Estimation of systematic error in an equatorial ocean model using data assimilation

Assimilation of temperature observations into an ocean model near the equator often results in a dynamically unbalanced state with unrealistic overturning circulations. The way in which these circulations arise from systematic errors in the model or its forcing is discussed. A scheme is proposed, based on the theory of state augmentation, which uses the departures of the model state from the observations to update slowly evolving bias fields. Results are summarized from an experiment applying this bias correction scheme to an ocean general circulation model. They show that the method produces more balanced analyses and a better fit to the temperature observations.

The influence of the QBO on the propagation of equatorial waves into the stratosphere

The variation of stratospheric equatorial wave characteristics with the phase of the quasi-biennial oscillation (QBO) is investigated using ECMWF Re-Analysis and NOAA outgoing longwave radiation (OLR) data. The impact of the QBO phases on the upward propagation of equatorial waves is found to be consistent and significant. In the easterly phase, there is larger Kelvin wave amplitude but smaller westward-moving mixed Rossby–gravity (WMRG) and n = 1 Rossby (R1) wave amplitude due to reduced propagation from the upper troposphere into the lower stratosphere, compared with the westerly phase. Differences in the wave amplitude exist in a deeper layer in summer than in winter, consistent with the seasonality of ambient zonal winds. There is a strong evidence of Kelvin wave amplitude peaking just below the descending westerly phase, suggesting that Kelvin waves act to bring the westerly phase downward. However, the corresponding evidence for WMRG and R1 waves is less clear. In the lower stratosphere there is zonal variation in equatorial waves. This reflects the zonal asymmetry of wave amplitudes in the upper troposphere, the source for the lower-stratospheric waves. In easterly winters the upper-tropospheric WMRG and R1 waves over the eastern Pacific region appear to be somewhat stronger compared to climatology, perhaps because of the accumulation of waves that are unable to propagate upward into the lower stratosphere. Vertical propagation features of these waves are generally consistent with theory and suggest a mixture of Doppler shifting by ambient flows and filtering. Some lower-stratosphere equatorial waves have a connection with preceding tropical convection, especially for Kelvin and R1 waves in winter.

Using seasonal hindcasts to understand the origin of the equatorial cold tongue bias in CGCMs and its impact on ENSO

The cold equatorial SST bias in the tropical Pacific that is persistent in many coupled OAGCMs severely impacts the fidelity of the simulated climate and variability in this key region, such as the ENSO phenomenon. The classical bias analysis in these models usually concentrates on multi-decadal to centennial time series needed to obtain statistically robust features. Yet, this strategy cannot fully explain how the models errors were generated in the first place. Here, we use seasonal re-forecasts (hindcasts) to track back the origin of this cold bias. As such hindcasts are initialized close to observations, the transient drift leading to the cold bias can be analyzed to distinguish pre-existing errors from errors responding to initial ones. A time sequence of processes involved in the advent of the final mean state errors can then be proposed. We apply this strategy to the ENSEMBLES-FP6 project multi-model hindcasts of the last decades. Four of the five AOGCMs develop a persistent equatorial cold tongue bias within a few months. The associated systematic errors are first assessed separately for the warm and cold ENSO phases. We find that the models are able to reproduce either El Niño or La Niña close to observations, but not both. ENSO composites then show that the spurious equatorial cooling is maximum for El Niño years for the February and August start dates. For these events and at this time of the year, zonal wind errors in the equatorial Pacific are present from the beginning of the simulation and are hypothesized to be at the origin of the equatorial cold bias, generating too strong upwelling conditions. The systematic underestimation of the mixed layer depth in several models can also amplify the growth of the SST bias. The seminal role of these zonal wind errors is further demonstrated by carrying out ocean-only experiments forced by the AOCGCMs daily 10-meter wind. In a case study, we show that for several models, this forcing is sufficient to reproduce the main SST error patterns seen after 1 month in the AOCGCM hindcasts.

