Improving dynamical-statistical subseasonal precipitation forecasts using deep learning: A case study in Southwest China

Subseasonal precipitation forecasting is challenging but critical for water management, energy supply, and disaster prevention. To improve regional subseasonal precipitation prediction, previous studies have proposed a dynamical-statistical projection model (DSPM). In this study, we develop a new method that combines the DSPM and deep learning (DL), called the DL-DSPM. The DSPM is developed using the observed relationships between large-scale atmospheric circulations and regional precipitation, and the dynamical forecasted atmospheric circulations from the European Centre for Medium-Range Weather Forecasts (ECMWF) model. The DL-DSPM improves upon the DSPM by correcting biases in atmospheric circulation forecasts from the ECMWF model using two DL models, namely, residual network and U-Net models. In the case of Southwest China (SWC), DL models can improve atmospheric circulation forecasts at lead times beyond 5 pentads, including large-scale drivers of SWC precipitation variability. The DL-DSPM outperforms the ECMWF model and DSPM forecasts in predicting precipitation anomalies beyond 4 and 5 pentads over most SWC regions, respectively. In addition, the DL-DSPM is more skillful than the ECMWF model and DSPM in predicting extreme precipitation events more than 4 pentads in advance. The successful combination of DL and the DSPM provides a new possible direction for DL applications in subseasonal precipitation forecasting.


Introduction
Subseasonal forecasts are forecasts with lead times more than two weeks, bridging weather forecasts and seasonal predictions.On this time scale, forecasts are crucial for public health, agricultural planning, water resource management, energy supply, and disaster mitigation (White et al 2017).However, subseasonal forecasting is challenging because the time range is too long for using atmospheric initial conditions to make future predictions, and too short for the slowly evolving boundary forcings to have a strong effect (Vitart and Robertson 2019).Current subseasonal forecasts are much less skillful than weather forecasts and seasonal predictions (White et al 2017).
To fill the gap in subseasonal forecasts, the World Weather Research Program and the World Climate Research Program initiated a subseasonal to seasonal (S2S) prediction project (Vitart et al 2017).The S2S project has created a database that consists of subseasonal forecasts and reforecasts from 12 state-ofthe-art dynamical models, which has helped the scientific community promote the understanding of S2S predictability and improve S2S forecasting in the last decade.Previous studies have suggested that predictability varies for different regions and different variables.Tropical systems, such as the Madden-Julian Oscillation, can be successfully forecasted more than three weeks in advance (Kang andKim 2010, Lim et al 2018), but the forecast skills sharply decrease in extratropical regions (de Andrade et al 2019, Son et al 2020).In addition, as one of the most important variables, precipitation has been found to be more difficult to predict than other variables on subseasonal timescales (Vitart 2014, Liang and Lin 2018, Liu et al 2021, Krishnamurthy and Stan 2022).One reason is that precipitation is produced from complex parameterized processes that are not well understood and described in dynamical models (Tapiador et al 2019).Therefore, improving extratropical precipitation predictions is urgently needed.
An effective way to improve precipitation predictions is to postprocess dynamical forecasts and produce hybrid dynamical-statistical precipitation predictions.To this end, various statistical methods have been proposed, including the methods correcting mean and variance bias (Xu and Yang 2012, Bruyère et  Forecasting weather and predicting climate using machine learning, especially deep learning (DL), has recently become a hot topic.One popular method for this purpose is to use preceding predictors in observations or reanalysis data to predict succeeding predictands (e.g.Ham et al 2019, Weyn et al 2021, Ling et al 2022, Bi et al 2023, Xie et al 2023).Another method is the postprocessing of dynamical forecasts.Kim et al (2021) used the Long Short-Term Memory to correct the biases of the amplitude and phase of the Madden-Julian oscillation.U-Net has been used for the postprocessing of global and regional dynamical forecasts (e.g.Han et al 2021, Horat andLerch 2023).A residual network (ResNet) is helpful in correcting subseasonal forecasts of extreme high temperatures (Jin et al 2022).Although DL models have made significant achievements in the bias correction of subseasonal dynamical forecasts, the application of DL models still has great untapped potential in this area.Inspired by the dynamical-statistical projection model (DSPM) proposed by Wu et al (2022) (hereafter W22) and the applications of DL models, we propose an improved hybrid dynamicalstatistical subseasonal precipitation prediction framework called the DL-DSPM.
In this study, we choose Southwest China (SWC) as our target region to assess the DL-DSPM method.One main reason is that SWC is characterized by complex terrain and is strongly influenced by monsoonal precipitation; therefore, it is seriously affected by frequent natural disasters, such as flooding and mudslides, that are induced by heavy precipitation (Qu et al 2016, Shi et al 2016).On the subseasonal timescale, precipitation in SWC is influenced by diverse intraseasonal oscillations from the tropics and extratropics (Nie andSun 2022, 2023b).The complicated variability in precipitation in SWC makes its forecasting a great challenge.Guo et al (2021) corrected biases in the subseasonal forecasts of summer precipitation over SWC based on paired high-correlation modes between observed and forecasted precipitation.Guo et al (2023) integrated multiple DL models to improve subseasonal predictions of station precipitation in Chongqing (within SWC).Despite the achievements of previous studies, more efforts are still needed to develop new methods to improve subseasonal precipitation forecasting in SWC.

