Seasonal Forecast of Nonmonsoonal Winter Precipitation over the Eurasian Continent Using Machine-Learning Models

QiFeng Qian aKey Laboratory of Geoscience Big Data and Deep Resource of Zhejiang Province, School of Earth Sciences, ZheJiang University, HangZhou, Zhejiang, China

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XiaoJing Jia aKey Laboratory of Geoscience Big Data and Deep Resource of Zhejiang Province, School of Earth Sciences, ZheJiang University, HangZhou, Zhejiang, China

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Hai Lin bRecherche en Prévision Numérique Atmosphérique, Environment and Climate Change Canada, Dorval, Quebec, Canada

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Ruizhi Zhang aKey Laboratory of Geoscience Big Data and Deep Resource of Zhejiang Province, School of Earth Sciences, ZheJiang University, HangZhou, Zhejiang, China

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Abstract

In this study, four machine-learning (ML) models [gradient boost decision tree (GBDT), light gradient boosting machine (LightGBM), categorical boosting (CatBoost), and extreme gradient boosting (XGBoost)] are used to perform seasonal forecasts for nonmonsoonal winter precipitation over the Eurasian continent (30°–60°N, 30°–105°E) (NWPE). The seasonal forecast results from a traditional linear regression (LR) model and two dynamic models are compared. The ML and LR models are trained using the data for the period of 1979–2010, and then these empirical models are used to perform the seasonal forecast of NWPE for 2011–18. Our results show that the four ML models have reasonable seasonal forecast skills for the NWPE and clearly outperform the LR model. The ML models and the dynamic models have skillful forecasts for the NWPE over different regions. The ensemble means of the forecasts including the ML models and dynamic models show higher forecast skill for the NWEP than the ensemble mean of the dynamic-only models. The forecast skill of the ML models mainly benefits from a skillful forecast of the third empirical orthogonal function (EOF) mode (EOF3) of the NWPE, which has a good and consistent prediction among the ML models. Our results also illustrate that the sea ice over the Arctic in the previous autumn is the most important predictor in the ML models in forecasting the NWPE. This study suggests that ML models may be useful tools to help improve seasonal forecasts of the NWPE.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: XiaoJing Jia, jiaxiaojing@zju.edu.cn

Abstract

In this study, four machine-learning (ML) models [gradient boost decision tree (GBDT), light gradient boosting machine (LightGBM), categorical boosting (CatBoost), and extreme gradient boosting (XGBoost)] are used to perform seasonal forecasts for nonmonsoonal winter precipitation over the Eurasian continent (30°–60°N, 30°–105°E) (NWPE). The seasonal forecast results from a traditional linear regression (LR) model and two dynamic models are compared. The ML and LR models are trained using the data for the period of 1979–2010, and then these empirical models are used to perform the seasonal forecast of NWPE for 2011–18. Our results show that the four ML models have reasonable seasonal forecast skills for the NWPE and clearly outperform the LR model. The ML models and the dynamic models have skillful forecasts for the NWPE over different regions. The ensemble means of the forecasts including the ML models and dynamic models show higher forecast skill for the NWEP than the ensemble mean of the dynamic-only models. The forecast skill of the ML models mainly benefits from a skillful forecast of the third empirical orthogonal function (EOF) mode (EOF3) of the NWPE, which has a good and consistent prediction among the ML models. Our results also illustrate that the sea ice over the Arctic in the previous autumn is the most important predictor in the ML models in forecasting the NWPE. This study suggests that ML models may be useful tools to help improve seasonal forecasts of the NWPE.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: XiaoJing Jia, jiaxiaojing@zju.edu.cn

1. Introduction

Unlike the climate in monsoon regions, which is impacted by seasonal reversals of the prevailing wind direction between winter and summer, the climate in mid- to high-latitude central Eurasian areas (30°–60°N, 30°–105°E) (marked by the red-outlined rectangle in Fig. 1a) is mainly controlled by nonmonsoon airflow (e.g., An et al. 2015, their Fig. 2). Far from the ocean, the climate in these nonmonsoonal Eurasian areas (NME) is characteristically arid and semiarid (e.g., Li et al. 2015). Previous work revealed that the central Eurasian continent has warmed twofold when compared with the global mean in the past century (e.g., Giorgi 2006; Chen et al. 2009; Huang et al. 2016; Hu et al. 2016) and is projected to continuously warm at a high rate (e.g., Christensen et al. 2013; Peng et al. 2020). Observational data show that increased temperature has led to a decrease in snow cover and glacial shrinkage over central Asia (e.g., Sorg et al. 2012). The annual rainfall over the central Eurasian continent is also reported to have increased over the last several decades and will increase under a global warming background in the future, although the enhanced annual precipitation is found to be unified with different seasons (e.g., Huang et al. 2012; Huang et al. 2014; Jiang et al. 2020a).

Fig. 1.
Fig. 1.

The regressed spatial distributions of (a) EOF1, (c) EOF2, and (e) EOF3 using corresponding PCs for the NWPE for the period of 1979–2010 obtained using regression, and the corresponding PCs for (b) EOF1 (PC1), (d) EOF2 (PC2), and (f) EOF3 (PC3). The numbers in the top-right corners of (a), (c), and (e) are the percentages of variance explained by the three EOF modes. The stippled regions in (a), (c), and (e) represent the 95% confidence level.

