Copula based post-processing for improving the NMME precipitation forecasts

The skill of North American multimodel ensemble (NMME) seasonal forecasts in East Africa (EA), which encompasses one of the most food and water insecure areas of the world, is evaluated using deterministic, categorical, and probabilistic evaluation methods. The skill is estimated for all three primary growing seasons: March–May (MAM), July–September (JAS), and October–December (OND). It is found that the precipitation forecast skill in this region is generally limited and statistically significant over only a small part of the domain. In the case of MAM (JAS) [OND] season it exceeds the skill of climatological forecasts in parts of equatorial EA (Northern Ethiopia) [equatorial EA] for up to 2 (5) [5] months lead. Temperature forecast skill is generally much higher than precipitation forecast skill (in terms of deterministic and probabilistic skill scores) and statistically significant over a majority of the region. Over the region as a whole, temperature forecasts also exhibit greater reliability than the precipitation forecasts. The NMME ensemble forecasts are found to be more skillful and reliable than the forecast from any individual model. The results also demonstrate that for some seasons (e.g. JAS), the predictability of precipitation signals varies and is higher during certain climate events (e.g. ENSO). Finally, potential room for improvement in forecast skill is identified in some models by comparing homogeneous predictability in individual NMME models with their respective forecast skill.

This paper assesses the skill of the Saudi-King Abdulaziz University coupled ocean–atmosphere Global Climate Model, namely Saudi-KAU CGCM, in forecasting the El Niño-Southern Oscillation (ENSO)-related sea surface temperature. The model performance is evaluated based on a reforecast of 38 years from 1982 to 2019, with 20 ensemble members of 12-month integrations. The analysis is executed on ensemble mean data separately for boreal winter (December to February: DJF), spring (March to May: MAM), summer (June to August: JJA), and autumn (September to November: SON) seasons. It is found that the Saudi-KAU model mimics the observed climatological pattern and variability of the SST in the tropical Pacific region. A cold bias of about 0.5–1.0 °C is noted in the ENSO region during all seasons at 1-month lead times. A statistically significant positive correlation coefficient is observed for the predicted SST anomalies in the tropical Pacific Ocean that lasts out to 6 months. Across varying times of the year and lead times, the model shows higher skill for autumn and winter target seasons than for spring or summer ones. The skill of the Saudi-KAU model in predicting Niño 3.4 index is comparable to that of state-of-the-art models available in the Copernicus Climate Change Service (C3S) and North American Multi-Model Ensemble (NMME) projects. The ENSO skill demonstrated in this study is potentially useful for regional climate services providing early warning for precipitation and temperature variations on sub-seasonal to seasonal time scales.

Precipitation is an important and difficult climate variable to predict. Skillful sub-seasonal precipitation forecast can provide useful information for agriculture and water resources management communities. Nevertheless, sub-seasonal forecasts have been given less attention compared with forecasts of shorter/longer time horizons. Recently, the S2S database has made sub-seasonal to seasonal forecasts/reforecasts from 11 operational centers available to researchers. In this work, reforecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) spanning over a 20-year period were evaluated. Raw and post-processed precipitation forecasts were put against observed precipitation series of a number of synoptic stations with different precipitation regimes for all months of the year. By comparison, precipitation forecasts were more skillful in wet months. Raw forecasts in December and February were better than that in other months, while the weakest results were detected in August. There was no significant relationship between precipitation regime and prediction skill. Furthermore, quantile mapping (QM), Bayesian model averaging (BMA), and QM_BMA combination were adopted for post-processing. BMA outperformed QM and QM_BMA through improving the correlation coefficient between observations and average of ensemble forecasts; however, BMA performed weaker in other evaluation criteria, in particular in humid regions. It is concluded that the application of post-processing techniques greatly improved the results of ensemble precipitation forecasts. However, in a number of stations/months, the forecast results were not acceptable even after post-processing.