Data
We use the S2S forecast data from the European Centre for Medium-Range Weather Forecasts (ECMWF) model considering the good performance of this model in forecasting precipitation (de Andrade et al 2019, He et al 2020).The ECMWF model runs twice a week, and each run integrates for 46 d.The real-time forecasts and reforecasts contain 51 and 11 members, respectively.The reforecasts used in this study are run during May-September (the rainy season of SWC) from 2018 to 2022.The ECMWF model reforecasts adopt an on-the-fly strategy covering the past 20 years.Thus, the reforecast data cover the period from 1998 to 2021.We also use real-time forecasts initialized during May-September from 2019 to 2022.The precipitation data are on 1.5 • × 1.5 • grids.Other variables are linearly interpolated to 2.5 • × 2.5 • grids.
Daily observational precipitation data are from the CN05.1 dataset (Wu and Gao 2013) and are linearly interpolated to a 1.5 • × 1.5 • grid to be consistent with the ECMWF model data.The daily mean horizontal winds, geopotential height, and specific humidity in the reanalysis data with a 2.5 • × 2.5 • spatial resolution are calculated from the ECMWF reanalysis 5 (ERA5) datasets (Hersbach et al 2020).This study also uses daily outgoing longwave radiation (OLR) data on a 2.5 • × 2.5 • grid from the National Oceanic and Atmospheric Administration (Liebmann and Smith 1996).The common period of 1998-2022 is selected for this study.The periods of 1998-2015 and 2016-2018 are the training and validation periods, respectively.The period of 2019-2021 (2019-2022) is the test period for reforecasts (real-time forecasts).

The DL-DSPM method
The DL-DSPM method includes two modules, namely, the DL module and the DSPM module.The main statistical method that the DSPM relies on is singular value decomposition (SVD), which can extract simultaneously coupled relationships between large-scale atmospheric circulations and regional precipitation.Because atmospheric circulations can be much better forecasted than precipitation by dynamical models, precipitation prediction can be improved indirectly using well-forecasted atmospheric circulations and observed atmospheric circulation-precipitation relationships.The DSPM is similar to the spatial-temporal projection model proposed by Hsu et al (2015) and Zhu et al (2015) but replaces preceding observations of atmospheric variables with S2S model forecasts.
To eliminate the effects of synoptic-scale fluctuations, the atmospheric circulation-precipitation relationships are extracted from 5 day running mean anomalies.The anomaly data are obtained by subtracting the respective climatologies.The observed climatology is the calendar-day climatology during the training-validation period.The climatology of the ECMWF model is the mean value of 220 reforecast members (20 years × 11 ensemble members).The anomalous atmospheric variables and precipitation are processed by grid-cell z-score standardization according to the standard deviation during the training-validation period before constructing the DSPM.The major steps in constructing the DSPM are described in Text S1 in the supplementary material.
Potential atmospheric variables include 200 hPa and 850 hPa zonal winds (U200 and U850) and meridional winds (V200 and V850), 200 hPa, 500 hPa and 850 hPa geopotential heights (Z200, Z500, and Z850), 700-hPa specific humidity (SH700), and OLR.Considering that these variables are suitable for different latitudes and longitudes, the spatial domains of these variables vary.Geopotential heights are less suitable for the tropics, and OLR and SH700 are less suitable for high latitudes.Therefore, the spatial domains of the geopotential heights are 15 • -80 • N, 20 • -160 • E, the zonal and meridional winds are 10 • S-70 • N, 20 • -160 • E, and the SH700 and OLR are 20 • S-50 • N, 50 • -170 • E. Among the 9 candidate atmospheric variables, we select the variables that perform well in the DSPM using leave-one-yearout cross-validation during the training-validation period.For example, to perform a prediction in 1998 using U200, the data in 1998 are first excluded.Next, the coupled relationships between U200 and precipitation in SWC for the remaining years (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018) are established.The precipitation prediction in 1998 is obtained by substituting U200 in 1998 into the developed DSPM.Similarly, we obtain the precipitation prediction for each year and calculate the temporal correlation coefficient (TCC) between the observed and predicted precipitation.Finally, the four variables with the highest average TCC over SWC are selected, i.e.OLR, U200, SH700, and V200.The precipitation predicted by the DSPM or DL-DSPM is the average result from the 4 individual models.Other variables are not selected because the average model performance does not improve when incorporating five or more variables.
The DSPM performance largely relies on the forecasting ability of the ECMWF model for atmospheric circulations.Imperfect forecasts of atmospheric circulations lead to precipitation biases.Therefore, bias correction for ECMWF model forecasts of atmospheric circulations may improve precipitation prediction.In this study, we use DL models to correct the biases of atmospheric circulations forecasted by the ECMWF model.The entire DL-DSPM framework is presented in figure 1.More details on the DL models are described in the next section.

