X u a n Z h o u a,b,L i n C h e n a,b,*,J a n e t U m u h o z a a,b,c,Y i f e n g C h e n g'a,b,L u W a n g.a,b,R a n W a n g i a,b，

a Key Laboratory of Meteorological Disaster, Mitistry of Education (KLME)/Joint Intemnational Research Laboratory of Climate and Environmental Change(LCEC)/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD), Nanjing University of Information Science and Technology, Nanjing, China

b College of Atmospheric Science, Nanjing University of Information Science and Technology, Narnjing China

c Rwanda Meteorology Agency, Kigali, Rwanda

Previous studies have documented that rainfall in the tropical African regions shows an intrinsic intraseasonal variability (e.g.,Sandjon et al., 2014a, 2021 ); however, the specific intraseasonal features of rainfall in Rwanda and its surrounding region have not yet been paid much attention. In general, the forecasting skill of the Bureau of Rwandan Meteorology for rainfall in Rwanda during the rainy season reaches around several days in advance; however, the skill at the subseasonal time scale in Rwanda and its surrounding region remains unclear. As Rwanda is made up of hills and mountains in the north, west,central region and southern plateau and lowlands in the east, the topography influences the climate in Rwanda and its surrounding region,making local medium-range weather forecasts for the Rwandan region a challenging issue for current operational models. It is well accepted that subseasonal rainfall forecasting is of great practical significance but also a substantial challenge to the scientific community ( Coelho et al.,2018 ). In recent years, the World Weather Research Programme/World Climate Research Programme has established the Subseasonal to Seasonal Prediction project (S2S) for understanding the forecast skills of current dynamic models and improving them at the subseasonal-toseasonal time range ( Vitart et al. 2017 ). In recent years, the subseasonal forecasting skills for the global monsoon by different models have been evaluated (e.g., Liu et al., 2014 ; Nicolas et al., 2017 ; Li et al., 2020 ;Liu et al., 2020 ). For example, the National Centers for Environmental Prediction Climate Forecast System, version 2, has been reported to be skillful in forecasting global monsoon indices at lead times of about two weeks, while apparent interannual differences exist ( Liu et al., 2014 ).As the European Centre for Medium-Range Weather Forecasts (ECMWF)model is superior in many aspects of subseasonal forecasting among the S2S models (e.g., Kim et al., 2014 ; Zhou et al., 2019 ; Xie et al., 2020 ;Liyanaarachchige Don et al., 2021 ), we aim to evaluate the subseasonal forecasting skill for rainfall in Rwanda and its surrounding regions based on the reforecast experiment data yielded by the ECMWF model, which may represent the best level of current dynamic models ( Geoffrey et al.,2017 ).

The remainder of this paper is organized as follows: The data and methods employed are described in Section 2 . In Section 3 , the dominant modes of the intraseasonal oscillation (ISO) of the rainfall variability in Rwanda are revealed. In Section 4 , the subseasonal forecasting skills are assessed using the ECMWF model. Finally, a summary is given in Section 5 .

2. Data and methods

2.1. Data

Fig. 1. (a) Annual cycle of rainfall averaged in Rwanda. The gray line indicates the results from the raw daily data, and the bold black line indicates the slow annual cycle obtained from the first three Fourier harmonics. (b) Long rainy season (February—May) mean fields of rainfall (shading; units: mm d − 1 ) and 700-hPa winds (vectors; units: m s − 1 ) in tropical Africa. The red rectangle in (b)indicates the region of Rwanda.

The observational data employed in this study include daily data from the Global Precipitation Climatology Project (GPCP) dataset, version 1.1 ( Huffman et al., 2001 ), which has a horizontal resolution of 1°×1°, and daily winds at 700 hPa from ERA-Interim ( Dee et al., 2011 ),archived with a horizontal resolution of 1° × 1°. To evaluate the forecasting skill for intraseasonal rainfall variability over Rwanda and its surrounding area by dynamic models, the reforecast experiment results performed by the ECMWF model from the S2S database ( Vitart et al.,2017 ) are analyzed. We use five perturbed integrations from the version of CY40R1. This version of the Integrated Forecast System is first integrated for 10 days with a resolution of TL639 (about 32 km) in the atmospheric model, and for the remaining forecast days with a resolution of TL319 (about 64 km). The hindcast results during 1999—2010 are compared with the observation.