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

The NME has infertile land and relatively sparse vegetation cover with fragile ecosystems, and precipitation is important for agriculture, irrigation, runoff, and the hydrological cycle in these areas. Anomalous precipitation significantly impacts people’s lives and the economy, as well as social stability. Therefore, understanding the dynamic mechanisms of the variation in precipitation over NME and improving climate-forecasting skills are important. As compared with the numerous works devoted to examining precipitation over monsoonal areas, much less work has been conducted to investigate the factors that impact the variation in precipitation in NME. The climate in these regions is mainly influenced by upstream westerly winds throughout the year. Some work has shown that changes in the location and intensification of the subtropical westerly jet can influence the variation in precipitation over the central Eurasian continent (e.g., Zhang et al. 2006; Zhao et al. 2014; Fallah et al. 2016). Yao and Chen (2015) revealed that precipitation over the central Eurasian continent is significantly related to variations in Tibetan Plateau conditions and Asia polar vortices (Yao and Chen 2015). Continental-scale wave trains related to North Atlantic Ocean sea surface temperature (SST) also play important roles in modulating the climate over the central Eurasian continent (e.g., Wu et al. 2016; Jia et al. 2018). Boundary conditions, such as snow cover and/or sea ice, may also impact the central Eurasian climate by modulating atmospheric circulations (e.g., Li and Wang 2012; Chen et al. 2016; Wang et al. 2019)

It is known that numerical models perform relatively poorly in simulating seasonal forecasts over the mid- to high-latitude continent as compared with tropical regions (e.g., Zwiers 1996). In recent years, machine-learning (ML) models have been applied to climate forecasting (e.g., Richman and Leslie 2012; Badr et al. 2014; Iglesias et al. 2015; Chi and Kim 2017; Cohen et al. 2019; Kämäräinen et al. 2019). Even with limited training data, some work has shown that ML models perform comparably well and even better than dynamic models for certain variables in climate forecasts over some regions (e.g., Nooteboom et al. 2018; Hwang et al. 2019; Ham et al. 2019; Qian et al. 2020). For example, in a recent work, Qian et al. (2020) used two ML models to perform seasonal forecasts of winter temperatures in North America. Their results indicate that the two ML models produce a better seasonal forecast skill for the winter temperature over central North America than two dynamical models. Considering the importance of precipitation for the central Eurasian continent and the low seasonal forecast skill of numerical dynamic models over NME, ML models might provide an additional way to help improve the seasonal forecast skill of climate in this region. In the current work, we perform seasonal forecasting of the nonmonsoonal winter precipitation over Eurasian areas (NWPE) using four ML models. Our results show that the ML models perform reasonably well in forecasting the NWPE as compared with dynamic numerical models and clearly outperform the traditional linear regression (LR) model. The ensemble mean forecasts of NWPE including both the ML models and the dynamic models result in better forecast skill over NME than using the dynamic models only. Additionally, we found that the Arctic sea ice anomaly in the preceding autumn has the greatest contribution to the ML model forecast for the NWPE.

The paper is organized as follows. In section 2, the dataset and two dynamic models used in the current work are described. The method of the seasonal-forecasting experiment and the four ML models involved in this work are introduced in section 3. Section 4 describes the three leading modes of the NWPE from an empirical orthogonal function (EOF) analysis and the selection of their respective predictors. Section 5 compares the seasonal forecast results among the four ML models, the LR model and the two dynamic models. The summary is presented in section 6.

2. Data and the dynamic models

a. Data

The datasets used in the current work are described as follows:

  1. The monthly precipitation data (version TS4.03) are from the Climate Research Unit (CRU) of the University of East Anglia (Harris et al. 2014), with a spatial resolution of 0.5° × 0.5° and a time span from 1901 to 2019.

  2. The Rutgers University Global Snow Laboratory Weekly Northern Hemisphere Snow Cover Extent (SCE) Data (Robinson et al. 2012), which has a horizontal resolution of 25 km and covers the period from October 1966 to the present, are used. These snow data are converted to monthly mean data following Z. Wang et al. (2017).

  3. Monthly mean SST and sea ice concentration (SIC) data gridded at a 1° × 1° resolution are obtained from the Met Office Hadley Center (Rayner et al. 2003), with a time span from 1870 to the present.

  4. Monthly mean 70-hPa geopotential height (Z70) data from January 1979 to the present with a regular 2.5° × 2.5° resolution are from the National Centers for Environment Prediction–Department of Energy (NCEP–DOE) Reanalysis II (Kanamitsu et al. 2002).

Some conventional climate indices are obtained from the Earth System Research Laboratory of the National Oceanic and Atmospheric Administration (NOAA) and have a time span from 1948 to the present. Specifically, the Niño-3.4 index, Niño-4 index, Niño-3 index and Niño1+2 index are defined as the mean SSTAs over the Niño-3.4 region (5°S–5°N, 170°–120°W), Niño-4 region (5°S–5°N, 160°E–150°W), Niño-3 region (5°S–5°N, 150°–90°W) and Niño-1+2 region (0°–10°S, 90°–80°W), respectively. The Arctic Oscillation (AO) index is constructed by projecting monthly mean 1000-hPa height anomalies onto the loading pattern of the AO, which is defined as the first leading mode from the EOF analysis of monthly mean 1000-hPa height anomalies. The North Atlantic Oscillation (NAO) index and the Pacific–North America (PNA) index are defined by applying the rotated principal component analysis technique to monthly mean standardized 500-hPa height anomalies, as described in Barnston and Livezey (1987).