Seasonal persistence of ozone and zonal wind anomalies in the equatorial stratosphere

Analysis of the variability of equatorial ozone profiles in the Satellite Aerosol and Gas Experiment‐corrected Solar Backscatter Ultraviolet data set demonstrates a strong seasonal persistence of interannual ozone anomalies, revealing a seasonal dependence to equatorial ozone variability. In the lower stratosphere (40–25 hPa) and in the upper stratosphere (6–4 hPa), ozone anomalies persist from approximately November until June of the following year, while ozone anomalies in the layer between 16 and 10 hPa persist from June to December. Analysis of zonal wind fields in the lower stratosphere and temperature fields in the upper stratosphere reveals a similar seasonal persistence of the zonal wind and temperature anomalies associated with the quasi‐biennial oscillation (QBO). Thus, the persistence of interannual ozone anomalies in the lower and upper equatorial stratosphere, which are mainly associated with the well‐known QBO ozone signal through the QBO-induced meridional circulation, is related to a newly identified seasonal persistence of the QBO itself. The upper stratospheric QBO ozone signal is argued to arise from a combination of QBO‐induced temperature and NOx perturbations, with the former dominating at 5 hPa and the latter at 10 hPa. Ozone anomalies in the transition zone between dynamical and photochemical control of ozone (16–10 hPa) are less influenced by the QBO signal and show a quite different seasonal persistence compared to the regions above and below.

Symmetric stability of compressible zonal flows on a generalized equatorial β plane

Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial � plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector. A version of the energy–Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity has the same sign as latitude and the Rayleigh centrifugal stability condition that absolute angular momentum increase toward the equator on surfaces of constant pressure is satisfied. The result generalizes earlier results for hydrostatic and incompressible systems and for systems that do not account for the nontraditional Coriolis force terms. The stability of particular equilibrium zonal velocity, entropy, and density fields is assessed. A notable case in which the effect of the nontraditional Coriolis force is decisive is the instability of an angular momentum profile that decreases away from the equator but is flatter than quadratic in latitude, despite its satisfying both the centrifugal and convective stability conditions.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part II: combined effects of gravity waves and equatorial planetary waves

This study examines the effect of combining equatorial planetary wave drag and gravity wave drag in a one-dimensional zonal mean model of the quasi-biennial oscillation (QBO). Several different combinations of planetary wave and gravity wave drag schemes are considered in the investigations, with the aim being to assess which aspects of the different schemes affect the nature of the modeled QBO. Results show that it is possible to generate a realistic-looking QBO with various combinations of drag from the two types of waves, but there are some constraints on the wave input spectra and amplitudes. For example, if the phase speeds of the gravity waves in the input spectrum are large relative to those of the equatorial planetary waves, critical level absorption of the equatorial planetary waves may occur. The resulting mean-wind oscillation, in that case, is driven almost exclusively by the gravity wave drag, with only a small contribution from the planetary waves at low levels. With an appropriate choice of wave input parameters, it is possible to obtain a QBO with a realistic period and to which both types of waves contribute. This is the regime in which the terrestrial QBO appears to reside. There may also be constraints on the initial strength of the wind shear, and these are similar to the constraints that apply when gravity wave drag is used without any planetary wave drag. In recent years, it has been observed that, in order to simulate the QBO accurately, general circulation models require parameterized gravity wave drag, in addition to the drag from resolved planetary-scale waves, and that even if the planetary wave amplitudes are incorrect, the gravity wave drag can be adjusted to compensate. This study provides a basis for knowing that such a compensation is possible.