DL models
We construct two parallel DL models, a ResNet model and a U-Net model, in this study.The two models have good performance in previous bias-correction tasks (Han et 2(a)).The residual block was proposed by He et al (2016).Different from the conventional convolutional neural network, the residual block introduces skip connections (or residual connections), allowing the network to bypass several layers and directly connect earlier layers to later layers (figure 2(c)), which makes ResNet easier to optimize.U-Net has a U-shaped encoderdecoder structure (figure 2(b)).The input data first pass through a convolutional layer.Next, the feature maps are passed through encoders with 2 × 2 max-pooling and then decoders with upsampling and skipping connections.Finally, the feature maps pass through another convolutional layer.Different from the conventional U-Net, which was first proposed by Ronneberger et al (2015), we replace convolutional layers with residual blocks, as shown in figure 2(c).More details on the hyperparameters used in the DL models are given in text S2.We train 5 randomly initialized members for each model.The final results are the average of the 5 members.The variability of biascorrected atmospheric variables should be adjusted by multiplying the ratios of standard deviation on the training-validation set before and after bias correction on each grid.
The input data of the DL models are standardized anomalies of the ensemble mean of the ECMWF model forecasts of an atmospheric variable.To be in line with W22, the first consecutive 6 pentads (days 1-30) are the targets of bias correction in this study.The corresponding values in the ERA5 reanalysis dataset are taken as the ground truth.Thus, the number of channels of the input and output data is 6.The outputs of the DL models are projected to the DSPM pentad by pentad, and the final results for the 6 pentads are obtained separately.The domains of the variables for bias correction are slightly larger than those for SVD analysis.The OLR and SH700 domain is 25 • S-52.5 • N, 22.5 • E-180 • , and the U200 and V200 domain is 20 • S-77.5 • N, 12.5 • -170 • E.

Definition of extreme precipitation
The observed extreme precipitation threshold is defined as the 90th percentile of the 5 day running mean raw precipitation from May to September during the training-validation period at each grid.The predicted extreme precipitation threshold is similar to that of the observations but for the predicted pentadmean precipitation in the training-validation set.Hence, the predicted extreme precipitation threshold is a function of lead time.An extreme precipitation event (EPE) on a grid is identified if the precipitation is greater than its extreme precipitation threshold.

Evaluation metrics
The prediction skills for precipitation and atmospheric anomalies are evaluated using the TCC and pattern correlation coefficient (PCC) metrics.The root-mean-square error (RMSE) is another commonly used metric to evaluate deterministic forecasts, but we find that the RMSE is highly correlated with the standard deviation of subseasonal precipitation forecasts.Due to the large bias of subseasonal precipitation forecasts, the RMSE can be reduced by multiplying all precipitation predictions by a number less than 1.Considering that such a process lacks meaning, we do not use the RMSE in this study.The model performances in predicting EPEs are evaluated using the threat score (TS).The details of these metrics are described in Text S3.