2.2. Methods

To investigate the ISO features, we firstly obtain the precipitation anomaly through removing the annual cycle of precipitation, and then a five-day running mean is calculated for the precipitation anomaly to remove the synoptic-scale signals. A spectral analysis is conducted on the time series of the aforementioned precipitation anomaly of each year,and then the multi-year average is calculated to reveal the dominant intraseasonal periods of these modes. A composite analysis is also used based on the intraseasonal rainfall events selected according to the standardized intraseasonal rainfall index to show the evolutionary features of intraseasonal rainfall and circulation anomalies.

Fig. 2. (a) Multi-year long rainy season (February—May) mean power spectrum of the Rwanda rainfall anomaly after removal of the climatology and synoptic fluctuations by a 5-day running mean. The red dashed line denotes the 99% confidence level. (b) Correlation coefficients between the intraseasonal rainfall at each grid point and the intraseasonal component of Rwanda-averaged (within the red box) rainfall during the 36 long rainy seasons (1979—2015). The regions above the 95% confidence level are shaded. The relatively larger region marked by the black box (8°S—3°N, 29°—37°E) is the key region where its 10—25-day variability of rainfall co-varies with that in Rwanda, referred to as “Rwanda and its adjacent areas ”throughout this paper. The contours in (b) denote the long rainy seasonal mean surface pressure; and the red, blue, and green contours indicate 1000 hPa, 925 hPa, and 850 hPa, respectively.

To assess the forecasting skill of the ECMWF model for intraseasonal rainfall variability in Rwanda, we compare the proposed rainfall and wind indices in the reforecast experiment and the observation using the temporal correlation coefficient (TCC), which is estimated as

whereXiis the observed rainfall or wind index, andfiis the predicted rainfall and wind indices for a lead time ofτdays.Nis the number of forecasts, and an overbar represents the time average. A five-day running mean is applied to the daily rainfall and wind indices to remove the synoptic-scale signals. Thet-test is used to statistically evaluate the significance of the forecasting skill for the monsoon indices, as in other studies (e.g., Liu et al., 2014 ).

3. Dominant intraseasonal rainfall mode over Rwanda

Fig. 1 (a) shows the annual cycle of rainfall averaged in Rwanda. The slow annual cycle (represented by the first three Fourier harmonics)shows that there are two rainy seasons in Rwanda, which are termed as the long rainy season (February—May) and short rainy season (October—December) by the local population. As described in the introduction,the rainfall in the short rainy season may be most associated with the movement of the ITCZ, so this study mainly focuses on the intraseasonal rainfall variability and its forecasting skill during the long rainy season.Fig. 1 (b) displays the background mean states during the long rainy season. The spatial pattern of the climatological winds shows that easterly trade winds dominate in the equatorial Africa sector. In terms of mean rainfall, a relatively large (small) amount of rainfall appears in the regions west (east) of Rwanda, corresponding to a zonal contrast of mean moisture over the land areas of equatorial Africa during the long rainy season.

To reveal the intraseasonal rainfall mode in Rwanda, we calculate the multi-year mean power spectrum of the Rwandan rainfall anomaly from February to May. As shown in Fig. 2 (a), the main power is concentrated on the wave band of 10—25 days, most of which is generally above the 99% confidence level. This is consistent with a previous study(Sandjon et al., 2014b) ; that is, there is a 10—25-day intraseasonal rainfall variability over Central Africa for the period 1996—2009.