The middle-atmosphere Hadley circulation and equatorial inertial adjustment

In the tropical middle atmosphere the climatological radiative equilibrium temperature is inconsistent with gradient-wind balance and the available angular momentum, especially during solstice seasons. Adjustment toward a balanced state results in a type of Hadley circulation that lies outside the “downward control” view of zonally averaged dynamics. This middle-atmosphere Hadley circulation is reexamined here using a zonally symmetric balance model driven through an annual cycle. It is found that the inclusion of a realistic radiation scheme leads to a concentration of the circulation near the stratopause and to its closing off in the mesosphere, with no need for relaxational damping or a rigid lid. The evolving zonal flow is inertially unstable, leading to a rapid process of inertial adjustment, which becomes significant in the mesosphere. This short-circuits the slower process of angular momentum homogenization by the Hadley circulation itself, thereby weakening the latter. The effect of the meridional circulation associated with extratropical wave drag on the Hadley circulation is considered. It is shown that the two circulations are independent for linear (quasigeostrophic) zonal-mean dynamics, and interact primarily through the advection of temperature and angular momentum. There appears to be no significant coupling in the deep Tropics via temperature advection since the wave-driven circulation is unable to alter meridional temperature gradients in this region. However, the wave-driven circulation can affect the Hadley circulation by advecting angular momentum out of the Tropics. The validity of the zonally symmetric balance model with parameterized inertial adjustment is tested by comparison with a three-dimensional primitive equations model. Fields from a middle-atmosphere GCM are also examined for evidence of these processes. While many aspects of the GCM circulation are indicative of the middle-atmosphere Hadley circulation, particularly in the upper stratosphere, it appears that the circulation is obscured in the mesosphere and lower stratosphere by other processes.

Balance model for equatorial long waves

Geophysical fluid models often support both fast and slow motions. As the dynamics are often dominated by the slow motions, it is desirable to filter out the fast motions by constructing balance models. An example is the quasi geostrophic (QG) model, which is used widely in meteorology and oceanography for theoretical studies, in addition to practical applications such as model initialization and data assimilation. Although the QG model works quite well in the mid-latitudes, its usefulness diminishes as one approaches the equator. Thus far, attempts to derive similar balance models for the tropics have not been entirely successful as the models generally filter out Kelvin waves, which contribute significantly to tropical low-frequency variability. There is much theoretical interest in the dynamics of planetary-scale Kelvin waves, especially for atmospheric and oceanic data assimilation where observations are generally only of the mass field and thus do not constrain the wind field without some kind of diagnostic balance relation. As a result, estimates of Kelvin wave amplitudes can be poor. Our goal is to find a balance model that includes Kelvin waves for planetary-scale motions. Using asymptotic methods, we derive a balance model for the weakly nonlinear equatorial shallow-water equations. Specifically we adopt the ‘slaving’ method proposed by Warn et al. (Q. J. R. Meteorol. Soc., vol. 121, 1995, pp. 723–739), which avoids secular terms in the expansion and thus can in principle be carried out to any order. Different from previous approaches, our expansion is based on a long-wave scaling and the slow dynamics is described using the height field instead of potential vorticity. The leading-order model is equivalent to the truncated long-wave model considered previously (e.g. Heckley & Gill, Q. J. R. Meteorol. Soc., vol. 110, 1984, pp. 203–217), which retains Kelvin waves in addition to equatorial Rossby waves. Our method allows for the derivation of higher-order models which significantly improve the representation of Rossby waves in the isotropic limit. In addition, the ‘slaving’ method is applicable even when the weakly nonlinear assumption is relaxed, and the resulting nonlinear model encompasses the weakly nonlinear model. We also demonstrate that the method can be applied to more realistic stratified models, such as the Boussinesq model.

Observations of diurnal and spatial variability of radiative forcing by equatorial deep convective clouds

From geostationary satellite observations of equatorial Africa and the equatorial east Atlantic during May and June 2000 we explore the radiative forcing by deep convective cloud systems in these regions. Deep convective clouds (DCCs) are associated with a mean radiative forcing relative to non–deep convective areas of −39 W m−2 over the Atlantic Ocean and of +13 W m−2 over equatorial Africa (±10 W m−2 in both cases). We show that over land the timing of the daily cycle of convection relative to the daily cycle in solar illumination and surface temperature significantly affects the mean radiative forcing by DCCs. Displacement of the daily cycle of DCC coverage by 2 hours changes their overall radiative effect by ∼10 W m−2, with implications for the simulation of the radiative balance in this region. The timing of the minimum DCC cover over land, close to noon local time, means that the mean radiative forcing is nearly maximized.

