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Characteristics of precipitation estimates for rate and amount from three global high-resolution precipitation products (HRPPs), four global climate data records (CDRs), and four reanalyses are compared. All datasets considered have at least daily temporal resolution. Estimates of global precipitation differ widely from one product to the next, with some differences likely due to differing goals in producing the estimates. HRPPs are intended to produce the best snapshot of the precipitation estimate locally. CDRs of precipitation emphasize homogeneity over instantaneous accuracy. Precipitation estimates from global reanalyses are dynamically consistent with the large-scale circulation but tend to compare poorly to rain gauge estimates since they are forecast by the reanalysis system and precipitation is not assimilated. Regional differences among the estimates in the means and variances are as large as the means and variances, respectively. Even with similar monthly totals, precipitation rates vary significantly among the estimates. Temporal correlations among datasets are large at annual and daily time scales, suggesting that compensating bias errors at annual and random errors at daily time scales dominate the differences. However, the signal-to-noise ratio at intermediate (monthly) time scales can be large enough to result in high correlations overall. It is shown that differences on annual time scales and continental regions are around 0.8 mm day−1, which corresponds to 23 W m−2. These wide variations in the estimates, even for global averages, highlight the need for better constrained precipitation products in the future.

Convectively coupled equatorial waves (CCEWs) are modes of tropical variability that are often seen as potentially beneficial for sub‐seasonal predictions. Quantifying this potential has been proven difficult in operational forecast systems because tropical variability tends to be poorly represented in such models. The European Center for Medium‐Range Weather Forecasts (ECMWF) is a potential exception because it has been shown to have much improved representation of the tropics. Here, ECMWF reforecasts are used to investigate the predicted evolution of CCEWs and how they might impact sub‐seasonal predictions. It is shown that the ECMWF system is able to generate variability consistent with various modes of CCEWs, but CCEWs tend to be weaker in amplitude and their propagation characteristics often deviate from observations. This study suggests that model advancements aimed at improving the deterministic representation of CCEWs are still needed in order to better understand and utilize tropical sources of sub‐seasonal predictive skill. Plain Language Summary Accurate weather forecasts leverage on proper characterization of the current state of the atmosphere and on predictable atmospheric phenomena that constrain the evolution of that state. Tropical weather forecasting is challenging in both aspects: observations are more sparse than in the extratropics, and the evolution of the atmosphere is constrained by large‐scale forcings such as tropical rainfall. This study focuses on the contribution of equatorial waves to low latitude weather forecast skill because these types of disturbances are known to modulate tropical rainfall, which feed back strongly onto the disturbances themselves. The main finding is that the initial state tends to be fairly well represented in forecast systems; however, within a day or two the amplitude of these waves becomes weaker than in observations, which is a decay time much faster than their typical one‐to‐three week lifetimes. Along with errors in the waves propagation characteristics, this loss of amplitude suggests that equatorial waves do not impact precipitation forecast within the models as much as theory and observations imply they should. Key Points Convectively coupled equatorial waves (CCEWs) are a potential source of global sub‐seasonal precipitation skill Operational forecast model's representation of CCEWs has greatly advanced over the last two decades Deviations from observations often attenuate the role of CCEWs as sources of sub‐seasonal predictive skill

The dynamics and momentum budget of the quasi-biennial oscillation (QBO) are examined in ERA5. Because of ERA5’s higher spatial resolution compared to its predecessors, it is capable of resolving a broader spectrum of atmospheric waves and allows for a better representation of the wave–mean flow interactions, both of which are of crucial importance for QBO studies. It is shown that the QBO-induced mean meridional circulation, which is mainly confined to the winter hemisphere, is strong enough to interrupt the tropical upwelling during the descent of the westerly shear zones. Since the momentum advection tends to damp the QBO, the wave forcing is responsible for both the downward propagation and for the maintenance of the QBO. It is shown that half the required wave forcing is provided by resolved waves during the descent of both westerly and easterly regimes. Planetary-scale waves account for most of the resolved wave forcing of the descent of westerly shear zones and small-scale gravity (SSG) waves with wavelengths shorter than 2000 km account for the remainder. SSG waves account for most of the resolved forcing of the descent of the easterly shear zones. The representation of the mean fields in the QBO is very similar in ERA5 and ERA-Interim but the resolved wave forcing is substantially stronger in ERA5. The contributions of the various equatorially trapped wave modes to the QBO forcing are documented in Part II.

