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Conceptual Model Analysis of the Influence of Temperature

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Conceptual Model Analysis of the Influence of Temperature Conceptual Model Analysis of the Influence of Temperature Feedbacks on Polar Amplification Ashley E. Payne August 16, 2015 1 Introduction Polar amplification, the increased response of surface warming at high latitudes to radia- tive forcing relative to the global mean, is found in idealized models, paleoclimate records and in observations of the Arctic [3, 4, 7]. However, attribution of its causes is a complex problem because of the high degree of interaction between the different mechanisms at work. Recent research has focused on the role of longwave feedbacks in polar amplification. Win- ton [2006] used twelve climate models from the fourth IPCC assessment report to compare the relative magnitudes of various feedbacks in the Arctic and globally for CO2 doubling in 1%/year CO2 increase experiments. He found that a large portion of the enhanced warming in the Arctic is attributable to the effect of longwave feedbacks, which include cloud, water vapor and temperature effects. Neutralizing the surface albedo feedback at high latitudes by replacing it by its global mean value in the feedback calculation still resulted in some degree of Arctic amplification relative to the global mean, indicating that the surface albedo feedback is important, but not dominant, in explaining polar amplification. The temperature feedback can be broken into the Planck feedback, the background equilib- rium response of the climate system, and the lapse rate feedback, the non-uniform change in temperature vertically. Both have been argued to be important to polar amplification in re- cent work. Pithan and Mauritsen [2014] performed a feedback analysis on data from phase 5 of the Coupled Model Intercomparison Project (CMIP5) and found that the tempera- ture feedback dominates Arctic amplification, attributing this dominance to the interaction between the Planck feedback and the lapse rate feedback. Pithan and Mauritsen [2014] at- tribute a large part of the polar amplification to the Planck response itself, arguing that colder temperatures, as found at high latitudes relative to the low latitudes, require greater temperature increases for a given radiative forcing. The role of the lapse rate feedback in relation to the surface albedo feedback was investigated in Graversen et al. [2014] . By sup- pressing the lapse rate feedback in Community Climate System Model, version 4 (CCSM4) simulations, they found that a portion of polar amplification can be explained by its effect at high latitudes. However, the high level of interaction with the surface albedo feedback makes it difficult to consider the lapse rate independently. 317 The complexity of the problem highlights the importance of a simplified approach to gain in- sight into the roles of the Planck feedback and the lapse rate feedback on polar amplification. Here, we use a hierarchy of simple conceptual models to isolate the two different feedbacks and investigate whether (and if so, how much) polar amplification can be attributed to each. As discussed in Pithan and Mauritsen [2014], the Planck feedback is indeed much weaker in the colder high-latitudes. However, we argue that this by itself cannot cause polar am- plification. Instead, it is the qualitative difference in the lapse rate response between the low- and high-latitudes which is expected to contribute to polar amplification. While the low-latitude lapse rate is set by moist convection and is expected to decrease with increasing temperatures, leading to a negative lapse rate feedback, in the high-latitudes, models gen- erally suggest a destabilization of the vertical temperature profile with warming [6], leading to positive lapse rate feedback. The paper is organized as follows. In section 2, we describe our model setup, data, and method of quantifying feedback parameters. In section 3 we describe the radiative equilib- rium response of surface temperature to increases in emissivity in a simple two-layer energy balance model. Against this equilibrium baseline, we investigate the Planck feedback and the lapse rate feedback in sections 4 and 5, respectively, using a hierarchy of models. In section 6, we look at the impact of these feedbacks on polar amplification, with and without the water vapor feedback. We summarize our results and future directions in section 7. 