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.

Equatorial waves (EWs) are synoptic‐ to planetary‐scale propagating disturbances at low latitudes with periods from a few days to several weeks. Here, this term includes Kelvin waves, equatorial Rossby waves, mixed Rossby–gravity waves, and inertio‐gravity waves, which are well described by linear wave theory, but it also other tropical disturbances such as easterly waves and the intraseasonal Madden–Julian Oscillation with more complex dynamics. EWs can couple with deep convection, leading to a substantial modulation of clouds and rainfall. EWs are amongst the dynamic features of the troposphere with the longest intrinsic predictability, and models are beginning to forecast them with an exploitable level of skill. Most of the methods developed to identify and objectively isolate EWs in observations and model fields rely on (or at least refer to) the adiabatic, frictionless linearized primitive equations on the sphere or the shallow‐water system on the equatorial ‐plane. Common ingredients to these methods are zonal wave‐number–frequency filtering (Fourier or wavelet) and/or projections onto predefined empirical or theoretical dynamical patterns. This paper gives an overview of six different methods to isolate EWs and their structures, discusses the underlying assumptions, evaluates the applicability to different problems, and provides a systematic comparison based on a case study (February 20–May 20, 2009) and a climatological analysis (2001–2018). In addition, the influence of different input fields (e.g., winds, geopotential, outgoing long‐wave radiation, rainfall) is investigated. Based on the results, we generally recommend employing a combination of wave‐number–frequency filtering and spatial‐projection methods (and of different input fields) to check for robustness of the identified signal. In cases of disagreement, one needs to carefully investigate which assumptions made for the individual methods are most probably not fulfilled. This will help in choosing an approach optimally suited to a given problem at hand and avoid misinterpretation of the results.

Despite decades of research on the role of moist convective processes in large-scale tropical dynamics, tropical forecast skill in operational models is still deficient when compared to the extratropics, even at short lead times. Here we compare tropical and Northern Hemisphere (NH) forecast skill for quantitative precipitation forecasts (QPFs) in the NCEP Global Forecast System (GFS) and ECMWF Integrated Forecast System (IFS) during January 2015–March 2016. Results reveal that, in general, initial conditions are reasonably well estimated in both forecast systems, as indicated by relatively good skill scores for the 6–24-h forecasts. However, overall, tropical QPF forecasts in both systems are not considered useful by typical metrics much beyond 4 days. To quantify the relationship between QPF and dynamical skill, space–time spectra and coherence of rainfall and divergence fields are calculated. It is shown that while tropical variability is too weak in both models, the IFS is more skillful in propagating tropical waves for longer lead times. In agreement with past studies demonstrating that extratropical skill is partially drawn from the tropics, a comparison of daily skill in the tropics versus NH suggests that in both models NH forecast skill at lead times beyond day 3 is enhanced by tropical skill in the first couple of days. As shown in previous work, this study indicates that the differences in physics used in each system, in particular, how moist convective processes are coupled to the large-scale flow through these parameterizations, appear as a major source of tropical forecast errors.

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.

There is a longstanding challenge in numerical weather and climate prediction to accurately model tropical wave variability, including convectively coupled equatorial waves (CCEWs) and the Madden–Julian oscillation. For subseasonal prediction, the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS) has been shown to be superior to the NOAA Global Forecast System (GFS) in simulating tropical variability, suggesting that the ECMWF model is better at simulating the interaction between cumulus convection and the large-scale tropical circulation. In this study, we experiment with the cumulus convection scheme of the ECMWF IFS in a research version of the GFS to understand which aspects of the IFS cumulus convection scheme outperform those of the GFS convection scheme in the tropics. We show that the IFS cumulus convection scheme produces significantly different tropical moisture and temperature tendency profiles from those simulated by the GFS convection scheme when it is coupled with other physics schemes in the GFS physics package. We show that a consistent treatment of the interaction between parameterized convective plumes in the GFS planetary boundary layer (PBL) and the IFS convection scheme is required for the GFS to replicate the tropical temperature and moisture profiles simulated by the IFS model. The GFS model with the IFS convection scheme, and the consistent treatment between the convection and PBL schemes, produces much more organized convection in the tropics, and generates tropical waves that propagate more coherently than the GFS in its default configuration due to better simulated interaction between low-level convergence and precipitation.