The methods and basis for atmospheric predictability is different for seasonal range prediction versus that for the daily or even hourly forecasts one obtains from television, radio, or your cell phone “apps”. Weather forecasting developed during the early 20th century through the study of typical phenomena that impact people’s lives such as mid-latitude cyclones and anticyclones, fronts, and their attendant structures. The underlying physics assumes that momentum, energy, and mass are conserved on the appropriate time and space scales. The equations that represent these principles form the basis of numerical models that aide the weather forecaster by predicting the evolution of atmospheric fluid elements with time. This type of weather forecasting has a well-known limit of about 10-14 days  because of the size and rotation rate of the Earth, as well as the mixture of gasses that make up our atmosphere (see  and references therein for more detail). Beyond this limit, statistical techniques must be utilized to construct the monthly or seasonal forecasts that are routinely available via the Climate Prediction Center (CPC), which is part of the National Oceanic and Atmospheric Administration (NOAA).
Monthly and seasonal range forecasts, which are routinely provided beyond one year, are constructed using a variety of statistical techniques. These include, but are not limited to, using persistence, contingency models, and analogues. A persistence forecast is the simplest and means that what is happening this month or season will continue to happen during the next period. Persistence can be defined also as projecting the next month or season forecast based on a trend observed over the past few observation periods. Contingency forecasts are constructed based on the statistics compiled from past observations under certain background atmosphere-ocean conditions, the most influential of these being El Niño and Southern Oscillation (ENSO - e.g. El Niño, neutral, and La Niña). Analogue forecasts are similar in that we say that conditions this month very closely resemble those from a previous month at some time in the past. Then, we forecast that our next month’s conditions will be similar to the month that followed the historical month identified as an analogue. The contingency and analogue techniques require knowledge of the dominant teleconnections impacting weather and climate on the time scale of a few weeks to a few years, or even decades. The work of  (and references therein) provide the basis for using contingency and analogues techniques in this part of the world.
Teleconnections are defined as weather or climate conditions that correlate strongly over large regions of the earth . These correlations are driven concurrently by the underlying surface conditions and their impact on the jet stream (and vice-versa), and have been noted by many researchers since the early 1930s . Patterns influencing the weather and climate of the Midwest USA including Missouri have been noted since the 1940s  (and references therein). At the University of Missouri, efforts began in the 1980s to relate Pacific Ocean region conditions to Midwest USA weather and climate  using teleconnections such as ENSO and the Pacific North American (PNA)  pattern. The work of  found that the monthly Pacific Region sea surface temperatures (SSTs) can be classified into seven different clusters representing different phases of ENSO (three El Niño, two La Niña, and two neutral) that are associated with different configurations of the jet stream. Then, these general circulation conditions correlate to monthly temperature and precipitation conditions in the Midwest overall and Missouri specifically.
Efforts to build on  in order to produce more detailed contingency models of local temperature and precipitation variations that include the influence of ENSO-related interannual variability and interdecadal variability as related to the Pacific Decadal Oscillation (PDO) culminated in the work of . This study  shows that the typical surface conditions defined by Pacific SSTs and then the interannual variation of temperature and precipitation conditions across the central USA including Missouri have an interdecadal signal. Similar information can be obtained through the Useful-to-Usable (U2U) website (e.g. http://mrcc.isws.illinois.edu/U2U/CPV/), but they use the ENSO and Arctic Oscillation (AO). Winter (December – February) and Summer (June – August) temperature and precipitation forecasts have been produced by this research group since 2002.
As part of the work proposed for the Missouri EPSCOR project, the correlation of crop yields (specifically corn and soybean) to seasonal ENSO and PDO conditions were performed by . Traditionally, ENSO was thought to have little influence on summer season conditions since ENSO generally is strongest during October to December and wanes during the spring. The work of  showed that summer season temperature and precipitation conditions in the Missouri region correlate more strongly with the direction of the ENSO transition (e.g. warm and dry summers correlate strongly with transitions from El Niño to La Niña conditions). Also,  demonstrated that this transitional ENSO association is observed also over distant parts of the Northern Hemisphere. The results of  correlated crop yields to these ENSO transition periods for Missouri during much of the 20th and into the 21st centuries. This work was followed by  who examined the variability and changes in bioclimatic potential over the last 35 years, and the implications for future climate change.
Thus, the key to generating a good seasonal temperature and precipitation forecast requires knowing the current observational conditions, but also the projected state of ENSO for the upcoming fall. ENSO state forecasts are generated by CPC and can be found on their website or at the International Research Institute for Climate and Society (Earth Institute, Columbia University - https://iri.columbia.edu/our-expertise/climate/forecasts/enso/current/). These ensemble-type forecasts are generated using both statistical models and dynamic models (General Circulation Models – GCMs). The predictive skill of the seasonal forecasts generated here versus climatology borrows short range weather forecasting using the “Forecast Skill” score  (and references therein), and modified by . The scores were then compared in order to determine if our forecasts are better statistically than climatology and others. The performance of our forecasts versus climatology and the CPC forecasts are shown under the “SCORES” tab on this website. Additionally, predictability on the sub-seasonal time-scale is a recent topic of interest in the meteorological and climate communities. Statistical and dynamic predictability in the one to four week time-scale may have many agricultural applications such as when to plant, harvest, or apply irrigation and/or fertilizer. These forecasts range from being at the limit of dynamic predictability, but are less than traditional 30-day forecast period and will utilize many of the ideas of monthly and seasonal range forecasting described above. The use of teleconnections for forecasting on the one to four week time-period is especially skillful in identifying anomalous temperature  (or precipitation) conditions.
Lastly, atmospheric blocking is a long-lived, large-scale, quasi-stationary ridge in the jet stream that can influence the weather over large portions of the globe during their lifetime. Their episodic occurrence can dictate regional weather and climate conditions for an entire season or more , . Atmospheric blocking and large-scale atmospheric flow regimes ,  persist for approximately 8 – 14 days, typically, which is similar to the dynamic weather predictability limit identified above. In order to identify these large-scale flow regime transitions, or the onset and decay of blocking, a quantity called Integrated Enstrophy (IE) has proven to be useful. IE was developed by  and is related to atmospheric entropy and predictability . The ability to identify the onset or termination of flow regimes, especially anomalous regimes such as those that occurred during spring 2018 , would not only have benefits for improving short and medium range weather forecasts, but have wide societal applications. Finally,  demonstrated that the predictability implied by flow regime transition would not change appreciably for near term (mid-century) mid-range climate warming scenario.