Forecast System Research Articles

Evaluation of a forecasting system to facilitate decision-making for the chemical control of Asian soybean rust

Evaluation of a forecasting system to facilitate decision-making for the chemical control of Asian soybean rust

Performance Evaluation of a National Seven-Day Ensemble Streamflow Forecast Service for Australia

The Australian Bureau of Meteorology offers a national operational 7-day ensemble streamflow forecast service covering regions of high environmental, economic, and social significance. This semi-automated service generates streamflow forecasts every morning and is seamlessly integrated into the Bureau’s Hydrologic Forecasting System (HyFS). Ensemble rainfall forecasts, European Centre for Medium-Range Weather Forecasts (ECMWF), and Poor Man’s Ensemble (PME), available in the Numerical Weather Prediction (NWP) suite, are used to generate these streamflow forecasts. The NWP rainfall undergoes pre-processing using the Catchment Hydrologic Pre-Processer (CHyPP) before being fed into the GR4H rainfall–runoff model, which is embedded in the Short-term Water Information Forecasting Tools (SWIFT) hydrological modelling package. The simulated streamflow is then post-processed using Error Representation and Reduction In Stages (ERRIS). We evaluated the performance of the operational rainfall and streamflow forecasts for 96 catchments using four years of operational data between January 2020 and December 2023. Performance evaluation metrics included the following: CRPS, relative CRPS, CRPSS, and PIT-Alpha for ensemble forecasts; NSE, PCC, MAE, KGE, PBias, and RMSE; and three categorical metrics, CSI, FAR, and POD, for deterministic forecasts. The skill scores, CRPS, relative CRPS, CRPSS, and PIT-Alpha, gradually decreased for both rainfall and streamflow as the forecast horizon increased from Day 1 to Day 7. A similar pattern emerged for NSE, KGE, PCC, MAE, and RMSE as well as for the categorical metrics. Forecast performance also progressively decreased with higher streamflow volumes. Most catchments showed positive performance skills, meaning the ensemble forecast outperformed climatology. Both streamflow and rainfall forecast skills varied spatially across the country—they were generally better in the high-runoff-generating catchments, and poorer in the drier catchments situated in the western part of the Great Dividing Range, South Australia, and the mid-west of Western Australia. We did not find any association between the model forecast skill and the catchment area. Our findings demonstrate that the 7-day ensemble streamflow forecasting service is robust and draws great confidence from agencies that use these forecasts to support decisions around water resource management.

A flexible tropical cyclone vortex initialization technique for GFDL SHiELD

Tropical cyclone (TC) intensity forecasting poses challenges due to complex dynamical processes and data inadequacies during model initialization. This paper describes efforts to improve TC intensity prediction in the Geophysical Fluid Dynamics Laboratory (GFDL) System for High-resolution prediction on Earth-to-Local Domains (SHiELD) model by implementing a Vortex Initialization (VI) technique. The GFDL SHiELD model, relying on the Global Forecast System (GFS) analysis for initialization, faces deficiencies in initial TC structure and intensity. The VI method involves adjusting the TC vortex inherited from the GFS analysis and merging it back into the environment at the observed location, enhancing the analyzed representation of storm structure. We made modifications to the VI package implemented in the operational Hurricane Analysis and Forecast System, including handling initial condition data, reducing input domain size, and improving storm intensity enhancement. Experiments using the T-SHiELD configuration demonstrate that using VI significantly improves the representation of initial TC intensity and size, enhancing TC predictions, particularly in storm intensity and outer wind forecasts within the first 48 h.

A User-Focused Approach to Evaluating Probabilistic and Categorical Forecasts

Abstract A user-focused verification approach for evaluating probability forecasts of binary outcomes (also known as probabilistic classifiers) is demonstrated that is (i) based on proper scoring rules, (ii) focuses on user decision thresholds, and (iii) provides actionable insights. It is argued that when categorical performance diagrams and the critical success index are used to evaluate overall predictive performance, rather than the discrimination ability of probabilistic forecasts, they may produce misleading results. Instead, Murphy diagrams are shown to provide better understanding of overall predictive performance as a function of user probabilistic decision threshold. It is illustrated how to select a proper scoring rule, based on the relative importance of different user decision thresholds, and how this choice impacts scores of overall predictive performance and supporting measures of discrimination and calibration. These approaches and ideas are demonstrated using several probabilistic thunderstorm forecast systems as well as synthetic forecast data. Furthermore, a fair method for comparing the performance of probabilistic and categorical forecasts is illustrated using the FIxed Risk Multicategorical (FIRM) score, which is a proper scoring rule directly connected to values on the Murphy diagram. While the methods are illustrated using thunderstorm forecasts, they are applicable for evaluating probabilistic forecasts for any situation with binary outcomes.