Bias correction for atmospheric variables
The ResNet and U-Net models are separately trained to correct the biases of the ECMWF model forecasts for each atmospheric variable.On the validation set, ResNet (U-Net) performed better for OLR and SH700 (U200 and V200).Therefore, bias correction for OLR and SH700 is based on ResNet and for U200 and V200 is based on U-Net.
The improvement in forecast skills after bias correction increases with lead time.For the forecasts in pentads 1-2 (3-4), there are no (limited) skill gains for any of the atmospheric variables (figure not shown).This may be because the ECMWF model is skillful in forecasting short-term atmospheric circulations and leaves little room for improvement.However, for forecasts in pentads 5-6 (days 21-30), which we are more concerned about for subseasonal forecasting, the skills in most areas have visibly improved after bias correction for all the variables, with the area-weighted average of TCCs after bias correction being 0.01-0.03higher than the values before bias correction (figure 4).Such improvements may give the DL-DSPM an advantage over the standard DSPM.show that the TCCs increase after bias correction in most areas (figure S2), suggesting that the DL models can improve the forecasting of atmospheric variable evolution.

Precipitation and EPE predictions of on the reforecast test set
TCC skills are evaluated for precipitation anomaly predictions of the ECMWF model, DSPM, and DL-DSPM on the reforecast test set (figure 5).The precipitation anomaly forecasts of the ECMWF model are very skillful in the first 2-3 pentads (figures 5(a) and (b)).However, TCC skills sharply decrease with lead time, with poor skills over large areas beyond 4 pentads (figures 5(c)-(e)).Compared with that of the ECMWF model, the skill of the DSPM decreases more slowly, with lower skills for predictions in pentads 1-3 in advance (figures 5(f) and (g)) but higher skills for predictions beyond 4 pentads (figures 5(h)-(j)).This suggests that more reliable precipitation predictions can be produced by combining dynamical forecasts of atmospheric circulations and the relationships between atmospheric circulations and precipitation.
The advantages of the DL-DSPM over the DSPM and ECMWF model are more directly reflected in the area-weighted average of TCCs (figure S3(a)) and time-average PCCs (figure S3(b)) of precipitation anomalies over SWC.The DL-DSPM outperforms the ECMWF model (DSPM) for predictions beyond 4 (5) pentads.Quantitatively, the average TCC and PCC of the DL-DSPM are approximately 0.1 greater than those of the ECMWF model beyond pentad 5. Therefore, the precipitation predicted by DL-DSPM is more skillful than that of the ECMWF model and DSPM on the subseasonal timescale.Therefore, the precipitation predicted by the DL-DSPM is more skillful than that of the ECMWF model and DSPM on the subseasonal timescale.The improvement of the DL-DSPM over the DSPM in precipitation prediction is due to the improvement in the prediction of the temporal variability of atmospheric variables.
The prediction of EPEs is another focus of this study.Before evaluating the EPE predictions, the distributions of extreme precipitation thresholds are first compared among the observations and predictions of the ECMWF model, DSPM, and DL-DSPM.The thresholds for precipitation predictions in pentad 6 are taken as an example.The observed extreme precipitation thresholds over SWC decrease from southeast to northwest (figure S4 The TS skills of the predicted EPEs are subsequently assessed (figure 6).Similar to the TCC results, the ECMWF model performs well in predicting EPEs for short lead times, but the skill quickly decreases with increasing lead time.In contrast, the TSs of the DSPM and DL-DSPM slowly decrease with increasing lead time.Consequently, the DSPM and DL-DSPM outperform the ECMWF model beyond pentad 4. In addition, the TS skills of the DL-DSPM are also greater than those of the DSPM beyond pentad 4 over most areas of SWC, especially over northern SWC.For lead times beyond 4 pentads, the area-weighted averages of the TS skills of the DL-DSPM are 0.03-0.04(0.01-0.02) greater than those of the ECMWF model (DSPM).Compared with the ECMWF model, the TS skills of the DL-DSPM exceed 0.2 beyond pentad 4 in some areas over northern SWC.Therefore, the combination of DL and the DSPM can effectively improve subseasonal EPE prediction than can the ECMWF model or DSPM alone.