b. The Canadian CanCM4i model

This study uses an atmosphere–ocean coupled dynamic models provided by the Environment and Climate Change Canada (ECCC), which is called the Canadian Centre for Climate Modeling and Analysis (CCCma) Coupled Climate Model, version 4, with improved sea ice initialization (CanCM4i; Merryfield et al. 2013). CanCM4i is part of the second version of the Canadian Seasonal to Interannual Prediction System (CanSIPSv2; Lin et al. 2020). The atmospheric component of CanCM4i is on T63 grids, corresponding to a resolution of approximately 2.8°, with 35 levels in the vertical direction and an atmosphere top at 1 hPa. CanCM4i is initialized at the beginning of each month and produce forecasts of 10 ensemble members with all integrations starting from the same date and lasting for 12 months (Lin et al. 2020). (The forecast results of CanCM4i, with a resolution of 1° × 1° and a time span from 2011 to 2019, are obtained from https://collaboration.cmc.ec.gc.ca/cmc/saison/hindcast_2011_2019/.) In the present work, forecasts initialized at 0000 UTC 1 December, that is, December–February (DJF) forecasts with a 0-month lead, are analyzed for comparison with the statistical models that use data available before 1 December. The winter (DJF) of 2011 refers to the average of the three months from December 2011 to February 2012. The other model of CanSIPSv2, GEM-NEMO, is not used because of a recently identified problem in the land surface initial condition during 2014–18.

c. The NCEP CFSv2 model

The NCEP Climate Forecast System, version 2 (CFSv2; Saha et al. 2014), is an atmosphere–ocean coupled dynamic model. The model’s atmospheric component is on T126 grids in the horizontal direction (approximately a 100-km grid resolution), and the model has 64 sigma-pressure hybrid vertical levels. The initial conditions for the CFSv2 operational forecasts are from the real-time operational Climate Data Assimilation System, version 2 (CDASv2), and it is possible to use CFSv2 for both subseasonal (1–6 weeks) and seasonal forecasts. In operation, there are 16 CFSv2 runs per day: 4 runs out to 9 months, 3 runs out to 1 season, and 9 runs out to 45 days. The four 9-month runs are initialized at 0000, 0600, 1200, and 1800 UTC each day. The three 1-season runs are initialized at 0000 UTC each day. There are three runs initialized at 0600, 1200, and 1800 UTC each day, which form the nine 45-day runs. In the present study, the monthly mean of 9-month forecasts initialized at 0000 UTC 1 December are used for a comparison with the ML models. (The CFSv2 9-month forecasts on T126 grids from 2011 to the present are obtained from https://www.ncdc.noaa.gov/data-access/model-data/model-datasets/climate-forecast-system-version2-cfsv2).

3. Seasonal-forecasting method and machine-learning models

a. Seasonal-forecasting method

The method to perform the seasonal forecasting follows that used by Qian et al. (2020) for their forecasts for winter surface air temperature over North America. Specifically, the observational winter precipitation field over the NWPE can be decomposed into EOF (spatial patterns) modes and corresponding principal components (PCs; time series) as follows:
PRE(x,y,t)=i=1nPCi(t)×EOFi(x,y),
where EOFi represents the spatial distribution of the ith leading EOF mode of the winter precipitation in the observations, PCi represents the corresponding temporal evolution of the ith EOF mode, and n denotes the total number of EOF modes.

In our seasonal-forecasting experiments, only the leading three EOFs are used to construct the forecast field, and the remaining EOFs are considered to be residuals and are omitted. By retaining several leading modes of the EOFs, the model space is reduced, and small-scale unpredictable features are filtered out (Chen and Yuan 2004; Wu et al. 2013). This multivariate linear model is advantageous because it is easy to analyze the forecast skill contributed by each EOF mode. In the seasonal-forecasting experiment, the PCs for the three leading EOFs are predicted by ML models that are constructed with predictors selected from different fields from the previous autumn [September–November (SON)]. In this study, the ML models are trained and constructed using the data for the period of 1979–2010, and then these ML models are applied to perform the seasonal forecast for the leading three PCs of NWPE for 2011–18. Then, EOF1, EOF2, and EOF3, obtained from the observational and predicted PCs, are used to construct the seasonal forecast fields for NWPE according to Eq. (1).

b. Machine-learning models

In the current work, four ML models are used to perform the seasonal forecast experiments: the gradient boosting decision tree (GBDT) model (Friedman 2001, 2002), the light gradient boosting machine (LightGBM) model (Ke et al. 2017), the categorical features supported gradient boosting (CatBoost) model (Prokhorenkova et al. 2018), and the extreme gradient boosting (XGBoost) model (Chen and Guestrin 2016). These ML models show reasonable forecasting performances in previous work (e.g., Li et al. 2020; Huang et al. 2019; Ju et al. 2019; Zamani Joharestani et al. 2019; Fan et al. 2018). In fact, the LightGBM, CatBoost, and XGBoost models are modified versions of the GBDT model (Liang et al. 2020). The four ML models are all tree ensemble ML models, which means that the contribution of each predictor to the forecasts can be evaluated. In addition to the four ML models, the traditional LR model is also used to perform seasonal forecasting for the NWPE for the purpose of comparison. The contribution of each predictor is evaluated using the methods proposed by Breiman et al. (1984). A brief introduction to GBDT, LightGBM, CatBoost, and XGBoost and how to evaluate the contribution of predictors can be found in appendix A.

4. Major modes of NWPE and the selected predictors

The EOF analysis is performed on the winter precipitation over the NME (30°–60°N, 30°–105°E, represented by the red-outlined rectangle in Fig. 1a) for the period of 1979–2010 to obtain the leading precipitation modes of NWPE. Only the three leading EOF modes are well separated from each other and from the rest of the other EOFs according to the criteria of North et al. (1982). The three leading EOF modes and their corresponding PCs are presented in Fig. 1. The first three EOF modes account for 24.54%, 15.31%, and 11.19% of the total variance in NWPE, respectively. The positive phase of the first EOF (EOF1) has significant negative precipitation anomalies over a large area of the southwestern NME, extending from the east Mediterranean Sea to the western Tibetan Plateau (TP). Significant positive anomalies emerge over central-northern NME (Fig. 1a). The positive phase of the second EOF (EOF2) is characterized by significant positive anomalies dominating the east Mediterranean Sea centered in the Caspian Sea, and significant negative anomalies lie to the southwest of the TP and eastern China (Fig. 1c). For the third EOF (EOF3), significant negative anomalies dominate southern Europe centered in the Black Sea, while significant positive anomalies prevail to the north of the TP and to the south of the Caspian Sea, central-eastern TP, and southeastern China (Fig. 1e). The spatial distributions of the three leading EOF modes indicate that they are associated with large-scale variability over the Eurasian continent. All three PCs are characterized by alternating positive and negative values, implying that these PCs are mainly dominated by interannual variations. As precipitation data have some uncertainties (Strauch et al. 2012), we also performed the above EOF analysis using other precipitation datasets. Similar results were obtained (figures not shown), suggesting that the results of the above EOF analysis are robust.