This study asks the question of whether GCMs are ready to be operationalized for streamflow forecasting in South Asian river basins, and if so, at what temporal scales and for which water management decisions are they likely to be relevant? The authors focused on the Ganges, Brahmaputra, and Meghna basins for which there is a gridded hydrologic model calibrated for the 2002–10 period. The North American Multimodel Ensemble (NMME) suite of eight GCM hindcasts was applied to generate precipitation forecasts for each month of the 1982–2012 (30 year) period at up to 6 months of lead time, which were then downscaled according to the bias-corrected statistical downscaling (BCSD) procedure to daily time steps. A global retrospective forcing dataset was used for this downscaling procedure. The study clearly revealed that a regionally consistent forcing for BCSD, which is currently unavailable for the region, is one of the primary conditions to realize reasonable skill in streamflow forecasting. In terms of relative RMSE (normalized by reference flow obtained from the global retrospective forcings used in downscaling), streamflow forecast uncertainty (RMSE) was found to be 38%–50% at monthly scale and 22%–35% at seasonal (3 monthly) scale. The Ganges River (regulated) experienced higher uncertainty than the Brahmaputra River (unregulated). In terms of anomaly correlation coefficient (ACC), the streamflow forecasting at seasonal (3 monthly) scale was found to have less uncertainty (>0.3) than at monthly scale (<0.25). The forecast skill in the Brahmaputra basin showed more improvement when the time horizon was aggregated from monthly to seasonal than the Ganges basin. Finally, the skill assessment for the individual seasons revealed that the flow forecasting using NMME data had less uncertainty during monsoon season (July–September) in the Brahmaputra basin and in postmonsoon season (October–December) in the Ganges basin. Overall, the study indicated that GCMs can have value for management decisions only at seasonal or annual water balance applications at best if appropriate historical forcings are used in downscaling. The take-home message of this study is that GCMs are not yet ready for prime-time operationalization for a wide variety of multiscale water management decisions for the Ganges and Brahmaputra River basins.

Climate forecast skill and teleconnections on seasonal time scales over Central Africa based on the North American Multi-Model Ensemble (NMME)

The National Center for Environmental Predictions (NCEP) has produced an ensemble meteorological reforecast product by using a fixed version of Global Forecast System (GFS) ensemble prediction system since 1 January 1979. The 15‐member ensemble product, with a global coverage at a 2.5° × 2.5° spatial resolution and a 14‐day lead time, has been used successfully by the River Forecast Centers of the National Weather Service (NWS) to produce basin scale precipitation and temperature ensemble forecasts in the US for several years now. This study evaluates the predictive skill of post‐processed ensemble forecasts based on GFS precipitation reforecast in China's Huai river basin. The evaluation is carried out in 15 sub‐areas of the Huai river basin and covers the 1/1/1981–31/12/2003 period. The Ensemble Pre‐Processing system version 3 (EPP3), developed at NWS, is used to develop joint probability distributions between forecasted ensemble mean precipitation and corresponding observations and to generate individual ensemble members that preserve space–time correlation of the observed precipitation data. Several statistical verification measures are used to quantify the goodness of fit between post‐processed (i.e. EPP3 processed) ensemble mean and observation and to assess the ensemble spread. Results indicate that the post‐processed forecasts have meaningful predictive skill for the first few days for ensemble daily precipitation forecasts. Predictive skill of ensemble forecasts of cumulative precipitation for lead times up to 14 days are significant. The forecast skill is highly dependent on seasonality, with relatively lower skills seen for wet summer season, when convective storm patterns dominate, as compared with other seasons. The predictive skill of the post‐processed ensemble precipitation is much better than the raw forecasts and the climatological ensemble forecasts. The results from this study suggest that the NCEP's GFS reforecasts can be a valuable resource for places other than the US. Copyright © 2012 John Wiley & Sons, Ltd.

Like many other Middle East countries, Iran has been suffering from severe water shortages over the last two decades, as evidenced by significant decline in surface water and groundwater levels. The observed changes in water storage can be attributed to the mutually reinforcing effects of human activities, climatic variability, and of course the climate change. The objective of this study is to analyze the dependency of atmospheric CO2 increase on the water shortage of Iran, for which we investigate the spatial relationship between water storage change and CO2 concentration using large scale satellite data. We conduct our analysis using water storage change data from GRACE satellite and atmospheric CO2 concentration from GOSAT and SCIAMACHY satellites during 2002–2015. To analyze the long-term behavior of time series we benefit from Mann-Kendal test and for the investigation of the relationship between atmospheric CO2 concentration and total water storage we use Canonical Correlation Analysis (CCA) and Regression model. Our Results show that the water storage change anomaly and CO2 concentration are negatively correlated especially in northern, western, southwest (Khuzestan province), and also southeast (Kerman, Hormozgan, Sistan, and Baluchestan provinces) of Iran. CCA results reveal that in the most of northern regions, the decrease in water storage is significantly influenced by the increase of CO2 concentration. The results further show that precipitation in the highland and peaks does not seem to be influenced by the long and short-term variation in CO2 concentration. Besides, our results show that the CO2 concentration is slightly correlated with a weak positive trend in evapotranspiration over agricultural areas. Thus, the indirect effect of CO2 on increasing evapotranspiration is observed spatially in the whole of Iran. The results of the regression model between total water storage change and carbon dioxide (R2 = 0.91)/water discharge/water consumption show that carbon dioxide has the highest effect on total water storage change at large scale. The results of this study will contribute to both water resource management and mitigation plans to achieve the goal of CO2 emission reduction.