Two univariate indices of the Madden–Julian oscillation (MJO) based on outgoing longwave radiation (OLR) are developed to track the convective component of the MJO while taking into account the seasonal cycle. These are compared with the all-season Real-time Multivariate MJO (RMM) index of Wheeler and Hendon derived from a multivariate EOF of circulation and OLR. The gross features of the OLR and circulation of composite MJOs are similar regardless of the index, although RMM is characterized by stronger circulation. Diversity in the amplitude and phase of individual MJO events between the indices is much more evident; this is demonstrated using examples from the Dynamics of the Madden–Julian Oscillation (DYNAMO) field campaign and the Year of Tropical Convection (YOTC) virtual campaign. The use of different indices can lead to quite disparate conclusions concerning MJO timing and strength, and even as to whether or not an MJO has occurred. A disadvantage of using daily OLR as an EOF basis is that it is a much noisier field than the large-scale circulation, and filtering is necessary to obtain stable results through the annual cycle. While a drawback of filtering is that it cannot be done in real time, a reasonable approximation to the original fully filtered index can be obtained by following an endpoint smoothing method. When the convective signal is of primary interest, the authors advocate the use of satellite-based metrics for retrospective analysis of the MJO for individual cases, as well as for the analysis of model skill in initiating and evolving the MJO.

This paper describes stratospheric waves in ERA5 and evaluates the contributions of different types of waves to the driving of the quasi-biennial oscillation (QBO). Because of its higher spatial resolution compared to its predecessors, ERA5 is capable of resolving a broader spectrum of waves. It is shown that the resolved waves contribute to both eastward and westward accelerations near the equator, mainly by the way of the vertical flux of zonal momentum. The eastward accelerations by the resolved waves are mainly due to Kelvin waves and small-scale gravity (SSG) waves with zonal wavelengths smaller than 2000 km, whereas the westward accelerations are forced mainly by SSG waves, with smaller contributions from inertio-gravity and mixed Rossby–gravity waves. Extratropical Rossby waves disperse upward and equatorward into the tropical region and impart a westward acceleration to the zonal flow. They appear to be responsible for at least some of the irregularities in the QBO cycle.

Variability of the Madden‐Julian Oscillation (MJO) inferred from tropical in‐situ observations during 1940–2023 is examined, and compared to that derived from reanalyzes. MJO assessments are challenging because characterizing MJO behavior outside of the satellite era suffers from a lack of detailed information about its observed state, remote signals and often relies on climate models' typically poor MJO representation. This study shows that, while tropical soundings are spatially and temporally sparse, they are still useful for better understanding multi‐decadal MJO amplitude variability. The similarities between variability of the MJO derived from (imperfect) reanalysis products and (sparse) tropical station observations suggest that decadal changes during the last 60 years are physical and not necessarily related to changes in the observational network. The larger differences in MJO amplitude between station and reanalysis prior to 1960 suggest that sparse tropical observations are a barrier to fully characterizing long‐term MJO evolution during the 20th$20\\text{th}$century. Plain Language Summary The Madden‐Julian Oscillation (MJO) is a prominent element of intraseasonal (30‐ to 90‐day) variability in the tropical atmosphere that interacts with faster (weather) and slow (climate) atmospheric processes. The goal of this study is to assess our confidence in various aspects of observed MJO multi‐decadal variability in light of the drastic changes in the global observing system over the last century. We find robust features, for example, an increase in MJO amplitude from the 1960s to 1990s and a decrease in amplitude thereafter to recent times. Those are in contrast to the larger MJO behavior uncertainties prior to 1960, where sparse and infrequent observations in the tropics limit our ability to clearly identify the MJO. Key Points Sparse observations in space and time hinder assessment of long‐term Madden‐Julian Oscillation (MJO) behavior Robust MJO features include an increase in amplitude from 1960 to 1980s and a decrease in amplitude thereafter MJO behavior prior to 1960 is uncertain due to disparities between station observations and reanalyzes

