Is the subdominant part of the energy spectrum due to downscale energy cascade hidden in quasi-geostrophic turbulence?

In systems governing two-dimensional turbulence, surface quasi-geostrophic turbulence, (more generally $\alpha$-turbulence), two-layer quasi-geostrophic turbulence, etc., there often exist two conservative quadratic quantities, one ``energy''-like and one ``enstrophy''-like. In a finite inertial range there are in general two spectral fluxes, one associated with each conserved quantity. We derive here an inequality comparing the relative magnitudes of the ``energy'' and ``enstrophy'' fluxes for finite or infinitesimal dissipations, and for hyper or hypo viscosities. When this inequality is satisfied, as is the case of 2D turbulence,where the energy flux contribution to the energy spectrum is small, the subdominant part will be effectively hidden. In sQG turbulence, it is shown that the opposite is true: the downscale energy flux becomes the dominant contribution to the energy spectrum. A combination of these two behaviors appears to be the case in 2-layer QG turbulence, depending on the baroclinicity of the system.Comment: 23 pages; accepted at Discrete and Continuous Dynamical Systems B; Major revisio

A New Proof on Net Upscale Energy Cascade in 2D and QG Turbulence

A general proof that more energy flows upscale than downscale in two-dimensional (2D) turbulence and barotropic quasi-geostrophic (QG) turbulence is given. A proof is also given that in Surface QG turbulence, the reverse is true. Though some of these results are known in restricted cases, the proofs given here are pedagogically simpler, require fewer assumptions and apply to both forced and unforced cases.Comment: v1: submitted to J. Fluid. Mech v2: revised and accepted by J. Fluid. Mech, 17 page

Solar cycle as a distinct line of evidence constraining Earth’s transient climate response

Severity of warming predicted by climate models depends on their Transient Climate Response (TCR). Inter-model spread of TCR has persisted at ~ 100% of its mean for decades. Existing observational constraints of TCR are based on observed historical warming response to historical forcing and their uncertainty spread is just as wide, mainly due to forcing uncertainty, and especially that of aerosols. Contrary, no aerosols are involved in solar-cycle forcing, providing an independent, tighter, constraint. Here, we define a climate sensitivity metric: time-dependent response regressed against time-dependent forcing, allowing phenomena with dissimilar time variations, such as the solar cycle with 11-year cyclic forcing, to be used to constrain TCR, which has a linear time-dependent forcing. We find a theoretical linear relationship between the two. The latest coupled atmosphere-ocean climate models obey the same linear relationship statistically. The proposed observational constraint on TCR is about [Formula: see text] as narrow as existing constraints. The central estimate, 2.2 oC, is at the midpoint of the spread of the latest generation of climate models, which are more sensitive than those of the previous generations

Modulation of the Period of the Quasi-Biennial Oscillation by the Solar Cycle

The authors examine the mechanism of solar cycle modulation of the Quasi-Biennial Oscillation (QBO) period using the Two-and-a-Half-Dimensional Interactive Isentropic Research (THINAIR) model. Previous model results (using 2D and 3D models of varying complexity) have not convincingly established the proposed link of longer QBO periods during solar minima. Observational evidence for such a modulation is also controversial because it is only found during the period from the 1960s to the early 1990s, which is contaminated by volcanic aerosols. In the model, 200- and 400-yr runs without volcano influence can be obtained, long enough to establish some statistical robustness. Both in model and observed data, there is a strong synchronization of the QBO period with integer multiples of the semiannual oscillation (SAO) in the upper stratosphere. Under the current level of wave forcing, the period of the QBO jumps from one multiple of SAO to another and back so that it averages to 28 months, never settling down to a constant period. The “decadal” variability in the QBO period takes the form of “quantum” jumps; these, however, do not appear to follow the level of the solar flux in either the observation or the model using realistic quasi-periodic solar cycle (SC) forcing. To understand the solar modulation of the QBO period, the authors perform model runs with a range of perpetual solar forcing, either lower or higher than the current level. At the current level of solar forcing, the model QBO period consists of a distribution of four and five SAO periods, similar to the observed distribution. This distribution changes as solar forcing changes. For lower (higher) solar forcing, the distribution shifts to more (less) four SAO periods than five SAO periods. The record-averaged QBO period increases with the solar forcing. However, because this effect is rather weak and is detectable only with exaggerated forcing, the authors suggest that the previous result of the anticorrelation of the QBO period with the SC seen in short observational records reflects only a chance behavior of the QBO period, which naturally jumps in a nonstationary manner even if the solar forcing is held constant, and the correlation can change as the record gets longer

Nonstationary Synchronization of Equatorial QBO with SAO in Observations and a Model