Most potential seasonal predictability of the atmosphere is from the interactions of slow-varying boundaries (e.g., ocean and land) and some low-frequency large-scale circulation patterns. In this study, the potential predictors of NWPE from the previous autumn, including the SST, SCE, SIC, and Z70, are constructed following Lin and Wu (2011) and Qian et al. (2020). Here, Z70 represents the stratospheric circulation contribution to the climate variation, as revealed by previous work (e.g., L. Wang et al. 2017). In addition, some conventional climate indices are also examined and used in this study. The predictors used to construct the ML models are selected according to the temporal correlation coefficient (TCC) between the variation in these potential predictors and the three leading PCs. Because the selection of predictors is important to ML models, we also try other methods to construct predictors [e.g., performing EOF analysis of SST, SCE, SIC, and Z70 following L. Wang et al. (2017) and Kämäräinen et al. (2019)], however, these predictors are weakly correlated with the three leading PCs (results are not shown). ML models may need considerable length of predictors to train a robust instance, but the length of predictors is limited by reliable observation of SCE and SIC and the length of Z70 reanalysis data. Please see appendix B for the reasons why these predictors are considered.

Figure 2 shows the TCC maps between the autumn SST and the three PCs. In Figs. 25, the regions with significant positive and negative TCCs are marked by red and blue rectangles, respectively. The letters beside these rectangles also denote the area-weighted average of the variables in these rectangles. For example, in Fig. 2a, “A” represents the area-weighted average of SST in the blue-outlined rectangle (labeled A) on its right side over the northern Indian Ocean, and the blue-outlined rectangle denotes the autumn Indian SST that is significantly negatively correlated with PC1. Over the Indian Ocean, there are two blue-outlined rectangles (“A” and “B”) and one red-outlined rectangle (“D”) that are significantly correlated with PC1. Accordingly, the Indian Ocean SST predictor (SST-Indian) associated with PC1 is calculated as (DAB)/3. Similarly, the Pacific Ocean SST predictor (SST-Pacific) associated with PC1 is calculated as (C + EF)/3, and the Atlantic Ocean SST predictor (SST-Atlantic) related to PC1 is only constructed with G. The SSTs over both the Indian Ocean and the Pacific Ocean are not significantly correlated with PC2 (Fig. 2b). The Atlantic Ocean SST predictor associated with PC2 is only constructed with H. For PC3, the Pacific Ocean SST predictor is calculated with I, and the Atlantic Ocean SST predictor is calculated as (J + K)/2.

Fig. 2.
Fig. 2.

Correlation coefficient maps between the SON SST and (a) PC1, (b) PC2, and (c) PC3 for the 1979–2010 period. Stippled areas indicate correlation coefficients that are significant at the 95% confidence level. The outlined boxes denote regions used to construct snow cover indices. The black letters (A–K) are regional labels. The Indian Ocean SST index for PC1 is calculated by (DAB)/3, where A, B, and D represent the area-weighted average of SSTs in the respectively labeled regions. The Pacific Ocean SST index for PC1 is calculated by (C + EF)/3. The Atlantic Ocean SST indices for PC1 and PC2 are calculated by averaging the SST over regions G and H, respectively. The Pacific Ocean SST index for PC3 is calculated by averaging the SST over region I. The Atlantic Ocean SST index for PC3 is calculated by (J + K)/2.

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

Fig. 3.
Fig. 3.

Correlation coefficient maps between the SON SCE over the EU and (a) PC1, (b) PC2, and (c) PC3 for the 1979–2010 period. Stippled areas indicate correlation coefficients that are significant at the 95% confidence level. The outlined boxes denote regions used to construct snow cover indices. The black letters (L–O) are regional labels. The EU SC index associated with PC1 is calculated by averaging the SCE over region L. The EU SC index associated with PC2 is calculated by (M + N)/2, where M and N represent the area-weighted average of SCE in the respectively labeled regions. The EU SC index associated with PC3 is calculated by averaging the SCE over region O.

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

Fig. 4.
Fig. 4.

Correlation coefficient maps between the SON SCE over (left) NA and (right) TP and (a),(b) PC1; (c),(d) PC2; and (e),(f) PC3 for the 1979–2010 period. Stippled areas indicate correlation coefficients that are significant at the 95% confidence level. The outlined boxes denote regions used to construct snow cover indices. The black letters (P–S) are regional labels. The NA SC index associated with PC1 is calculated by averaging the SCE over region P. The NA SC index associated with PC2 is calculated by (Q + R)/2, where Q and R represent the area-weighted average of SCE in the respectively labeled regions. The TP SC index associated with PC3 is calculated by averaging the SCE over region S.

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

Fig. 5.
Fig. 5.