Diabatic balance model for the equatorial atmosphere

Using an asymptotic expansion, a balance model is derived for the shallow-water equations (SWE) on the equatorial beta-plane that is valid for planetary-scale equatorial dynamics and includes Kelvin waves. In contrast to many theories of tropical dynamics, neither a strict balance between diabatic heating and vertical motion nor a small Froude number is required. Instead, the expansion is based on the smallness of the ratio of meridional to zonal length scales, which can also be interpreted as a separation in time scale. The leading-order model is characterized by a semigeostrophic balance between the zonal wind and meridional pressure gradient, while the meridional wind v vanishes; the model is thus asymptotically nondivergent, and the nonzero correction to v can be found at the next order. Importantly for applications, the diagnostic balance relations are linear for winds when inferring the wind field from mass observations and the winds can be diagnosed without direct observations of diabatic heating. The accuracy of the model is investigated through a set of numerical examples. These examples show that the diagnostic balance relations can remain valid even when the dynamics do not, and the balance dynamics can capture the slow behavior of a rapidly varying solution.

Observational constraints on atmospheric and oceanic cross-equatorial heat transports: revisiting the precipitation asymmetry problem in climate models

Satellite based top-of-atmosphere (TOA) and surface radiation budget observations are combined with mass corrected vertically integrated atmospheric energy divergence and tendency from reanalysis to infer the regional distribution of the TOA, atmospheric and surface energy budget terms over the globe. Hemispheric contrasts in the energy budget terms are used to determine the radiative and combined sensible and latent heat contributions to the cross-equatorial heat transports in the atmosphere (AHT_EQ) and ocean (OHT_EQ). The contrast in net atmospheric radiation implies an AHT_EQ from the northern hemisphere (NH) to the southern hemisphere (SH) (0.75 PW), while the hemispheric difference in sensible and latent heat implies an AHT_EQ in the opposite direction (0.51 PW), resulting in a net NH to SH AHT_EQ (0.24 PW). At the surface, the hemispheric contrast in the radiative component (0.95 PW) dominates, implying a 0.44 PW SH to NH OHT_EQ. Coupled model intercomparison project phase 5 (CMIP5) models with excessive net downward surface radiation and surface-to-atmosphere sensible and latent heat transport in the SH relative to the NH exhibit anomalous northward AHT_EQ and overestimate SH tropical precipitation. The hemispheric bias in net surface radiative flux is due to too much longwave surface radiative cooling in the NH tropics in both clear and all-sky conditions and excessive shortwave surface radiation in the SH subtropics and extratropics due to an underestimation in reflection by clouds.

Modulation of equatorial Pacific westerly/easterly wind events by the Madden-Julian oscillation and convectively-coupled Rossby waves

Synoptic wind events in the equatorial Pacific strongly influence the El Niño/Southern Oscillation (ENSO) evolution. This paper characterizes the spatio-temporal distribution of Easterly (EWEs) and Westerly Wind Events (WWEs) and quantifies their relationship with intraseasonal and interannual large-scale climate variability. We unambiguously demonstrate that the Madden–Julian Oscillation (MJO) and Convectively-coupled Rossby Waves (CRW) modulate both WWEs and EWEs occurrence probability. 86 % of WWEs occur within convective MJO and/or CRW phases and 83 % of EWEs occur within the suppressed phase of MJO and/or CRW. 41 % of WWEs and 26 % of EWEs are in particular associated with the combined occurrence of a CRW/MJO, far more than what would be expected from a random distribution (3 %). Wind events embedded within MJO phases also have a stronger impact on the ocean, due to a tendency to have a larger amplitude, zonal extent and longer duration. These findings are robust irrespective of the wind events and MJO/CRW detection methods. While WWEs and EWEs behave rather symmetrically with respect to MJO/CRW activity, the impact of ENSO on wind events is asymmetrical. The WWEs occurrence probability indeed increases when the warm pool is displaced eastward during El Niño events, an increase that can partly be related to interannual modulation of the MJO/CRW activity in the western Pacific. On the other hand, the EWEs modulation by ENSO is less robust, and strongly depends on the wind event detection method. The consequences of these results for ENSO predictability are discussed.