Precipitation and EPE predictions on the real-time test set
Considering that real-time forecasts are the data for operational forecasting, we also evaluate the precipitation predictions on the real-time test set.Resembling the TCC and PCC skills on the reforecast test set, the DL-DSPM is more skillful than the ECMWF model (DSPM) for predictions beyond pentad 4 (5) (figure S5).However, the advantages of the DL-DSPM over the DSPM are reduced compared to the results on the reforecasts.One possible reason is that the increase in ensemble members (from 11 to 51) reduces the forecast biases of atmospheric circulations.However, the increase in ensemble members also reduces the amplitude of atmospheric circulation variability.The standard deviations of the 51-member averaged atmospheric circulation are slightly lower than those of the DL-DSPM-corrected circulation, and such differences increase with lead time (figure not shown).Consequently, the precipitation amplitude tends to be underestimated by the DSPM compared to the DL-DSPM, which makes the DL-DSPM more effective at EPE prediction than the DSPM for realtime forecasts.As expected, the DL-DSPM shows the highest TS skill among the three models in predicting EPEs over SWC for the predictions beyond pentad 4 (figure S6), which resembles the results on the reforecast test set.The skill gains are mainly distributed over northern and central SWC.Therefore, the DL-DSPM outperforms the ECMWF model and DSPM for subseasonal precipitation and real-time EPE forecasts.

Summary and discussion
Skillful subseasonal precipitation predictions are valuable but difficult.In this study, we propose a new subseasonal precipitation forecast method, the DL-DSPM, by integrating DL with the DSPM.Compared to dynamical precipitation forecasts, the DSPM has been found to be effective in improving subseasonal precipitation predictions by combining the linkages between large-scale atmospheric circulations in the ERA5 reanalysis dataset and observational regional precipitation, as well as atmospheric circulations forecasted by the ECMWF model.The DL-DSPM is an improved version of the DSPM that incorporates two parallel DL models, ResNet and U-Net.The role of DL models is to correct the biases of dynamical forecasts of atmospheric variables for 6 consecutive pentads (days 1-30).The model performances for predicting precipitation anomalies and EPEs are separately assessed on the reforecast and real-time test sets.
We take SWC as a case study to validate the model performances.OLR, U200, SH700, and V200 are the four selected atmospheric variables for the DSPM.The improvements in the accuracy of the atmospheric variable forecasts derived from the DL models increase with lead time.Benefiting from bias correction of the atmospheric variables, the DL-DSPM shows greater TCC and PCC skills than the ECMWF model (DSPM) for precipitation anomaly predictions beyond pentad 4 (5) over SWC.Moreover, according to the TS skills, the DL-DSPM performs better than the ECMWF model and DSPM in predicting EPEs beyond 4-pentad lead times.
We also compared our results with those of the QM method, which is computationally less expensive and widely used as a benchmark in precipitation forecast postprocessing.For precipitation anomaly predictions, the performances of the QM-processed results are close to those of the ECMWF forecasts (figure not shown).For the predictions of EPEs, the QM-processed results show higher TS skills than the ECMWF forecasts but lower TS skills than the DSPM and DL-DSPM results (figure S7).Therefore, our bias-correction approach is superior to the QM approach.
Although the DL-DSPM shows encouraging improvements in subseasonal precipitation prediction skills, there are still possibilities for further advancements.One possible method is to try other DL techniques, such as Vision Transformer (Dosovitskiy et al 2020), to correct biases in dynamical forecasts of atmospheric circulations.In addition, boundary forcings, including sea surface temperature and soil moisture, may have the potential to optimize the DL-DSPM.The performance of the DL-DSPM also depends on whether the atmospheric circulation-precipitation relationship can be well captured.Finding a better method than SVD (e.g. an appropriate DL model) could also help improve the DL-DSPM.
The DL-DSPM has shown promising potential for precipitation prediction within 6 pentads across SWC.Whether it can perform well for predictions beyond 6 pentads deserves further investigation.Additionally, the DL-DSPM can be easily extended to other regions and seasons by changing atmospheric variables and their domains accordingly.To construct the DL-DSPM, the ECMWF model can also be replaced by other dynamical models.Overall, this study provides a new idea for subseasonal precipitation prediction.The DL-DSPM is expected to play an active role in more applications.
al 2014, Xu et al 2021), the quantile mapping (QM) method (Piani et al 2010, Themeßl et al 2011, Li et al 2019), Bayesian analysis-based methods (Schepen et al 2018, Specq and Batte 2020, Li et al 2021), a method based on the relationship between precipitation forecast biases and sea surface temperature (He et al 2020), a method based on rainy days (Liu et al 2023a), an adaptive bias correction method (Mouatadid et al 2023), and a dynamical-precipitation-forecast-independent method that relies on dynamical forecasts of atmospheric circulations and the relationships between observed atmospheric circulations and precipitation (Wu et al 2022, Zhang et al 2023).

