This study compares trends in the Hadley cell (HC) strength using different metrics applied to the ECMWF ERA5 and ERA-Interim reanalyses for the period 1979–2018. The HC strength is commonly evaluated by metrics derived from the mass-weighted zonal-mean stream function in isobaric coordinates. Other metrics include the upper tropospheric velocity potential, the vertical velocity in the mid-troposphere, and the water vapour transport in the lower troposphere. Seven known metrics of HC strength are complemented here by a metric of the spatially averaged HC strength, obtained by averaging the stream function in the latitude–pressure (
The Hadley circulation is a thermally forced overturning circulation consisting of two symmetrical cells, which span between the tropics and the subtropics. Each cell consists of the ascending branch in the deep tropics, which is associated with enhanced precipitation, poleward upper tropospheric flow, and the descending motion in the subtropics that suppresses rainfall. The cell is completed by a frictional return flow in the lower troposphere. Therefore, potential changes in the Hadley cells (HCs), either to their strength or their meridional extent, will have a profound impact on the global hydrological cycle
Several studies of HC strength using reanalyses suggested strengthening of both the northern Hadley cell (NHC) and southern Hadley cell (SHC) in recent decades. However, the reported magnitude and uncertainty of the trends differ
The majority of studies describe the HC by the mass-weighted zonal-mean stream function the maximum (minimum) values of the maximum (minimum) value of the vertical average of the maxima (minima) of
The strength of the overall Hadley circulation can also be evaluated using the velocity potential in the upper branch of the HC (located in the upper troposphere). The meridional divergent flow is strongest there, which is associated with the maximal upward motions in the layer beneath
In the past few years, several studies have compared different metrics of the tropical expansion
The paper is organized as follows: Section
Two modern ECMWF reanalyses are analysed: ERA5
A new, energy-based metric is a product of a multivariate normal-mode function decomposition and it requires both wind components and a pseudo-geopotential field that combines the hydrostatic geopotential and the mean sea level pressure term (see Sect.
ERA5 has a higher model resolution than ERA-Interim (0.3
The trends and their uncertainties are compared for several metrics of HC strength:
Maximum (minimum) of annual/seasonal-mean stream function between 40 Maximum (minimum) of annual/seasonal-mean stream function at predefined pressure levels (e.g. 400, 500 hPa etc.) within 40 Stream function value at the location of climatological (1979–2018) annual/seasonal-mean maximum (minimum) of the NHC (SHC) strength, An average of maximum (minimum) values of annual/seasonal-mean Maximum of the zonal-mean velocity potential Minimum of the zonal-mean vertical (pressure) velocity Spatially averaged HC strength, which is obtained by spatially averaging the stream-function field in the latitude–pressure plane. For the NHC, it yields Effective wind for water vapour transport An energy-based metric
Seasonal-mean climatology of Hadley circulation (red and blue contours) and its trends (shading) in ERA5 reanalysis between 1979 and 2018. Red contours indicate positive climatological stream-function values, i.e.
The described metrics have different properties. Metrics (1)–(4), (7), and (8) distinguish between the two Hadley cells, whereas metrics (5), (6), and (9) do not. Metrics (1)–(3) are sensitive to the vertical inhomogeneities in the strength of the Hadley cell by definition. Metric (8) describes only the return flow of the Hadley circulation in the lower troposphere. Metric (4) averages over the vertical, but not the meridional, inhomogeneity. Metrics (5) and (6) only describe the ascending branch of the Hadley circulation. New metric (7) alleviates the sensitivity to the spatial (meridional and vertical) inhomogeneities by spatial averaging. The same applies to the new metric (9), which is a global metric largely different from all other metrics and applied here without any special tuning. Metrics (8) and (9) include nonlinear terms (Eqs.
In the following section, we explore the sensitivity of the trends to different metrics of HC strength.
Trends are evaluated from the time series of
Figure
The sensitivity of the trends in the annual-mean and seasonal-mean HC strength to the stream-function metrics (1)–(4) and (7), described in Sect. 2.2, is shown in Fig.
Trends in NHC strength
The differences between trends in seasonal-means at different pressure levels are even larger. For example, the winter NHC exhibits a large and significant strengthening in the lower troposphere (700–800 hPa) with trends around
The differences in the trends in seasonal-means at various pressure levels point towards the unreliability of the trend. Furthermore, magnitudes of the differences between metrics are of the same order as the uncertainties of the derived trends for individual metrics. Thus, by measuring the maximum HC strength at a selected pressure level, e.g. 500 hPa (as in metric 2), the estimated trends are affected by the limitation of the metric.