The longitudinal variation of equatorial waves due to propagation on a varying zonal flow

The general 1-D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behaviour are found, depending on the sign of the group velocity (cg) and a wave property, B. For B positive the wave energy and the wave number vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang (1988) occurs where cg goes to zero. However for B negative they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analysed in detail using the theory. For non-dispersive Kelvin waves, B reduces to 2, and analytic solution is possible. B is positive for all the waves considered, except for the westward moving mixed Rossby-gravity (WMRG) wave which can have negative as well as positive B. Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic are not consistent with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher latitude wave activity.

ENSO related variation of equatorial MRG and Rossby waves and forcing from higher latitudes

The contrasting behaviour of westward-moving mixed Rossby-gravity (WMRG) and the first Rossby (R1) waves in El Niño (EN) and La Niña (LN) seasons is documented with a focus on the Northern Hemisphere winter. The eastward-moving variance in the upper troposphere is dominated by WMRG and R1 structures that appear to be Doppler-shifted by the flow and are referred to as WMRG-E and R1-E. In the East Pacific and Atlantic the years with stronger equatorial westerly winds have the stronger WMRG and WMRG- E. In the East Pacific, R1 is also a maximum in LN. However, R1-E exhibits an eastward-shift between LN and EN. The changes with ENSO phase provide a test-bed for the understanding of these waves. In the East Pacific and Atlantic, the stronger WMRG-E and WMRG with stronger westerlies are in accord with the dispersion relation with simple Doppler-shifting by the zonal flow. The possible existence of free waves can also explain stronger R1 in EN in the Eastern Hemisphere. 1-D free wave propagation theory based on wave activity conservation is also important for R1. However, this theory is unable to explain the amplitude maxima for other waves observed in the strong equatorial westerly regions in the Western Hemisphere, and certainly not their ENSO-related variation. The forcing of equatorial waves by higher latitude wave activity and its variation with ENSO phase is therefore examined. Propagation of extratropical eastward-moving Rossby wave activity through the westerly ducts into the equatorial region where it triggers WMRG-E is favoured in the stronger westerlies, in LN in the East Pacific and EN in the Atlantic. It is also found that WMRG is forced by Southern Hemisphere westward-moving wavetrains arching into the equatorial region where they are reflected. The most significant mechanism for both R1 and R1-E appear to be lateral forcing by subtropical wavetrains.

Interaction of equatorial waves through resonance with the diurnal cycle of tropical heating

In this work, a new theoretical mechanism is presented in which equatorial Rossby and inertio-gravity wave modes may interact with each other through resonance with the diurnal cycle of tropical deep convection. We have adopted the two-layer incompressible equatorial primitive equations forced by a parametric heating that roughly represents deep convection activity in the tropical atmosphere. The heat source was parametrized in the simplest way according to the hypothesis that it is proportional to the lower-troposphere moisture convergence, with the background moisture state function mimicking the structure of the ITCZ. In this context, we have investigated the possibility of resonant interaction between equatorially trapped Rossby and inertio-gravity modes through the diurnal cycle of the background moisture state function. The reduced dynamics of a single resonant duo shows that when this diurnal variation is considered, a Rossby wave mode can undergo significant amplitude modulations when interacting with an inertio-gravity wave mode, which is not possible in the context of the resonant triad non-linear interaction. Therefore, the results suggest that the diurnal variation of the ITCZ can be a possible dynamical mechanism that leads the Rossby waves to be significantly affected by high frequency modes.