Radić (2022) used CNN-LSTM in rainfall-runoff settings using spatial data to predict streamflow at 226 stream gauges across southwestern Canada. They used gridded climate reanalysis data to train and predict streamflow and demonstrated the efficiency and suitability of the CNN-LSTM model for spatiotemporal hydrological modeling. Li et al. (2023) proposed a CNN-LSTM in rainfall-runoff settings that introduces actual evaporation as an additional training target and demonstrates the value of spatial information in hydrological modeling. Mohammed & Corzo (2024) applied CNN-LSTM in regional rainfall-runoff settings to simultaneously predict daily streamflow in 86 catchments across the US, adding the value by using spatial signals in the model. However, to the author's knowledge, no studies have investigated using CNN-LSTM in time-series settings. The contribution of this study is as follows:

• 1. Applying and testing LSTM and CNN-LSTM models for 32 Nebraska HUC8 basins in time-series settings.

• 2. Comparing the efficiency of those models in predicting streamflow for Nebraska HUC8 basins.

• 3. Investigating the added value of using CNN-LSTM in time-series settings for streamflow prediction.

In this study, we used data from three sources. Precipitation (m) and 2-m temperature (K) gridded data were obtained from ERA5-Land (9 km × 9 km) (Muñoz-Sabater et al. 2021), which is the fifth-generation atmospheric reanalysis from the European Centre for Medium-Range Weather Forecasts (ECMWF). Daily streamflow (cfs) data were collected from the United States Geological Survey (USGS) and the Nebraska Department of Natural Resources (NeDNR). The datasets from the ERA5-Land were aggregated on daily timescales by taking an average over the basin for LSTM since LSTM models cannot process gridded data. For the CNN-LSTM model, gridded data were used.

We know that hydrology is complex and has many underlying physics that govern the streamflow. However, we are only taking into consideration precipitation and temperature because these are the two principal meteorological inputs for hydrological modeling (Essou et al. 2016; Anderson & Radić 2022). This approach showcases the enhanced improvement in streamflow prediction achieved by using CNN-LSTM in time-series settings. Thus, taking a parsimonious approach, we tried to build a simpler model with few predictor variables to compare the efficacy of models.

In CNN, strides are the number of pixels the filter moves each time during the convolution operation. Padding refers to adding pixels of zero around the input image borders. Padding is done so that when the filters slide over the edge pixels, there is meaningful information for it to process rather than an empty space. The output size depends on the input dimensions, strides, padding, and filter size.

In this experiment, we utilized the LSTM neural network for time-series modeling. The lagged values of predictors (precipitation and 2-m temperature) and the lagged streamflow values were input to calculate streamflow at time t. The gridded datasets underwent basin averaging, as LSTM models cannot directly handle spatial data in their raw form. They were aggregated to form coherent input sequences for the LSTM model. The objective was to forecast streamflow at time t by examining t–n lagged predictors along with the target value.

The strategy for applying a CNN-LSTM model for time-series analysis involved representing lagged streamflow values as channels. The original 1-D discharge time series underwent a transformation into a 2-D tensor by duplicating values across the spatial grid. This integration allowed the streamflow data to be seamlessly concatenated with meteorology grids along the channel dimension. The model's input was comprised of a 6-month long video encompassing 182 frames. Each frame was equipped with three channels representing precipitation, 2-m temperature, and streamflow. These frames underwent a series of time-distributed convolution and pooling layers, as depicted in Figure 2. The CNN component efficiently extracted crucial features from each frame, generating 182 vectors that encapsulate spatially learned features for a specific day. Subsequently, these feature vectors traversed through the LSTM layer to capture temporal dependencies. The dense layer further mapped the discharge values derived from the LSTM output.

The initial step in our experiment involved transforming the datasets into the requisite format for model training. Then, it was split into training and testing sets in a 70:30 ratio. The validation split was 0.3, meaning 30% of the training data was used for validation. The datasets were normalized using the standard scaler method, subtracting the mean and dividing by the standard deviation. Only the training period datasets were used to calculate the mean and standard deviation. For consistency and to see the effectiveness of models, we used the same parameter across all the experiments carried out. The activation function, batch size, optimizer, and dropout were kept the same for all the experiments. We used Relu as the activation function, Adam as the optimizer, and the epoch and batch size were kept 100 and 50, respectively. Dropout, kernel initializer (he_uniform), and gradient norm were used to avoid overfitting, vanishing, and exploding gradient problems. The models were trained using the mean square error as the loss function (Pokharel & Ghimire 2023). The number of LSTM layers and neurons was kept the same for the LSTM and CNN-LSTM models. Table 1 shows the CNN-LSTM internal architecture. The use of 1 × 1 convolutional filters followed by an increase to 3 × 3 filters provided a way to manage model complexity, control the number of feature maps, and reduce computational requirements in CNNs, leading to more efficient and effective network architectures (Lin et al. 2013; Szegedy et al. 2014, 2015; Anderson & Radić 2022). We also used a single LSTM layer with 80 neurons, as it was found in the previous studies that using a single LSTM layer with more neurons performed better than multiple layers with fewer neurons (Kratzert et al. 2018; Anderson & Radić 2022).

All the basins were trained separately using the same configuration as discussed above. Finally, all the model performances were evaluated using Kling–Gupta efficiency (KGE) (Gupta et al. 2009).

In considering the applicability of the CNN-LSTM model in regions with established streamflow gauges, its usefulness remains evident. This model proves advantageous due to the persistent challenges associated with achieving accurate streamflow measurements. These include the influence of backwater from ice or debris, such as log jams, and algae and aquatic growth in the stream (Kiang et al. 2018). Additionally, sediment movement and the potential malfunction of measurement equipment further increase the chance of inaccurate streamflow measurement. The precision and accuracy of these measurements are of high importance, as they directly influence the reliability of hydrologic models, and any inaccuracies directly translate into uncertainties within hydrologic models (Dos Santos et al. 2021). Furthermore, accurate streamflow is critical for various sectors, such as water resources planning and management, agriculture water management, disaster mitigation, and infrastructure safety.

This study presented a new approach for implementing a CNN-LSTM model using lagged streamflow data in a time-series setting. The performance of the CNN-LSTM and LSTM models was compared across 32 basins in Nebraska. The key finding is that the CNN-LSTM model, trained on 1-D streamflow data and gridded precipitation and temperature inputs, demonstrates improved performance over the LSTM model in 21 of the 32 test basins. These results suggest the feasibility and potential benefits of applying CNN-LSTM (time-series setting) models for streamflow prediction tasks. The model's ability to capture intricate spatial patterns and signals between predictors and targets surpasses the capabilities of standard LSTM recurrent networks. However, the study also uncovered degradation in CNN-LSTM performance as compared to the standard LSTM in some basins that are characterized by high streamflow magnitudes and extensive irrigated croplands.

The value of this study lies in demonstrating a new approach of using CNN-LSTM for streamflow prediction and its potential benefits. While this study used the same set of hyperparameters to showcase the efficacy of CNN-LSTM in time-series settings throughout all basins, it should be noted that other variables such as solar radiation, wind, vapor pressure, and some basin static attributes such as slope, soil, and land characteristics could result in even better model performances.

The authors acknowledge funding from the University of Nebraska Collaboration Initiative Grant (Award Number 32370).

The ERA5-Land data is available from https://cds.climate.copernicus.eu/datasets/reanalysis-era5-land?tab=download.

The authors declare there is no conflict.