It has often been suggested that the period of the quasi-biennial oscillation (QBO) has a tendency to synchronize with the semiannual oscillation (SAO). Apparently the synchronization is better the higher up the observation extends. Using 45 yr of the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) data of the equatorial stratosphere up to the stratopause, the authors confirm that this synchronization is not just a tendency but a robust phenomenon in the upper stratosphere. A QBO period starts when a westerly SAO (w-SAO) descends from the stratopause to 7 hPa and initiates the westerly phase of the QBO (w-QBO) below. It ends when another w-SAO, a few SAO periods later, descends again to 7 hPa to initiate the next w-QBO. The fact that it is the westerly but not the easterly SAO (e-SAO) that initiates the QBO is also explained by the general easterly bias of the angular momentum in the equatorial stratosphere so that the e-SAO does not create a zero-wind line, unlike the w-SAO. The currently observed average QBO period of 28 months, which is not an integer multiple of SAO periods, is a result of intermittent jumps of the QBO period from four SAO to five SAO periods. The same behavior is also found in the Two and a Half Dimensional Interactive Isentropic Research (THINAIR) model. It is found that the nonstationary behavior in both the observation and model is caused not by the 11-yr solar-cycle forcing but by the incompatibility of the QBO’s natural period (determined by its wave forcing) and the “quantized” period determined by the SAO. The wave forcing parameter for the QBO period in the current climate probably lies between four SAO and five SAO periods. If the wave forcing for the QBO is tuned so that its natural period is compatible with the SAO period above (e.g., at 24 or 30 months), nonstationary behavior disappears

Transient Climate Response in Coupled Atmospheric–Ocean General Circulation Models

The equilibrium climate sensitivity (ECS) has a large uncertainty range among models participating in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) and has recently been presented as “inherently unpredictable.” One way to circumvent this problem is to consider the transient climate response (TCR). However, the TCR among AR4 models also differs by more than a factor of 2. The authors argue that the situation may not necessarily be so pessimistic, because much of the intermodel difference may be due to the fact that the models were run with their oceans at various stages of flux adjustment with their atmosphere. This is shown by comparing multimillennium-long runs of the Goddard Institute for Space Studies model, version E, coupled with the Hybrid Coordinate Ocean Model (GISS-EH) and the Community Climate System Model, version 4 (CCSM4) with what were reported to AR4. The long model runs here reveal the range of variability (~30%) in their TCR within the same model with the same ECS. The commonly adopted remedy of subtracting the “climate drift” is ineffective and adds to the variability. The culprit is the natural variability of the control runs, which exists even at quasi equilibration. Fortunately, for simulations with multidecadal time horizon, robust solutions can be obtained by branching off thousand-year-long control runs that reach “quasi equilibration” using a new protocol, which takes advantage of the fact that forced solutions to radiative forcing forget their initial condition after 30–40 yr and instead depend mostly on the trajectory of the radiative forcing

The global warming hiatus: Slowdown or redistribution?

Global mean surface temperatures (GMST) exhibited a smaller rate of warming during 1998-2013, compared to the warming in the latter half of the 20th Century. Although, not a "true" hiatus in the strict definition of the word, this has been termed the "global warming hiatus" by IPCC (2013). There have been other periods that have also been defined as the "hiatus" depending on the analysis. There are a number of uncertainties and knowledge gaps regarding the "hiatus." This report reviews these issues and also posits insights from a collective set of diverse information that helps us understand what we do and do not know. One salient insight is that the GMST phenomenon is a surface characteristic that does not represent a slowdown in warming of the climate system but rather is an energy redistribution within the oceans. Improved understanding of the ocean distribution and redistribution of heat will help better monitor Earth's energy budget and its consequences. A review of recent scientific publications on the "hiatus" shows the difficulty and complexities in pinpointing the oceanic sink of the "missing heat" from the atmosphere and the upper layer of the oceans, which defines the "hiatus." Advances in "hiatus" research and outlooks (recommendations) are given in this report

Resolving a long-standing model-observation discrepancy on ozone solar cycle response

To have the capability for long‐term prediction of stratospheric ozone (O_3), chemistry‐climate models have often been tested against observations on decadal timescales. A model‐observation discrepancy in the tropical O_3 response to the 11 year solar cycle, first noted in 1993, persists for more than 20 years: While standard photochemical models predict a single‐peak response in the stratosphere, satellite observations show an unexpected double‐peak structure. Such discrepancy has led to the question of whether the current standard O_3 photochemistry is deficient. Various studies have explored uncertainties in photochemistry and dynamics but there has not been compelling evidence of model biases. Here we suggest that decadal satellite orbital drifts relative to the diurnal cycle could be the primary cause of the discrepancy. We show that the double‐peak structure can be reproduced by adding the A.M./P.M. diurnal difference to the single‐peak response predicted by the standard photochemistry. Thus we argue that the standard photochemistry is consistent with the observed solar cycle modulation in stratospheric O_3

A link between tropical intraseasonal variability and Arctic stratospheric ozone

Previous studies using satellite measurements showed evidence that subtropical upper troposphere/lower stratosphere ozone (O_3) can be modulated by tropical intraseasonal variability, the most dominant form of which is the Madden Julian Oscillation (MJO) with a period of 30–60 days. Here we further study the MJO modulation in the upper troposphere/lower stratosphere O_3 over the northern extratropics and the Arctic. Significant MJO-related O_3 signals (13–20 Dobson units) are found over the northern extratropics (north of 30°N). The O_3 anomalies change their magnitude and patterns depending on the phase of the MJO. Over the Arctic, the MJO-related O_3 anomalies are dominated by a wave number 2 structure and are anticorrelated with the geopotential height (GPH) anomalies at 250 hPa. The latter is similar to the findings in the previous studies over subtropics and indicates that the Arctic upper troposphere/lower stratosphere O_3 anomalies are associated with dynamical motions near the tropopause. The teleconnection from the tropics to the Arctic is likely through propagation of planetary waves generated by the equatorial heating that affects the tropopause height and O_3 at high latitudes