Correlation coefficient maps between the SON SIC over the (left) Arctic and the (right) Northern Hemisphere at a geopotential height of 70 hPa and (a),(b) PC1; (c),(d) PC2; and (e),(f) PC3 for the 1979–2010 period. Stippled areas indicate correlation coefficients that are significant at the 95% confidence level. The outlined boxes denote regions used to construct snow cover indices. The black letters (T–Z, A2, B2, and C2) are regional labels. The SIC index associated with PC1, PC2, and PC3 is respectively calculated by averaging the SCE over regions T, X, and B2. The Z70 index associated with PC1 is calculated by (U + V + W)/3, where U, V, and W represent the area-weighted average of SIC in the respectively labeled regions. The Z70 index associated with PC2 is calculated by (Y + Z + A2)/3. The Z70 index associated with PC3 is calculated by averaging the 70-hPa geopotential height over region C2.

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

Figure 3 shows the TCC maps between autumn SCE over the Eurasian continent (EU) and the three PCs. Similar to Fig. 2, “L,” “M,” “N,” and “O” represent the area-weighted averages of SCE over the EU in their respectively labeled regions. According to Fig. 3, the EU SCE predictors (SCE-EU) associated with PC1, PC2 and PC3 are calculated with L, (M + N)/2, and O, respectively. The TCC maps between autumn SCE over North America (NA) (SCE-NA) (Figs. 4a,c,e) and TP (Figs. 4b,d,f) (SCE-TP) and the three PCs are depicted in Fig. 4. The NA SCE does not significantly correlate with PC3, and the TP SCE does not significantly correlate with PC1 and PC2. Thus, the NA SCE predictors associated with PC1 and PC2 are constructed with P and (Q + R)/2, respectively. The TP SCE predictor associated with PC3 is constructed with S. Figure 5 presents the TCC maps between the Northern Hemispheric autumn SIC (Figs. 5a,c,e) and Z70 (Figs. 5b,d,f) and the three PCs. According to Fig. 5, the associated SIC predictors for PC1, PC2, and PC3 are constructed with T, X, and B2, respectively. The Z70 predictors associated with PC1, PC2, and PC3 are calculated as (U + V + W)/3, (ZYA2)/3, and C2, respectively. The TCCs between the above selected predictors and the PCs are summarized in Table 1, which are all statistically significant at the 95% confidence level.

Table 1.

Correlation coefficient between the selected autumn predictors of SST, SCE, SI, Z70, and the three PCs. The correlation coefficients passing at the 95% confidence level are in boldface font and are used as predictors for PCs.

Table 1.

In addition to the constructed SST, SCE, SIC, and Z70 predictors, some conventional climate indices from the previous autumn, including the AO, NAO, PNA, and ENSO, may also be correlated with the three PCs. These climate indices reflect the possible impacts of large-scale atmospheric circulations or teleconnections on the climate over the central Eurasian continent. Thus, the TCCs between these indices and the three PCs are calculated and presented in Table 2. In Table 2, those indices with TCCs surpassing the 95% confidence level (in boldface font) are selected as autumn climate predictors. Specifically, only the Niño-3.4 index, the Niño-3 index and the Niño-4 index are significantly correlated with PC1 and are selected to build the ML models to predict PC1. Some predictors are not independent (e.g., Niño-3.4 index and Niño-3 index for PC1), which may result in the so-called collinearity phenomena in the traditional LR model and thus affect model accuracy (Lesaffre and Marx 1993). However, the boosted regression tree models, GBDT, LightGBM, CatBoost, and XGBoost, are not sensitive to collinearity (e.g., Ding et al. 2018) because the response of the boosted regression tree model to a certain predictor nonlinearly depends on other predictors at higher levels of trees, which eases the simultaneous interaction among predictors. Thus, this study does not consider the effect of collinearity.

Table 2.

Correlation coefficient between the selected autumn predictors of climate indices and the three PCs. The correlation coefficients passing at the 95% confidence level are in boldface font and are used as predictors for PCs.

Table 2.

5. Forecast results

In the last section, we select predictors for the leading three PCs from the previous autumn boundary conditions and some climate indices through correlation analysis using data for the period of 1979–2010. Then, these selected predictors are used to construct and train the ML models. Subsequently, these constructed ML models are applied to perform seasonal forecasts for the three PCs for 2011–18. The PC1–PC3 predicted by each ML model and the observation are presented in Fig. 6. Then, Eq. (1) is used to construct the forecast fields for the NWPE using the predicted PC1-PC3 and EOF1-EOF3 calculated from the observations (Figs. 1a,c,e). Up-to-date forecast results are obtained for 2019 and 20, which are shown in Figs. S1 and S2 in the online supplemental material.

Fig. 6.
Fig. 6.

Model-predicted and observed (a) PC1, (b) PC2 and (c) PC3 for the period of 2011–18.

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

a. The predicted PCs

The predicted PCs by ML models and the LR model, as well as the observed PCs, are shown in Fig. 6. The observations of PCs are obtained by projecting the EOFs of 1979–2010 onto the data of 2011–18. From Fig. 6, it can be clearly seen that ML models are more consistent in predicting PC3 when compared with PC1 and PC2. To quantify how well the ML models predict PC1–PC3, we calculate the Pearson correlation coefficient between the predicted PCs and the observation, and the results are presented in Table 3. The results show that the PC3 predicted by ML models is highly correlated with the observation (correlation coefficient higher than 0.8 and pass 95% confidence level), implying that the ML models can well capture the evolution of PC3. Although the ML models perform differently in predicting PC1 and PC2, some of these ML models still have reasonable skill in predicting PC1 (e.g., GBDT) and PC2 (e.g., CatBoost and GBDT). These results suggests that the best forecast skill of the ML models may be for PC3.

Table 3.

Correlation coefficient between the observed and predicted PCs. The correlation coefficients passing at the 95% confidence level are in boldface font.