Forecasting the Exceedances of PM2.5 in an Urban Area

Forecasting the Exceedances of PM2.5 in an Urban Area

Operational workflow to simulate biophysical variables, based on the coupled WRF/SEBAL models

Three subsystems including an atmospheric regional forecast and analysis system, satellite data retrieval and processing, and a surface energy balance model have been employed in a 24/7 operational system to measure and simulate some primary agricultural variables, including evapotranspiration, biomass production, and other associated productivity metrics such as NDVI and Albedo. The final products are generated in a daily routine, covering Iran as the domain of simulation. The WRF atmospheric model, VIIRS, and SENTINEL2 satellite data, as well as the SEBAL model (implemented in pySEBAL) are the main components of the operational system, with products in two different spatial resolutions of 375 m and 100 m. The output products can be used by farmers and stakeholders to manage agricultural water requirements and monitor biophysical parameters.

Predictive Modeling of Extreme Weather Forecasting Events: an LSTM Approach

For a variety of industries, including agriculture, water resource management, and flood forecasting, accurate rainfall prediction is crucial. The purpose of this research work is to improve rainfall forecast system by employing the Long Short-Term Memory (LSTM) based system. The LSTM utilized in the aforementioned study made predictions by using meteorological input variables such as temperature, humidity, and rainfall. Numerous elements affect the LSTM network's performance, such as the kind and volume of data, the suitability of the model architecture, and the tuning of hyperparameters. The dataset used for model training spans from January 2015 to December 2021 and includes rainfall data collected from the Zonal Agricultural Research Station (ZARS), Shenda Park, Kolhapur. Prior to model training, the input data undergoes rigorous preprocessing. This preprocessing involves data correction, achieved through moving averages, followed by feature scaling and normalization methods. These steps are crucial to align the dataset with the unique capabilities of the LSTM model. The total dataset has a R squared (R2) value 0.23517 and a mean squared error (MSE) value 92.1839, according to the simulated findings. These metrics affirm the robust performance of the LSTM model, suggesting a high probability of accurate rainfall predictions, particularly in non-linear and complex scenarios. Decision-makers in flood predictions, agriculture, and water resource management will find the knowledge gathered from this study to be useful. They emphasize how crucial it is to use cutting-edge techniques like LSTM to increase rainfall forecast accuracy and guide strategic planning in associated industries.

Physics schemes in the first version of NCEP operational hurricane analysis and forecast system (HAFS)

This document summarizes the physics schemes used in two configurations of the first version of the operational Hurricane Analysis and Forecast System (HAFSv1) at NOAA NCEP. The physics package in HAFSv1 is the same as that used in NCEP global forecast system (GFS) version 16 except for an additional microphysics scheme and modifications to sea surface roughness lengths, boundary layer scheme, and the entrainment rate in the deep convection scheme. Those modifications are specifically designed for improving the simulation of tropical cyclones (TCs). The two configurations of HAFSv1 mainly differ in the adopted microphysics schemes and TC-specific modifications in addition to model initialization. Experiments are made to highlight the impacts of TC-specific modifications and different microphysics schemes on HAFSv1 performance. Challenges and developmental plans of physics schemes for future versions of operational HAFS are discussed.

An ensemble-based data assimilation system for forecasting variability of the Northwestern Pacific ocean

AbstractAn adjoint-free four-dimensional variational (a4dVar) data assimilation (DA) is implemented in an operational ocean forecast system based on an eddy-resolving ocean general circulation model for the Northwestern Pacific. Validation of the system against independent observations demonstrates that fitting the model to time-dependent satellite altimetry during a 10-day DA window leads to substantial skill improvements in the succeeding 60-day hindcast. The a4dVar corrects representation of the Kuroshio path variation south of Japan by adjusting the dynamical balance between amplitude/wavelength of the meander and flow advection. A larger ensemble spread tends to reduce the skill in representing the observed sea surface height anomaly, suggesting that it is possible to use the ensemble information for quantifying the forecast error. The ensemble information is also utilized for modification of the background error covariance (BEC), which improves the accuracy of temperature and salinity distributions. The modified BEC yields the skill decline of the Kuroshio path variation during the 60-day hindcast period, and the ensemble sensitivity analysis shows that changes in the dynamical balance caused by the ensemble BEC result in such skill deterioration.