Bias correction of ensemble precipitation forecasts in the improvement of summer streamflow prediction skill

In this paper, the results of an examination of precipitation forecasts for 1–30-day leads from global models run at the European Centre for Medium-Range Weather Forecasts (ECMWF) and the National Centers for Environmental Prediction (NCEP) during November 2007–February 2008 are presented. The performance of the model precipitation forecasts are examined in global and regional contexts, and results of a case study of precipitation variations that are associated with a moderate to strong Madden–Julian oscillation (MJO) event are presented.The precipitation forecasts from the ECMWF and NCEP operational prediction models have nearly identical temporal correlation with observed precipitation at forecast leads from 2 to 9 days over the Northern Hemisphere during the cool season, despite the higher resolution of the ECMWF operational model, while the ECMWF operational model forecasts are slightly better in the tropics and the Southern Hemisphere during the warm season. The ECMWF Re-Analysis Interim (ERA-Interim) precipitation forecasts perform only slightly worse than the NCEP operational model, while NCEP’s Climate Forecast System low-resolution coupled model forecasts perform the worst among the four models. In terms of bias, the ECMWF operational model performs the best among the four model forecasts that were examined, particularly with respect to the ITCZ regions in both the Atlantic and Pacific. Local temporal correlations that were computed on daily precipitation totals for day-2 forecasts against observations indicate that the operational models at ECMWF and NCEP perform the best during the 4-month study period, and that all of the models have low to insignificant correlations over land and over much of the tropics. They perform the best in subtropical and extratropical oceanic regions.Also presented are results that show that striking improvements have been made over the past two decades in the ability of the models to represent precipitation variations that are associated with MJO. The model precipitation forecasts exhibit the ability to characterize the evolution of precipitation variations during a moderate–strong period of MJO conditions for forecast leads as long as 10 days.

Improving Subseasonal-to-Seasonal forecasts in predicting the occurrence of extreme precipitation events over the contiguous U.S. using machine learning models

The predictability of precipitation is hindered by finer-scale processes not captured explicitly in global numerical models, such as convective interactions, cloud microphysics, and boundary layer dynamics. However, there is growing demand across various sectors for medium- (3–10-day) and extended-range (10–30-day) quantitative precipitation forecasts (QPFs) and probabilistic QPFs (PQPFs). This study uses a novel statistical postprocessing technique, APPM, that combines analog postprocessing (AP) with probability matching (PM) to produce week-1 and week-2 accumulated precipitation forecasts over Taiwan. AP searches for historical predictions that closely resemble the current forecast and create an AP ensemble using the observed high-resolution precipitation patterns corresponding to these forecast analogs. Frequency counting and PM are then separately applied to the AP ensemble to produce calibrated and downscaled PQPFs and bias-reduced QPFs, respectively. Evaluation over a 22-yr (1999–2020) period shows that raw ensemble forecasts from the GEFS of NOAA/NWS/Environmental Modeling Center, collected for the subseasonal experiment, are underdispersive with a wet bias. In contrast, the AP ensemble spread well represents forecast uncertainty, leading to substantially more reliable and skillful probabilistic forecasts. Furthermore, the AP-based PQPF demonstrates superior discrimination ability and yields notably greater economic benefits for a wider range of users, with the maximum economic value increasing by 30%–50% for the week-2 forecast. Compared to the raw ensemble mean forecast, the calibrated QPF exhibits lower mean absolute error and explains 3–8 times more variance in observations. Overall, the APPM technique significantly improves week-1 and week-2 QPFs and PQPFs over Taiwan. Significance Statement There are two significant challenges in improving precipitation forecasts beyond a few days in Taiwan. First, large-scale numerical models often struggle with accurately predicting precipitation locations, magnitudes, and providing sufficient detail. Second, probabilistic precipitation forecasts have been unreliable, failing to convey accurate uncertainty information to users. In response to these challenges, this study has developed a relatively simple yet effective technique that corrects the spatiotemporal distribution of predicted precipitation and downscales the forecasts from a 1° to 1-km spatial resolution. Our results demonstrate that this technique significantly alleviates these two issues, resulting in more accurate precipitation forecasts and more reliable probabilistic precipitation forecasts within a 2-week timeframe.