Table 3.

b. The seasonal forecast for NWPE

In this section, the seasonal forecasts for the NWPE from the four ML models, the LR model and the two dynamic models are compared. The TCC maps between the observations and seasonal forecasts of the NWPE are presented in Fig. 7. The results show that high TCC skill for the four ML models occupies large areas of NME, with high TCCs appearing over the central to northern NWPE, as well as southwestern NME (Figs. 7a–d). The TCC skills for the four ML modes are generally low over southeastern NME. Among the four ML models, XGBoost has the highest TCC skill (Fig. 7d). The TCC skills for the four ML models obviously outperform the LR model (Fig. 7e). The spatial pattern of the TCC skill for the two dynamic models is somewhat different from those of the four ML models (Figs. 7f–h). High TCCs for the dynamic models mainly appear as a band over central NME with relatively low skill over northern and southern NME.

Fig. 7.
Fig. 7.

Correlation coefficients between (a) GBDT, (b) LightGBM, (c) CatBoost, (d) XGBoost, (e) LR, (f) CanCM4i, and (g) CFSv2 forecasts and the observed NWPE for the period of 2011–18. The GBDT, LightGBM, CatBoost, XGBoost and LR models are trained using 1979–2010 data and initialized using SON predictors in 2011–18.

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

Figure 8 presents the TCC skills of the ensemble mean of the four ML models (4ML, Fig. 8a), the two dynamic models (2DY, Fig. 8b) and the superensemble of 4ML and 2DY (4ML+2DY, Fig. 8c). These figures show that the 4ML has significant TCC skills over central to northern and western NME, while 2DY has good TCC skills band over central and western NME. Figures 8a and 8b suggest that the significant TCC skills for the ensembles of 4ML and 2DY have different spatial distributions, indicating that the ML model seasonal forecasts may provide additional forecast skill of NWPE for the dynamic model forecasts. To illustrate the difference in the ensemble mean of the four ML models and that of the two dynamic models, the differences in TCC skills between the 4ML and 2DY models is presented in Fig. 8d. The 4ML model clearly has higher TCC skills over central to northern and southwestern NME but has lower TCC skills over northwestern and southeastern NME. The above results confirm that the ML models and dynamic models have advantages in forecasting NWPE over different regions. Figure 8e presents the differences in the TCC skills between the ensemble mean of 4ML+2DY (Fig. 8c) and that of 2DY (Fig. 8b). The figure shows that the superensemble of 4ML+2DY has higher TCC skills than 2DY over most regions of NME, especially over northern and southwestern NME. These results confirm that ML models may work as supplementary tools to improve the seasonal forecast skill of the dynamic-only model for NWPE.

Fig. 8.
Fig. 8.

Correlation coefficients between (a) the ensemble of the four ML models (GBDT, LightGBM, CatBoost, and XGBoost, denoted 4ML), (b) the ensemble of two dynamic models (CanCM4i and CFSv2, denoted 2DY), and (c) the ensemble of 4 ML and 2DY (denoted 4ML+2DY) forecasts and the observed NWPE for the period of 2011–18. Also shown is the difference in correlations (d) between 4ML and 2DY and (e) between 4ML+2DY and 2DY.

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

The area-averaged TCC skills for the four ML models, the LR and the two dynamic models, as well as the ensemble mean of different models are presented in Fig. 9 for a further comparison. Clearly, the TCC skills for all four ML models perform better than that of the LR model. The XGBoost model has the highest area-averaged TCC skills among the four ML models (0.24). CanCM4i has higher area-averaged TCC skills than CFSv2 (0.28). The area-averaged TCC skill of the four ML models is 0.24, which is higher than that of the two dynamic models (0.17). The area-averaged TCC skill of 4ML+2DY is 0.21, which is higher than that of 2DY (0.17).

Fig. 9.
Fig. 9.

Domain-averaged correlation coefficients of the four ML models, the LR, and the two dynamic models and the ensemble mean of the four ML models (4ML), the ensemble mean of the two dynamic models (2DY), and the ensemble mean of the 4ML and 2DY models (4ML+2DY).

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

c. Analysis of the seasonal forecast skill sources of the ML models

In this section, the sources for the TCC skill of the ML models for the NWPE are analyzed. To examine the contribution of each EOF mode to the seasonal forecasts of NWPE in the empirical models, three sets of forecasted winter precipitation fields are reconstructed according to Eq. (1) but each set of forecasts uses only one EOF. The TCC maps between the reconstructed precipitation fields using individual EOFs and the observations for the four ML models and for the LR model are shown in Fig. 10. For the forecast precipitation reconstructed using EOF1 (the left column in Fig. 10), the XGBoost model shows higher TCC skills than the other empirical models. However, different from other models, the XGBoost model shows TCC skill over northwestern, central, and southern NME (Fig. 10j). The other ML models and the LR model show similar spatial distributions as the TCC skill but over limited regions, including southwestern and southeastern NME. For the seasonal forecast precipitation reconstructed using EOF2, the LightGBM has the lowest TCC skill when compared with other models, with only a few TCCs sporadically spread over the NME (Fig. 10e). The spatial distribution of the TCC skills for the remaining empirical models shows a similar pattern, with TCC skills mainly appearing over northwestern and central NME. This result is consistent with Table 3, in which the predicted PC2 of LightGBM shows a low correlation with the observation. In contrast, for the forecast winter precipitation reconstructed using EOF3, all empirical models show high TCC skills over vast regions of central and northern NME and with similar patterns, and the pattern is similar to those in Figs. 7 and 8a, suggesting that the seasonal forecast TCC skills of the ML models mainly originate from the contribution of a skillful forecast of PC3. The domain-averaged TCC skill of each model forecast using individual EOFs is calculated and presented in Fig. 11. Clearly, all empirical models show much higher skills in predicting EOF3 than EOF1 and EOF2. Table 1 shows that PC3 is associated with the predictors of SST-Atlantic, SST-Pacific, SCE-EU, SCE-TP, SIC, and Z70, implying that capturing the evolution of these predictors may help to improve the performance of seasonal forecasts of NWPE in the ML models.