Assimilation of GNSS tropospheric gradients into the Weather Research and Forecasting (WRF) model version 4.4.1

Abstract. In this study, we have incorporated tropospheric gradient observations from a Global Navigation Satellite Systems (GNSS) ground station network into the Weather Research and Forecasting (WRF) model through a newly developed observation operator. The experiments aim at testing the functionality of the developed observation operator and at analyzing the impact of tropospheric gradients on the sophisticated data assimilation (DA) system. The model was configured for a 0.1° mesh over Germany with 50 vertical levels up to 50 hPa. Our initial conditions were obtained from the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) data at 0.25° resolution, and conventional observations were obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF), restricted to mainly surface stations and radiosondes. We selected approximately 100 GNSS stations with high data quality and availability covering Germany. We performed DA every 6 h for June and July 2021. Four experiments were conducted: (1) a control run assimilating only conventional observations; (2) an impact run assimilating zenith total delays (ZTDs) on top of the control run; (3) an impact gradient run assimilating ZTDs and gradients on top of the control run; and (4) a gradient run assimilating only gradients on top of the control run. The error for the impact run was reduced by 32 % and 10 % for ZTDs and gradients, whereas the error for the impact gradient run was reduced by 35 % and 18 %, respectively. The gradient errors for the gradient run were nearly equal to those of the impact gradient. Overall, the newly developed operator for the WRFDA system works as intended. In particular, the combined assimilation of gradients and the ZTDs led to a notable improvement in the humidity field at altitudes above 2.5 km. With the operator codes developed and freely available to the WRF users, we aim to trigger further GNSS tropospheric gradient assimilation studies.

A Novel Approach of Cloud Computing Network for Authentication and Security Enhancement of IoT Enabled Cancer Forecasting System

Recently, a variety of approaches have been employed to address a broad spectrum of real-world issues; these methodology cover a variety of areas, including healthcare systems. Previous researchers concentrated on health-care monitoring software. It had several shortcomings, such as poor health-care data storage, time, expense, and processing complexity. This paper proposes a unique IoT-enabled and secured clinical monitoring paradigm to address these issues. Initially, implant several sensors to gather information on vital indicators like body temperature fluctuation. Phone numbers, marital status, heart rate deviation, residence, name, age, and blood pressure are among the patient's health information. The IoT medical sensor dataset is used in this investigation. During pre-processing, extra unnecessary attributes are removed, resulting in data size reduction and normalization. A convolutional neural network supporting the classification of cancer sickness that is based on the improved teaching-learning optimization (CNN-ITLO) method. The CNN-ITLO model ascertains whether or not the patient is cancer-prone based on the sensor input. The management of the hospital receives the gathered data after which it is analyzed. Lastly, the homomorphic encryption approach is used to encrypt and store the patient's data on the cloud. The Java platform will be used to carry out the recommended work. According to the experiment results, the suggested method performed better than current cutting-edge practices.

A new drought model for disaster risk management in the Punjab, Sindh and Baluchistan provinces of Pakistan

Drought poses a continual threat to both lives and livelihoods in the Global South. Although the impact on food security from drought could be reduced through early release of funds, the humanitarian sector typically reacts to crises rather than anticipates them. A significant challenge lies in devising a drought monitoring and forecasting system that can function across environmentally and economically diverse regions. This is particularly evident in Pakistan, which encompasses environments ranging from fertile riverbeds to arid deserts. This paper details the development, implementation, and operation of an anticipatory drought Disaster Risk Financing (DRF) programme for the provinces of Punjab, Sindh, and Baluchistan in Pakistan. Key to the DRF development are a new yield model for the primary crop in the target season (winter wheat), and a novel forecasting system for four seasonal drought indicators - namely winter wheat yield, precipitation, normalised difference vegetation index (NDVI) and vegetation health index (VHI). Formal evaluations demonstrate that the forecasts are skillful up to 2 months in advance of the end of the season – enabling anticipatory release of funds. The work presented here is applicable beyond Pakistan. Indeed, the model and the methodologies are sufficiently broad and adaptable to be utilised in arid and semi-arid regions across the Global South.