2 Data and Methods 2.1 Models Figure 1: Illustration of a simple two-layer energy balance model with a surface layer and an atmospheric layer. Fs is the incoming solar radiation, Fa is atmospheric heat transport, Ts is the temperature of the surface layer, Ta is the temperature of the atmospheric layer, a is the atmospheric emissivity and σ is the Stefan-Boltzmann constant. We investigate the role of the longwave temperature feedback using a hierarchy of simple models. The simplest is a two-layer one-dimensional energy balance model (EBM), in which the system is represented by two layers; the bottom layer represents the planetary boundary layer and the top layer represents the free troposphere (Fig. 1). Energy input to the system 318 is in the form of solar insolation, Fs and meridional atmospheric heat transport, Fa, which can be turned on or off. The temperatures of the surface layer and the atmospheric layer are represented by Ts and Ta, respectively. The influence of increasing CO2 concentration on warming is translated as increases in atmospheric emissivity, a, which is assumed to be less than one. For this simple model, we can write a system of equations that describe the balance of radiation in the two layers: dT C s = F + σT 4 σT 4, (1) s dt s a a − s dT C a = F + σT 4 2 σT 4, (2) a dt a a s − a a where, Cs and Ca are the heat capacities of the surface and atmospheric layers, respectively. Annual Hard average adjustment insolation to moist lapse rate Region specific Fixed RH albedos 80% Latent heat ________ ________ flux turned off at the radiation convection surface 5m slab diffusion ________ ________ ocean turbulence coupler Figure 2: An illustration of the column model composed using the CliMT package, in which various components are linked through a coupler. To step up complexity, we use a 26-layer radiative-convective column model. The model is based on the Climate Modelling and Diagnostics Toolkit (CliMT), available as a Python wrapper to various existing Fortran components [1]. Figure 2 describes the package set-up, in which ocean, radiation, convection and turbulence components interact using a coupler. With the CliMT package we set up two different configurations. The first is a column model equivalent of the simple two-layer EBM described previously, in which a grey-gas ra- diative scheme is coupled to a slab ocean and a simple turbulence scheme. For this model, as well as for the simple two-layer EBM described previously, the role of water vapor is 319 not incorporated. The second model has an added level of complexity, with a multi-band radiative scheme based on the Column Radiation Model by the NCAR Community Climate Model (CCM3). In order to maintain the energy budget of the column model, but also to constrain the role of moisture, we turn off latent heat flux at the surface and fix relative humidity to 80% in the model troposphere and to zero in the model stratosphere. When considered, convection is parameterized by hard adjustment to the moist adiabatic lapse rate. For each timestep, the temperature profile of the moist adiabatic lapse rate is calculated from the surface temperature. The intersection of this profile and the model- calculated temperature profile is found and all temperatures below that level are adjusted to the moist adiabat. The additional heat to the column due to this adjustment is pulled from the slab ocean and assumes efficient redistribution of heat from the surface throughout the column. For the column model, in order to provide some level of comparison to the simple two- layer model, we use the average of the temperature profile between 500 and 600 hPa to represent the atmospheric temperature, Ta. 2.2 Data We use ERA-Interim reanalysis to constrain parameter values in the following analysis, cal- culated as the climatological mean of the zonal average. In the following analysis, we will consider a “high-latitude” (HL) column and a “low-latitude” (LL) column. Parameter val- ues for each of these columns are estimated based on ERA-Interim reanalysis data at 80◦N 2 and 20◦N, respectively. An average insolation value of 367 W m− is used for non-region specific calculations. To approximate the role of meridional atmospheric heat transport, we use the zonally av- 2 eraged vertically integrated convergence of total energy flux (W m− ) (Fig. 3a). In a given location, for the column models, we represent the atmospheric heating profile as a normal distribution that is capped at the tropopause and constrained to integrate to the value of 1 total energy flux corresponding to its latitude, converted to units of K day− (Fig. 3b). 2.3 Feedback analysis In order to quantify the contribution of the Planck and lapse rate feedbacks to changes in the surface temperature, we use the partial radiative perturbation method [9]. By this method, a feedback, λx, is represented as: ∂R ∂x λ = , (3) x ∂x ∂T s where R is the radiation at the top of the atmosphere (TOA) and Ts is the surface temper- ature. As our focus is on temperature feedbacks, Eqn. 3 becomes: ∂R ∂T λ = , (4) T ∂T ∂T s 320 100 ) -2 50 0 -50 Convergence (W m a -100 -90 0 90 Low-latitudes b High-latitudes 200 400 600 Pressure (hPa) 800 -3 -2 -1 0 1 2 3 Heating Rate (K day-1) Figure 3: (a) Meridional variation of zonally averaged total energy flux calculated from ERA-Interim reanalysis (climatological mean over 1979 to 2013).
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