Fig. 10.
Fig. 10.

Correlation between the (a) EOF1 × PC1 forecast using GBDT, (b) EOF2 × PC2 forecast using GBDT, (c) EOF3 × PC3 forecast using GBDT, (d) EOF1 × PC1 forecast using LightGBM, (e) EOF2 × PC2 forecast using LightGBM, (f) EOF3 × PC3 forecast using LightGBM, (g) EOF1 × PC1 forecast using CatBoost, (h) EOF2 × PC2 forecast using CatBoost, (i) EOF3 × PC3 forecast using CatBoost, (j) EOF1 × PC1 forecast using XGBoost, (k) EOF2 × PC2 forecast using XGBoost, (l) EOF3 × PC3 forecast using XGBoost, (m) EOF1 × PC1 forecast using LR, (n) EOF2 × PC2 forecast using LR, and (o) EOF3 × PC3 forecast using LR and the observed NWPE for the period of 2011–18.

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

Fig. 11.
Fig. 11.

Domain-averaged correlation coefficient of each pair of EOF × PC for each method.

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

To further analyze the relative importance of each predictor for the seasonal forecast of NWPE in the ML models, the contribution of each predictor is evaluated and presented in Fig. 12. For the seasonal forecast of PC1, the contribution of each predictor to the forecasts is model dependent. For example, for the GBDT model (Fig. 12a), all predictors contribute almost equally to the model forecast, while in the CatBoost model, the SST-Atlantic predictor accounts for 48.43% of the contribution (Fig. 12g). For the XGBoost model, the SIC predictor accounts for 43.09% of the contribution (Fig. 12j), while it only accounts for 6.53% in the CatBoost model. The seasonal forecasts of PC2 show characteristics similar to those of PC1. The SCE-EU predictor has a relatively larger contribution to the forecast of PC2. For the seasonal forecasts of PC3, the SIC predictor contributes from 17.93% (GBDT) to 39.79% (XGBoost) for the ML models. For the XGBoost model, the SIC predictor contributes nearly 40% of the forecasts for all three PCs. As EOF3 is the major source of TCC forecast skill, and XGBoost shows the highest TCC skill among all the empirical models; therefore, the above results suggest that the SIC predictor plays an important role in the seasonal forecasting for NWPE in the empirical models. Specifically, the SIC over the Beaufort Sea may affect the variation in NWPE (Fig. 5a). Previous studies have revealed that the autumn SIC in the North Polar region can affect the winter Northern Hemisphere annular mode and then further affect the variation in winter precipitation over the Eurasian continent (e.g., Li and Wang 2012). Further studies on the dynamic mechanisms accounting for the SIC–NWPE relationship are worth to being examined in the future using both observational data and numerical models.

Fig. 12.
Fig. 12.

The contribution of each predictor (%) to the seasonal forecasts of PC1, PC2, and PC3 in the empirical model forecasts.

Citation: Journal of Climate 34, 17; 10.1175/JCLI-D-21-0113.1

6. Summary

In this study, we developed four ML models to obtain seasonal forecasts for NWPE using various climate predictors from the previous autumn. The forecast experiments mimicking the real-time forecasts and the TCC skills of the four ML models are compared with those from an LR model and two dynamic models.

The four ML models show reasonable TCC skills for the NWPE forecast and obviously outperform the traditional LR model. The ML models show high TCC skills over central, northern, and southwestern NME with similar spatial distributions of TCC skills. In contrast, the two dynamic models have high TCC skill over a band of central NME and western NME and limited TCC skills over northern and southwestern NME. Thus, the ML models and the dynamic models have TCC skills of the NWPE forecast over different regions of NME, suggesting that the ML models can be used as supplementary tools to improve the seasonal forecast of NWPE. The superensemble mean of all ML models and dynamic models shows higher TCC skills for NWPE than the ensemble mean of only dynamic models for almost most regions of NME. Further analysis shows that the high seasonal forecast skill of NWPE for the ML models is mainly contributed by a skillful forecast of EOF3 for NWPE. An analysis of the contribution of each predictor to the model forecasts shows that the SIC over the Arctic plays the most important role in the improved seasonal forecast for NWPE in the ML models.

Acknowledgments

This research is funded by the National Natural Science Foundation of China (Grant 42075050).

Data availability statement

The reanalysis data are available at https://www.esrl.noaa.gov/psd/data/gridded/. The original weekly Climate Data Record of Northern Hemisphere Snow Cover Extent is available from https://climate.rutgers.edu/snowcover/index.php. The Climate Research Unit precipitation data can be downloaded from http://www.cru.uea.ac.uk/data. The Hadley Center Sea Surface Temperature data and Sea Ice Concentration data are from https://www.metoffice.gov.uk/hadobs/hadisst. All climate indices are obtained from https://www.esrl.noaa.gov/psd/data/climateindices/list. The CanCM4i forecast data can be downloaded from the official website https://collaboration.cmc.ec.gc.ca/cmc/saison/hindcast_2011_2019/. The CFSv2 operational forecast data can be downloaded from the website https://www.ncdc.noaa.gov/data-access/model-data/model-datasets/climate-forecast-system-version2-cfsv2.