Assessing the potential impact of assimilating total surface current velocities in the Met Office’s global ocean forecasting system

Accurate prediction of ocean surface currents is important for marine safety, ship routing, tracking of pollutants and in coupled forecasting. Presently, velocity observations are not routinely assimilated in global ocean forecasting systems, largely due to the sparsity of the observation network. Several satellite missions are now being proposed with the capability to measure Total Surface Current Velocities (TSCV). If successful, these would substantially increase the coverage of ocean current observations and could improve accuracy of ocean current forecasts through data assimilation. In this paper, Observing System Simulation Experiments (OSSEs) are used to assess the impact of assimilating TSCV in the Met Office’s global ocean forecasting system. Synthetic observations are generated from a high-resolution model run for all standard observation types (sea surface temperature, profiles of temperature and salinity, sea level anomaly and sea ice concentration) as well as TSCV observations from a Sea surface KInematics Multiscale monitoring (SKIM) like satellite. The assimilation of SKIM like TSCV observations is tested over an 11 month period. Preliminary experiments assimilating idealised single TSCV observations demonstrate that ageostrophic velocity corrections are not well retained in the model. We propose a method for improving ageostrophic currents through TSCV assimilation by initialising Near Inertial Oscillations with a rotated incremental analysis update (IAU) scheme. The OSSEs show that TSCV assimilation has the potential to significantly improve the prediction of velocities, particularly in the Western Boundary Currents, Antarctic Circumpolar Current and in the near surface equatorial currents. For global surface velocity the analysis root-mean-square-errors (RMSEs) are reduced by 23% and there is a 4-day gain in forecast RMSE. There are some degradations to the subsurface in the tropics, generally in regions with complex vertical salinity structures. However, outside of the tropics, improvements are seen to velocities throughout the water column. Globally there are also improvements to temperature and sea surface height when TSCV are assimilated. The TSCV assimilation largely corrects the geostrophic ocean currents, but results using the rotated IAU method show that the energy at inertial frequencies can be improved with this method. Overall, the experiments demonstrate significant potential benefit of assimilating TSCV observations in a global ocean forecasting system.

The First Operational Version of Taiwan Central Weather Bureau’s One-Tier Global Atmosphere–Ocean Coupled Forecast System for Seasonal Prediction

Abstract The first version of the Taiwan Central Weather Bureau one-tier (TCWB1T) fully coupled global atmospheric and oceanic modeling forecast system had been developed and implemented as a routine operation for seasonal prediction at Central Weather Bureau (CWB) in 2017, with a minor revision in 2020. Based on NCEP CFSv1, the global atmospheric model in NCEP CFSv1 was replaced by CWB’s atmospheric global spectral model (GSM) and coupled with the GFDL MOM3. Several parameters have been tested and tuned in the CWB atmospheric GSM, achieving an optimal configuration with better sea surface temperature (SST) predictions for integration more than one year. Using NCEP CFSR as the initial condition, TCWB1T conducted hindcasts from 1982 to 2011 and forecasts from 2012 to 2019 to analyze its performance. The results of these hindcasts and forecasts show that the TCWB1T can make useful predictions as verified against the observations of OISST, ERSST, CFSR, and GPCP based on the methods of EOF, RMSE, anomaly correlation, ranked probability skill score (RPSS), reliability diagram (RD), and relative operating characteristics (ROCs). TCWB1T also has the same level of skill scores as NCEP CFSv2 and/or the ECMWF fifth-generation seasonal forecast system (SEAS5), based on EOF, anomaly pattern correlation, climatological bias, RMSE, temporal correlation, and anomaly correlation percentage of forecast skill. TCWB1T shows forecast skill that is better in winter than in summer. Overall, it indicates that TCWB1T can be used for seasonal ENSO predictions.