As Rwanda is a relatively small country, its intraseasonal variability of rainfall may co-vary with that in its surrounding regions. To determine the linkage between the intraseasonal rainfall anomaly over Rwanda with the ISV in its surrounding regions, we calculate a simultaneous correlation coefficient pattern of the 10—25-day rainfall intraseasonal component, which is obtained against the 10—25-day rainfall intraseasonal component over Rwanda. As shown in Fig. 2 (b), it is found that the intraseasonal rainfall anomaly over central-eastern equatorial Africa, primarily including Burundi, Uganda, the eastern part of the Democratic Republic of the Congo, northwestern Tanzania, and western Kenya, has significantly positive correlations with that in Rwanda.In this sense, the features of the major intraseasonal rainfall in Rwanda bear a close resemblance to the intraseasonal rainfall in a relatively larger region as shown by the black box (8°S—3°N, 29°—37°E) in Fig. 2 (b).This relatively larger region, whose 10—25-day variability of rainfall covaries with that in Rwanda, is referred to as “Rwanda and its adjacent areas ”throughout this paper. Note that the surface pressure over the study region is less than 700 hPa but greater than 850 hPa over some parts, which makes us choose 700 hPa to reveal the low-level wind signal associated with the precipitation in the following analysis.

Fig. 3. Composite evolution of anomalous precipitation (shading; units:mm d − 1 ) and 700-hPa winds (vectors; units: m s − 1 ) from day( − 6) to day(0)with an interval of 2 days. Day(0) denotes the peak day of the standardized intraseasonal rainfall index for each selected subseasonal event. The red rectangle indicates the region of Rwanda.

To reveal the evolutionary features of the 10—25-day rainfall mode during the long rainy season, we next carry out a composite analysis.Firstly, the 10—25-day filtered rainfall anomaly averaged in the key box(as shown in Fig. 2 (b)) is defined as the intraseasonal rainfall index for Rwanda and its adjacent regions (hereafter ISO_rainfall_index). Based on the time series of the standardized intraseasonal rainfall index, we then selected those strong rainfall events when the corresponding value of the standardized intraseasonal rainfall index exceeds 1.5, and the peak day is defined as day(0). The 10—25-day filtered rainfall and circulation anomalies are composited for the strong rainfall events. As shown in Fig. 3 , the temporal evolution of the intraseasonal rainfall anomaly and 700-hPa wind anomaly from day( − 6) to day(0) shows the typical development process from the neutral/dry phase to wet phase in Rwanda and its adjacent regions. On day( − 6), the Rwandan region belongs to a neutral (or a weak dry) phase from the perspective of the rainfall anomaly field, whereas weak westerly wind anomalies start to emerge to the west of Rwanda. On day( − 4) and day( − 2), the westerly wind anomaly is enhanced in the central equatorial Africa sector, and positive rainfall anomalies start to occur in Rwanda and its adjacent regions. On day(0),westerly wind anomalies occupy central-eastern equatorial Africa with a convergence center in Rwanda, and the positive rainfall anomalies reach peak status. It is suggested that the development of such intraseasonal rainfall anomalies is closely associated with the emergence of the westerly wind anomalies to the west of Rwanda. The physical mechanism of the link between the intraseasonal rainfall and intraseasonal wind anomalies is straightforward to understand. As indicated in Fig. 1 (a),there is abundant mean moisture to the west of Rwanda. In the context of the easterly trade winds, anomalous westerly winds can advect the relatively humid airmass from the Congo to Rwanda, generating a favorable situation for positive rainfall anomalies. In this sense, the largescale circulation condition (say, westerly wind anomalies to the west of Rwanda) is essential to the development of strong rainfall events in Rwanda and its adjacent areas on the 10—25-day time scale.

In addition, we also present the composite evolution results in a large domain (Fig. S1), and find that the corresponding circulation anomalies are closely linked to equatorial Rossby waves. As shown in Fig. S1(a),the low-level atmospheric circulation exhibits a pair of anomalous cyclonic gyres that straddle the equator on day( − 6). In the following days,this pair of anomalous cyclonic circulations slowly moves westward. It is worth mentioning that the aforementioned circulation features are similar to the features of equatorial Rossby waves ( Wang and Chen, 2016 ,2017 ), which exhibit a dominant 10—30-day time scale periodicity that is close to the 10—25-day time scale in this study. It is argued that the aforementioned westerly wind anomalies that are crucial to the intraseasonal rainfall variability in Rwanda are associated with this pair of anomalous cyclonic circulations.