Figure 1 .
Figure 1.A schematic diagram of the DL-DSPM framework.Inputs are represented by green boxes, outputs by the green oval, key steps by yellow boxes, singular value decomposition (SVD) patterns by blue boxes, and expansion coefficients (ECs) by pink boxes.The labels x and y represent standardized atmospheric variables and precipitation, respectively.The label n denotes the number of SVD modes.

Figure 2 .
Figure 2. Architecture of the deep learning models.(a) ResNet and (b) U-Net.The structure of the residual block in (a) and (b) is shown in (c).The input and output are examples of U200.The 3 numbers near the input and output are the number of channels, height, and width, respectively.

Figure 3 .
Figure 3. Singular value decomposition (SVD) analysis for large-scale 200 hPa zonal winds (U200) and precipitation anomalies over Southwest China (SWC).The SVD patterns of standardized (a) U200 and (b) SWC precipitation anomalies during May-September from 1998 to 2018, and (c) corresponding expansion coefficients for the first SVD mode during 2016-2018.(d)-(f) As in (a)-(c), but for the second mode.The percentages at the upper right corner of (c) and (f) are the covariance contributions.
U200 is first taken as an example to show the coupled relationships with precipitation over SWC (21 • -34.5 • N, 97 • -110.5 • E) extracted by the SVD analysis.The first two modes are shown in figure 3. The loading of U200 is mainly distributed over East Asia and tropical regions.In the first SVD mode, the anomalous 200-hPa easterlies over SWC and westerlies over central Asia and southern Asia (figure 3(a)) reduce precipitation over SWC (figure 3(b)).Anomalous westerlies (easterlies) to the north (south) of SWC (figure 3(d)) are favorable (unfavorable) for precipitation over northern (southern) SWC (figure 3(e)).These mechanisms were reported by Nie et al (2023) and Nie and Sun (2023a).The two paired expansion coefficients show high correlations, with TCCs above 0.6 (figures 3(c) and (f)).The highly coupled atmospheric variable and precipitation provide a foundation for the DSPM.

Figure 4 .
Figure 4. Differences in the TCC skills for atmospheric variable anomalies after and before bias correction on the reforecast test set.Differences in TCC skill for standardized (a), (b) OLR, (c), (d) U200, (e), (f) SH700, and (g), (h) V200 forecasted by the ECMWF model at lead times of 5-6 pentads after and before bias correction during May-September from 2019 to 2021.'Avg' in the upper right corner is the area-weighted average of the values.

Figure 5 .
Figure 5. TCC skills for precipitation over Southwest China (SWC) for the reforecast test set.TCC skills for precipitation anomalies during May-September from 2019 to 2021 predicted by the (a)-(e) ECMWF model, (f)-(j) DSPM, and (k)-(o) DL-DSPM at lead times of 2-6 pentads.Differences in the TCC skills for precipitation prediction (p)-(t) between the DL-DSPM and ECMWF model and (u)-(y) between the DL-DSPM and DSPM.Stippled areas are significant at the 95% confidence level.
(a)).The thresholds of the ECMWF model are generally lower than those of the observations, particularly over southeastern SWC (figure S4(b)), indicating an underestimation of the precipitation amplitude.In comparison, the thresholds of the DSPM and DL-DSPM resemble the observations (figures S4(c) and (d)), suggesting their good performances in precipitation amplitude predictions.

Figure 6 .
Figure 6.As in figure 5, but for TS skills for extreme precipitation events.'Avg' in the upper right corner is the area-weighted average value.
al 2021, Hess and Boers 2022, Ji et al 2022, Sun et al 2022, Lyu et al 2023, Liu et al 2023b).ResNet consists of a convolutional layer, four residual blocks, and another convolutional layer (figure