A novel optimization model based on fuzzy time series for short-term Air Quality Index forecasting

The problem of air quality forecasting has caused a heated discussion among scholars at home and abroad. Short term air quality forecasting substantially impacts regulatory effectiveness to improve environmental and human health. Therefore, many scholars have proposed a lot of Air Quality Index (AQI) forecasting models to improve air quality forecasting performance. However, the fuzziness of air quality data is often ignored, which may reduce the effectiveness of the forecasting. In this study, a new fuzzy forecasting system that includes a fuzzy time series, data preprocessing technique, multi-objective bat optimization algorithm, and forecasting algorithms is proposed to increase air quality forecasting performance and accuracy. To evaluate the forecasting system effectiveness, one-hour AQI data collected from four cities in China are applied in three experiments. The experiment results find that the proposed forecasting system can effectively utilize the fuzziness of air quality data, and it not only improves the forecasting accuracy but also achieves a higher degree of certainty, which can effectively assist air quality supervision.

Contributions of Initial Conditions and Meteorological Forecast to Subseasonal-to-Seasonal Hydrological Forecast Skill in Western Tropical South America

Abstract Hydrological predictions at subseasonal-to-seasonal (S2S) time scales can support improved decision-making in climate-dependent sectors like agriculture and hydropower. Here, we present an S2S hydrological forecasting system (S2S-HFS) for western tropical South America (WTSA). The system uses the global NASA Goddard Earth Observing System S2S meteorological forecast system (GEOS-S2S) in combination with the generalized analog regression downscaling algorithm and the NASA Land Information System (LIS). In this implementation study, we evaluate system performance for 3-month hydrological forecasts for the austral autumn season (March–May) using ensemble hindcasts for 2002–17. Results indicate that the S2S-HFS generally offers skill in predictions of monthly precipitation up to 1-month lead, evapotranspiration up to 2 months lead, and soil moisture content up to 3 months lead. Ecoregions with better hindcast performance are located either in the coastal lowlands or in the Amazon lowland forest. We perform dedicated analysis to understand how two important teleconnections affecting the region are represented in the S2S-HFS: El Niño–Southern Oscillation (ENSO) and the Antarctic Oscillation (AAO). We find that forecast skill for all variables at 1-month lead is enhanced during the positive phase of ENSO and the negative phase of AAO. Overall, this study indicates that there is meaningful skill in the S2S-HFS for many ecoregions in WTSA, particularly for long memory variables such as soil moisture. The skill of the precipitation forecast, however, decays rapidly after forecast initialization, a phenomenon that is consistent with S2S meteorological forecasts over much of the world.

How well can global ensemble forecasts predict tropical cyclones in the southwest Indian Ocean?

AbstractThe southwest Indian Ocean (SWIO) recently experienced its most active, costliest and deadliest cyclone season on record (2018–2019). The anticipation and forecasting of natural hazards, such as tropical cyclones, are crucial to preparing for their impacts, but it is important to understand how well forecasting systems can predict them. Despite the vulnerability of the SWIO to tropical cyclones, comparatively little research has focused on this region, including understanding the ability of numerical weather prediction systems to predict cyclones and their impacts in southeast Africa. In this study, we evaluate ensemble probabilistic and high‐resolution deterministic forecasts of tropical cyclones in the SWIO from 2010 to 2020, using two state‐of‐the‐art global forecasting systems: one from the European Centre for Medium‐Range Weather Forecasts (ECMWF) and the other from the U.K. Met Office. We evaluate predictions of the track, assessing the location of the centre of each storm and its speed of movement, as well as its intensity, looking at maximum wind speeds and minimum central pressure, and discuss how the forecasts have evolved over the 10‐year period. Overall, ECMWF typically provides more accurate forecasts, but both systems tend to underestimate translation speed and intensity. We also investigate the impact of the Madden‐Julian Oscillation (MJO) on tropical cyclones and their forecasts. The MJO impacts where and when tropical cyclones form, their tracks and intensities, which in turn impacts forecast skill. These results are intended to provide an increased understanding of the ability of global forecasting systems to predict tropical cyclones in the SWIO, for the purpose of decision making and anticipatory action.