This study examines the relationship between the MJO and convectively coupled equatorial waves (CCEWs) during the CINDY2011/DYNAMO field campaign using satellite-borne infrared radiation data, in order to better understand the interaction between convection and the large-scale circulation. The spatio-temporal wavelet transform (STWT) enables us to document the convective signals within the MJO envelope in terms of CCEWs in great detail, through localization of space–time spectra at any given location and time. Three MJO events that occurred in October, November, and December 2011 are examined. It is, in general, difficult to find universal relationships between the MJO and CCEWs, implying that MJOs are diverse in terms of the types of disturbances that make up its convective envelope. However, it is found in all MJO events that the major convective body of the MJO is made up mainly by slow convectively coupled Kelvin waves. These Kelvin waves have relatively fast phase speeds of 10–13 m s−1 outside of, and slow phase speeds of ~8–9 m s−1 within the MJO. Sometimes even slower eastward propagating signals with 3–5 m s−1 phase speed show up within the MJO, which, as well as the slow Kelvin waves, appear to comprise major building blocks of the MJO. It is also suggested that these eastward propagating waves often occur coincident with n = 1 WIG waves, which is consistent with the schematic model from Nakazawa in 1988. Some practical aspects that facilitate use of the STWT are also elaborated upon and discussed.

The relationship between n = 0 mixed Rossby–gravity waves (MRGs) and eastward inertio-gravity waves (EIGs) from Matsuno’s shallow-water theory on an equatorial beta plane is studied using statistics of satellite brightness temperature Tb and dynamical fields from ERA-Interim data. Unlike other observed convectively coupled equatorial waves, which have spectral signals well separated into eastward and westward modes, there is a continuum of MRG–EIG power standing above the background that peaks near wavenumber 0. This continuum is also present in the signals of dry stratospheric MRGs. While hundreds of papers have been written on MRGs, very little work on EIGs has appeared in the literature to date. The authors attribute this to the fact that EIG circulations are much weaker than those of MRGs for a given amount of divergence, making them more difficult to observe even though they strongly modulate convection. Empirical orthogonal function (EOF) and cross-spectral analysis of 2–6-day-filtered Tb isolate zonally standing modes of synoptic-scale convection originally identified by Wallace in 1971. These display antisymmetric Tb signals about the equator that propagate poleward with a period of around 4 days, along with westward-propagating MRG-like circulations that move through the Tb patterns. Further analysis here and in Part II shows that these signatures are not artifacts of the EOF approach but result from a mixture of MRG or EIG modes occurring either in isolation or at the same time.

A data‐driven dynamical filter is developed to characterize Madden‐Julian Oscillation (MJO) variability, by representing tropical variability with nonorthogonal empirical‐dynamical modes that allow for constructive and destructive interference. We find that two intraseasonal atmospheric modes, an “MJO‐fast” mode (∼ ${\\sim} $45 day period) and a newly identified “MJO‐slow” mode (∼ ${\\sim} $70 day period), alongside El Niño‐Southern Oscillation modes that are not entirely removed by temporal filtering, explain nearly all observed Real‐time Multivariate MJO (RMM) index‐based variability. The fastest growing, and most predictable, MJO events are initiated primarily by the MJO‐fast mode over the Indian Ocean, with subsequent progression across the Maritime Continent resulting from destructive and then constructive interference of the MJO‐fast and MJO‐slow modes. These events, which we demonstrate can be identified at forecast initialization time, are shown to be forecasts of opportunity in the ECMWF operational forecast model, with MJO skill extended by roughly a week compared to all other forecasts.

A precipitation climatology of Africa is documented using 12 years of satellite-derived daily data from the Global Precipitation Climatology Project (GPCP). The focus is on examining spatial variations in the annual cycle and describing characteristics of the wet season(s) using a consistent, objective, and well-tested methodology. Onset is defined as occurring when daily precipitation consistently exceeds its local annual daily average and ends when precipitation systematically drops below that value. Wet season length, rate, and total are then determined. Much of Africa is characterized by a single summer wet season, with a well-defined onset and end, during which most precipitation falls. Exceptions to the single wet season regime occur mostly near the equator, where two wet periods are usually separated by a period of relatively modest precipitation. Another particularly interesting region is the semiarid to arid eastern Horn of Africa, where there are two short wet seasons separated by nearly dry periods. Chiefly, the summer monsoon spreads poleward from near the equator in both hemispheres, although in southern Africa the wet season progresses northwestward from the southeast coast. Composites relative to onset are constructed for selected points in West Africa and in the eastern Horn of Africa. In each case, onset is often preceded by the arrival of an eastward-propagating precipitation disturbance. Comparisons are made with the satellite-based Tropical Rainfall Measuring Mission (TRMM) and gauge-based Famine Early Warning System (FEWS NET) datasets. GPCP estimates are generally higher than TRMM in the wettest parts of Africa, but the timing of the annual cycle and average onset dates are largely consistent.