Another notable feature of Figs.
Metric (1) exhibits significant year-to-year variability in the levels of
Metric (2) is sensitive to the vertical inhomogeneity of the trend in HC strength (as seen from
Vertically averaged maximum and minimum values of
The HC strength measured by metric (7) is on average weaker than in other
The time series
Time series of NHC strength
Trends in the annual-mean HC strength normalized by their climatological mean values: for the NHC
Annual-mean HC strength trends normalized by the climatological mean values of HC strength in ERA5 between 1979 and 2018. The trends derived from stream-function metrics (which distinguish between the NHC and the SHC) are separated from the trends derived from other metrics (which describe the two cells together). The values in parentheses denote the standard error of the trend estimates.
Correlations of time series, derived from different metrics of Hadley cell strength, described in Sect.
In general, the normalized stream-function metrics are well aligned in both HCs (Fig.
A widely utilized HC strength metric
The above results suggest that the
The time series of the other stream-function metrics, i.e.
Despite the high correlations, the relative trends in
The time series derived from
The velocity-potential metrics
The trends derived from the
The effective wind metric (8) aligns well with the stream-function metrics (Fig.
The unbalanced energy metric
To quantify the role of the stratospheric circulation in the uncertainties of the trends for the
In this study, we have analysed a number of metrics of the Hadley circulation strength including metrics based on the mass-weighted mean meridional stream function, velocity potential, pressure velocity
By analysing the stream-function trends in the latitude–pressure plane, we showed that the trends are spatially inhomogeneous, both meridionally and vertically (Figs.
Presented opposing trends suggest that the contribution of physical mechanisms that drive the Hadley cells and govern their strength (diabatic heating, friction processes, eddy heat and momentum fluxes, static stability etc.) are likely to vary with the chosen HC strength metric
Because of the different mechanisms involved in HC dynamics, the choice of the HC strength metric will ultimately depend on the application in a specific study. However, our results demonstrate that caution is needed when comparing HC trends from different studies using different metrics of HC strength. In light of all the results, we would suggest using the average stream function as the metric of overall HC strength whenever interested in the variability and trends in each Hadley cell separately. On the other hand, the unbalanced energy metric is a physically sound choice for analysing the changes in the global zonal-mean circulation.
Note that evaluations of HC strength and its trends may also benefit from analyses in alternative coordinate systems, such as thermodynamic coordinates
MODES software
As in Fig.
The area (red/blue) where the stream function is spatially averaged to evaluate NHC/SHC strength following metric (7) for the case of 1979–2018 average zonal-mean stream function in ERA5 reanalysis. The averaging area is data adaptive.
The 2018 mean horizontal winds for an unbalanced circulation component in ERA5 reanalysis, in different seasons, on the 200 hPa pressure level. Wind intensity is shown by the length of the wind vectors.
The 2018 mean Hadley circulation (red and blue contours) in ERA5 reanalysis computed from
As in Fig.
As in Fig.
Level of maximum and minimum stream function in annual-mean Hadley circulation between 1979 and 2018 in ERA5 and ERA-Interim reanalyses.
As in Fig.
As in Table
The results of this paper are based on the ERA-Interim reanalysis dataset, Copernicus Climate Change Service (C3S), available from
Data used to generate Figs. 2–5 and A3–A6 are publicly available at
MP performed numerical analysis and generated all figures. ŽZ devised the research, performed the modal analysis, and wrote the first draft of the manuscript. NŽ oversaw modal analysis. LB and NŽ provided additional insight and helped improve the manuscript for the final version.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
We thank three anonymous reviewers for their comprehensive reviews. Research of Nedjeljka Žagar contributes to the Cluster of Excellence 405 “CLICCS−Climate, Climatic Change, and Society” of the Center for Earth System Research and Sustainability (CEN) of Universität Hamburg.
This research has been supported by the Javna Agencija za Raziskovalno Dejavnost RS (grant no. J1-9431 and Programme P1-0188) and Trond Mohn Foundation (project BCPU, grant no. BFS2018TMT01).
This paper was edited by Juliane Schwendike and reviewed by three anonymous referees.