APPENDIX A

Brief Introduction to the ML Models

a. GBDT model

The GBDT model is a supervised ML model proposed by Friedman (2001, 2002), and this model is widely used for both classification and regression problems. The GBDT model uses decision tree models as weak learners and applies a gradient boosting strategy to these tree models to form a strong learner and to improve their overall performance. In the training process for the GBDT model, each weak learner measures the error observed in each tree node and then splits the tree node by a loss function. The GBDT model sorts all the input feature values and then enumerates all possible feature points to determine the optimal segmentation point. In addition, the GBDT model is an iterative algorithm that aims to continuously reduce the residual produced in the model training to obtain an integrated model of data classification or regression. Since the GBDT model balances the trade-off between variance and deviation, it shows a better generalization capability than other tree-based algorithms (Li et al. 2020). More details and computation procedures can be found in Friedman (2001, 2002).

b. LightGBM model

Since the GBDT model needs to enumerate all possible features during the construction of a decision tree, the construction of a decision tree will consume most of the computation time and computer memory in the GBDT. The LightGBM model is a GBDT-based model that adopts an improved histogram-based algorithm to speed up the training process and reduce memory consumption. The histogram-based algorithm divides the continuous eigenvalues into k intervals and then constructs a histogram with a width of k. This algorithm does not require additional memory for presorted results, and such rough partitioning is proven to speed up the training process and retain model accuracy. In addition, application of the histogram-based algorithm shows a regularization effect and prevents overfitting. In addition to the histogram-based algorithm, the LightGBM uses a leafwise generation strategy in the training process instead of the traditional depthwise strategy used by the GBDT. The leafwise generation strategy shows a better performance in reducing losses when growing the same leaf than the traditional depthwise strategy used by the GBDT. More details of the LightGBM model description can be found in Ke et al. (2017).

c. CatBoost model

The CatBoost model is also a GBDT-based ML model, which shows advantages in dealing with categorical features when compared with the GBDT model. The CatBoost model differs from the GBDT model in the following three aspects. 1) The CatBoost model can deal with categorical features during the training process rather than in the preprocessing period. Usually, categorical features need to be replaced with the corresponding average label value in the preprocessing period, and then, the average label value will be directly used for tree node splitting in the GBDT model. This process will lead to a conditional shift (Zhang et al. 2013). In contrast, no additional efforts are required in the preprocessing period when using CatBoost. When training the CatBoost model, for each data example, a random permutation is performed on the whole dataset, and an average label value is computed for the example of the same category value placed before the one given in the permutation. This process helps to reduce noise obtained in the low-frequency category. 2) The CatBoost model adopts a greedy strategy to combine multiple categorical features and their combinations in the tree with all categorical features of the dataset. 3) The CatBoost model overcomes the gradient bias of the GBDT model. In the GBDT model, each iteration generates a weak learner based on the gradient of the previous learner. However, this strategy will lead to biased pointwise gradient estimation, which will make the final model overfit. The CatBoost model applies a method called ordered boosting to change the gradient estimation method in the GBDT and successfully overcome the prediction shift caused by gradient bias. Details of the CatBoost model can be found in Prokhorenkova et al. (2018).

d. XGBoost model

The XGBoost model was proposed by Chen and Guestrin (2016) and is also based on the GBDT. When compared with the GBDT, the XGBoost model has better control of overfitting by introducing regularized model formalization. Specifically, the complexity of the tree leaves and the weight of each leaf node are explicitly included in the regularization term in the cost function. This strategy penalizes complex tree models and thus prevents the XGBoost model from overfitting. In addition, the XGBoost model does not use all the samples and features of the dataset but randomly takes part of the samples and features during training to improve the generalization capability of the model and prevent underfitting or overfitting. In addition to the XGBoost model’s attempt to avoid overfitting and underfitting, another notable difference between the XGBoost and GBDT models is that XGBoost introduces the second derivative of the cost function to optimize the cost function rather than using the first derivative only, which makes the optimization process more accurate. More details about the XGBoost model can be found in Chen and Guestrin (2016).

e. Evaluation of the contribution of each predictor

The GBDT methods use decision tree models as weak learners and apply a gradient boosting strategy to these tree models to form a strong learner and to improve their overall performance. Other methods, namely, LightGBM, CatBoost, and XGBoost, have been developed based on GBDT. Breiman et al. (1984) proposed a method to evaluate the relative importance of the predictor xk in a single decision tree T in GBDT as follows:
Ik2(T)=t=1J1τ^t2I[υ(t)=k],
where the summation is over the nonterminal nodes t of J-terminal node tree T, xk is the splitting variable associated with node t, and τ^t2 is the corresponding empirical improvement in squared error as a result of using predictor xk as a splitting variable for the nonterminal node t. In other words, when the predictor xk is used to split a tree node, the contribution of the predictor xk is evaluated by calculating the improvement in the model accuracy.
For the whole GBDT model {Tm}1M, the above equation can be generalized by its average over all the additive trees:
Ik2=1Mm=1MIk2(Tm).

APPENDIX B

Inclusion of SCE, SIC, and Z70 and the Consideration for the Limitation of Data Length

ML models may require predictors with considerable length for training; however, the data length is limited by reliable observations of SCE, SIC, and the length of Z70 reanalysis data. Snow cover satellite observation data are known to have large errors over the TP before 1975 (Robinson et al. 1993), and the data after 1975 are usually used in research (e.g., Z. Wang et al. 2017). In addition to the snow cover data, long-term sea ice concentration data also contain many uncertainties and may limit the performance of statistic models trained over a longer period of data (Kämäräinen et al. 2019). However, Lin and Wu (2011) and Qian et al. (2020) show that including the SCE over TP can improve the forecast skill of both LR and ML models for the winter surface air temperature over North America, implying that SCE may provide additional forecast skill if we use SCE from a recent time period. In this study, we also perform a sensitivity experiment (e.g., including and excluding SIC), and the results show that SIC can provide additional forecast skills (Fig. S3 in the online supplemental material). When a limited length of data is available, complex machine-learning models (e.g., convolution neural networks) may not be reliable. However, the tree-based ML models are suitable for small-sized datasets in the applications in other areas and thus are adopted in this study (e.g., Ogunleye and Wang 2019; Shaikhina et al. 2019; Jiang et al. 2020b; Liang et al. 2020).

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