4. Forecasting skill for intraseasonal rainfall and associated winds in Rwanda and its adjacent regions

In this section, we investigate the subseasonal forecasting skill of the state-of-the-art model (i.e., the ECMWF model) for the intraseasonal rainfall variability in Rwanda and its adjacent areas. In order to quantitatively assess the model forecast skill, two indices are examined in the following assessment. Specifically, as analyzed above, the aforementioned ISO_rainfall_index (i.e., 10—25-day filtered rainfall anomalies averaged in the key box in Fig. 2 (b)), which reflects the intraseasonal rainfall variability in Rwanda, is used. Additionally, an associated intraseasonal wind index (hereafter, ISO_wind_index), which is defined as the intraseasonal zonal wind anomaly at 700 hPa averaged over a larger box area (8°S—3°N, 15°—40°E) and can represent the dominant atmospheric circulation features related to the intraseasonal rainfall variability, is also used.

Fig. 4 (a, b) show the prediction skill for the seasonal evolution of rainfall and wind during the long rainy season (February—May) at different lead times. From the perspective of seasonal evolution, the multiyear mean of the predicted rainfall with different lead times (e.g., the green line in Fig. 4 (a) denotes predicted rainfall from the 0—4-day lead forecasts averaged for all the retrospective forecast years) is close to the observation (black line in Fig. 4 (a)). Likewise, the zonal wind at 700 hPa yielded by the forecasts with different lead days is also close to the observation. Although the forecast bias gradually increases as the lead time increases, the predicted evolution of the rainfall and zonal wind is close to the observation, indicating that the ECMWF model has the ability to simulate the seasonal evolution of the rainfall and low-level zonal wind in Rwanda and its adjacent regions.

Next, the prediction skill for the intraseasonal rainfall and wind variabilities in each year are examined. Fig. 4 (c, d) show the TCC between the predicted ISO_rainfall_index (or ISO_wind_index) and its observational counterpart as a function of lead time. The multi-year mean results show that the forecasting skill for the rainfall index is generally comparable to that for the wind index. Specifically, the forecasting skill for both the rainfall and wind index drops below the 99% confidence level in about 18 days. Therefore, it is concluded that the forecasting skill for the intraseasonal rainfall variability in Rwanda and its adjacent areas can reach 18 days on average.

Fig. 4. (a) Seasonal evolution of the rainfall averaged over Rwanda and its adjacent areas (i.e., 8°S—3°N, 29°—37°E) during the long rainy season (February—May)based on GPCP rainfall (black curve) and the corresponding predicted results at different leads. The green curve represents the prediction averaged over the lead time of 0—4 days; the blue curve denotes that of 5—9 days; the orange curve denotes that of 10—14 days; and the pink curve denotes that of 15—19 days. (b) As in (a)but for the zonal wind at 700 hPa averaged over a larger box area (8°S—3°N, 15°—40°E). The values in brackets represent the biases of the predictions (i.e., forecasts minus observation) averaged from February to May at different lead days. (c, d) Temporal correlations between observation and forecasts at different lead days for the (c) ISO_rainfall_index and (d) ISO_wind_index. Black dashed lines denote statistical significance of the correlation at the 99% confidence level. Shown are the three-point running mean of lead days.

As shown in Fig. 4 (c), the forecasting skill for the ISO_rainfall_index exhibits interannual differences. For instance, it takes 9 days for the rainfall index to fall into the range of unskillful predictions in 2007 and 2009, whereas it takes 26 days in 1999 and 2010. Such interannual differences in the forecasting skill may be associated with the background basic state, which may facilitate or disrupt the forecasting of intraseasonal variability in central-eastern equatorial Africa. For one thing, the oceanic Niño index, defined to reflect the large-scale sea surface temperature (SST) in the tropical Pacific, is − 0.2 K and − 0.4 K in 2007 and 2009, respectively; whereas, it is − 1.1 K and 0.7 K in 1999 and 2010,respectively. In contrast to the years of long rainy seasons in 2007 and 2009, the counterparts in 1999 and 2010 indicate that the background SST in the tropical Pacific shows marked large-scale SST signals, which may affect the 10—25-day rainfall variability in central-eastern equatorial Africa through its teleconnection effect. The discussion above just provides a hypothesis for thinking about the interannual difference of the intraseasonal rainfall forecast skill, but the specific physical reasons may be complicated and worthy of in-depth investigation in future studies.

5. Summary and conclusions