In this paper, I present computational procedures to obtian statistical tables. The tables of the asymptotic distribution and the exact distribution of Kolmogorov-Smirnov statistic D n for one population, the table of the distribution of the runs R, the table of the distribution of Wilcoxon signed-rank statistic W + and the table of the distribution of Mann-Whitney statistic U x using Mathematica, Version 3.9 under Window98. I think that it is an interesting cuestion because many statistical packages give the asymptotic significance level in the statistical tests and with these porcedures one can easily calculate the exact significance levels and the left-tail and right-tail probabilities with non-parametric distributions. I have used mathematica to make these calculations because one can use symbolic language to solve recursion relations. It's very easy to generate the format of the tables, and it's possible to obtain any table of the mentioned non-parametric distributions with any precision, not only with the standard parameters more used in Statistics, and without transcription mistakes. Furthermore, using similar procedures, we can generate tables for the following distribution functions: Binomial, Poisson, Hypergeometric, Normal, x 2 Chi-Square, T-Student, F-Snedecor, Geometric, Gamma and Beta.

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The quality of ensemble precipitation forecasts across the eastern United States is investigated, specifically, version 2 of the National Centers for Environmental Prediction (NCEP) Global Ensemble Forecast System Reforecast (GEFSRv2) and Short Range Ensemble Forecast (SREF) system, as well as NCEP’s Weather Prediction Center probabilistic quantitative precipitation forecast (WPC-PQPF) guidance. The forecasts are verified using multisensor precipitation estimates and various metrics conditioned upon seasonality, precipitation threshold, lead time, and spatial aggregation scale. The forecasts are verified, over the geographic domain of each of the four eastern River Forecasts Centers (RFCs) in the United States, by considering first 1) the three systems or guidance, using a common period of analysis (2012–13) for lead times from 1 to 3 days, and then 2) GEFSRv2 alone, using a longer period (2004–13) and lead times from 1 to 16 days. The verification results indicate that, across the eastern United States, precipitation forecast bias decreases and the skill and reliability improve as the spatial aggregation scale increases; however, all the forecasts exhibit some underforecasting bias. The skill of the forecasts is appreciably better in the cool season than in the warm one. The WPC-PQPFs tend to be superior, in terms of the correlation coefficient, relative mean error, reliability, and forecast skill scores, than both GEFSRv2 and SREF, but the performance varies with the RFC and lead time. Based on GEFSRv2, medium-range precipitation forecasts tend to have skill up to approximately day 7 relative to sampled climatology.

Obtaining high-quality quantitative precipitation forecasts is a key precondition for hydrological forecast systems. Due to multisource uncertainties (e.g., initial conditions, model structures and parameters), raw forecasts are subject to systematic biases; hence, statistical post-processing is often required to reduce these errors before the forecasts can proceed to hydrological applications. Machine learning (ML) algorithms are canonical statistical models, and they are diverse in type and variation. It is important to verify and compare their performance in the same scenario (e.g., precipitation post-processing). In this paper, we conduct a large-scale comparison study for the major ML models with diverse model structures and regularization strategies as post-processors for improving the quality of precipitation forecasts. Specifically, we compare the efficiency and effectiveness of 21 ML algorithms on solving this task. Daily reforecast precipitation with lead times up to 8 days from the Global Ensemble Forecast System and corresponding observations are employed to determine the usability of different models in the Yalong River basin in China. The performance of each model is validated by a group of carefully designed experiments and statistical metrics. The results reveal that improvements in model structures are more effective than regularization strategies. Among these algorithms, the optimized extra-trees regressor exhibit the best performance, effectively reduce overestimation and achieve the best skill in forecasting precipitation. Eleven ensemble members and a 2-day time window can be used as predictors to obtain the best model performance. The systematic experiments and findings also offer useful guidelines for other related studies.