Tropical cyclone wave data assimilation impact on air-ocean-wave coupled Hurricane Harvey (2017) forecast

The impact of surface wave assimilation on hurricane track and intensity forecasts has been investigated using a fully coupled air-ocean-wave tropical cyclone data assimilation and forecast modeling system. A new 3DVAR wave assimilation method in the Navy Coupled Ocean Data Assimilation system (NCODA) maps the 1D wave energy spectra from buoys to 2D directional wave energy spectra using the maximum likelihood method (MLM) and corrects the wave model forecast component directional wave energy spectra. The Coupled Ocean/Atmosphere Mesoscale Prediction System for Tropical Cyclone Prediction (COAMPS-TC) is used to conduct three Hurricane Harvey (2017) air-ocean-wave coupled data assimilation and forecasting experiments with and without the wave data assimilation. Hurricane Harvey traversed through the Western Gulf of Mexico from 24 August to 1 September, 2017 and made landfall in the Texas and Louisiana coast. Validation of track, maximum wind speed, significant wave height, and mean absolute wave periods show wave assimilation of the 1D wave energy spectra from 13 National Data Buoy Center (NDBC) buoys reduced the forecast errors of these parameters compared to experiments without the wave assimilation. In spite of this positive outcome, the wave assimilation is unable to reduce Harvey’s 0-120 h forecast mean wave direction errors and correlation compared to the NDBC buoy time series

High flow prediction model integrating physically and deep learning based approaches with quasi real-time watershed data assimilation

When operating a flood forecasting system, it is crucial to prioritize both promptness and accuracy, along with reflecting the latest watershed conditions. This study proposes a hybrid model for rainfall-induced high flow prediction that combines an instantaneous physically-based model and a deep learning-based rainfall loss model assimilating with quasi real-time watershed conditions. Its primary objective is to present immediate and reliable high flow predictions, ensuring stability in prediction procedures. The surface runoff component of the model is based on nonlinear instantaneous unit hydrograph (IUH) derived using a dynamic wave model, which considers the nonlinearity between the rainfall excess intensity and the time to peak and peak flow of the IUH. To account for rainfall loss, which can significantly influence rainfall-runoff quantity, Long Short-Term Memory (LSTM) model is employed to establish link between key rainfall loss parameters and the latest watershed conditions obtained from the Global Land Data Assimilation System (GLDAS). The application of the proposed model to 28 high flow events reveals several noteworthy outcomes. Firstly, unlike conventional models that depend on fixed parameter values specific to each event, the proposed model offers immediate, stable, and highly accurate high flow predictions without the need for manual calibration. Secondly, the prioritization of parameters reflecting watershed conditions varies between different watersheds and depends on the rainfall events. These findings indicate the necessity to estimate rainfall loss parameters individually for each rainfall-runoff event in each watershed, as no universal value exists for these parameters. Lastly, despite the limited number of test cases conducted in this study, the LSTM model achieved sufficiently accurate rainfall loss estimation for high flow prediction using only 50 datasets.

Development of Indian summer monsoon precipitation biases in two seasonal forecasting systems and their response to large-scale drivers

Abstract. The Met Office Global Coupled Model (GC) and the National Centers for Environmental Prediction (NCEP) Climate Forecast System (CFSv2) are both widely used for predicting and simulating the Indian summer monsoon (ISM), and previous studies have demonstrated similarities in the biases in both systems at a range of timescales from weather forecasting to climate simulation. In this study, ISM biases are studied in seasonal forecasting setups of the two systems in order to provide insight into how they develop across timescales. Similarities are found in the development of the biases between the two systems, with an initial reduction in precipitation followed by a recovery associated with an increasingly cyclonic wind field to the north-east of India. However, this occurs on longer timescales in CFSv2, with a much stronger recovery followed by a second reduction associated with sea surface temperature (SST) biases so that the bias at longer lead times is of a similar magnitude to that in GC. In GC, the precipitation bias is almost fully developed within a lead time of just 8 d, suggesting that carrying out simulations with short time integrations may be sufficient for obtaining substantial insight into the biases in much longer simulations. The relationship between the precipitation and SST biases in GC seems to be more complex than in CFSv2 and differs between the early part of the monsoon season and the later part of the monsoon season. The relationship of the bias with large-scale drivers is also investigated, using the boreal summer intraseasonal oscillation (BSISO) index as a measure of whether the large-scale dynamics favour increasing, active, decreasing or break monsoon conditions. Both models simulate decreasing conditions the best and increasing conditions the worst, in agreement with previous studies and extending these previous results to include CFSv2 and multiple BSISO cycles.