  An architecture consisting of a serial coupling of the one-dimensional
convolutional neural network (1D-CNN) and the long short-term memory (LSTM)
network, which is referred as CNNsLSTM, was proposed for hourly-scale
rainfall-runoff modeling in this study. In CNNsLTSM, the CNN component receives
the hourly meteorological time series data for a long duration, and then the
LSTM component receives the extracted features from 1D-CNN and the hourly
meteorological time series data for a short-duration. As a case study, CNNsLSTM
was implemented for hourly rainfall-runoff modeling at the Ishikari River
watershed, Japan. The meteorological dataset, consists of precipitation, air
temperature, evapotranspiration, and long- and short-wave radiation, were
utilized as input, and the river flow was used as the target data. To evaluate
the performance of proposed CNNsLSTM, results of CNNsLSTM were compared with
those of 1D-CNN, LSTM only with hourly inputs (LSTMwHour), parallel
architecture of 1D-CNN and LSTM (CNNpLSTM), and the LSTM architecture which
uses both daily and hourly input data (LSTMwDpH). CNNsLSTM showed clear
improvements on the estimation accuracy compared to the three conventional
architectures (1D-CNN, LSTMwHour, and CNNpLSTM), and recently proposed
LSTMwDpH. In comparison to observed flows, the median of the NSE values for the
test period are 0.455-0.469 for 1D-CNN (based on NCHF=8, 16, and 32, the
numbers of the channels of the feature map of the first layer of CNN),
0.639-0.656 for CNNpLSTM (based on NCHF=8, 16, and 32), 0.745 for LSTMwHour,
0.831 for LSTMwDpH, and 0.865-0.873 for CNNsLSTM (based on NCHF=8, 16, and 32).
Furthermore, the proposed CNNsLSTM reduces the median RMSE of 1D-CNN by
50.2%-51.4%, CNNpLSTM by 37.4%-40.8%, LSTMwHour by 27.3%-29.5%, and LSTMwDpH by
10.6%-13.4%.
