1 2 Abrut monsoon transitions as seen in aleo-records can be exlained by moisture-advection feedback 3 4 Long version of Comment on Near-linear resonse of mean monsoon strength to a broad range of radiative forcings by W.. Boos and T. Storelvmo 5 A. Levermann 1,2,3,*, V. Petoukhov 1, J. Schewe 1, H.J. Schellnhuber 1,4 6 7 8 9 10 1 Potsdam Institute for Climate Imact esearch, Potsdam, Germany 2 Columbia University, New York, USA 3 Potsdam University, Potsdam, Germany 4 Santa Fe Institute, Santa Fe, New Mexico, USA * corresondence should be addressed to: anders.levermann@ik-otsdam.de 11 12 13 Abrut monsoon changes exist in aleo-records 14 15 16 17 18 19 20 21 22 Paleo-climatic records show evidence of abrut and strong monsoon shifts during the last two glacial cycles (Burns et al. 2003; Wang 2005; Wang et al. 2008), the last deglaciation (Stager et al. 2011) and the Holocene (Guta et al. 2003; Hong et al. 2003; Wang 2005; Berkelhammer et al. 2013; Dixit et al. 2014) in India, the Bay of Bengal, and East Asia. While some of these shifts have been linked either to variations in solar insolation or to climatic changes in other arts of the lanet, they are often much more abrut and/or larger than exected for a linear resonse to external forcing, thus suggesting that monsoon systems may be caable of non-linear transitions. Such transitions were first reroduced in a concetual model by (Zickfeld et al. 2005) and 1
23 24 25 26 27 28 29 later for the more secific case of the Wang et al. 2008 data by (Schewe et al. 2012). Levermann et al. (2009) carved out the hysical mechanism for such transition in a very simle concetual model stating in the abstract "Though details of monsoon circulations are comlicated, observations reveal a defining moisture-advection feedback that dominates the seasonal heat balance and might act as an internal amlifier, leading to abrut changes in resonse to relatively weak external erturbations. Here we resent a minimal concetual model caturing this ositive feedback." 30 Both concetual models agree when oerating in hysically reasonable regime 31 32 33 34 35 36 37 38 39 40 41 42 Boos & Storelvmo (2015) based their article on the statement that the introduction of adiabatic cooling into the concetual monsoon model of Levermann et al. (2009) eliminates the abrut transitions. That is not true as can be seen in their figure 1a. Boos & Storelvmo obtain the same abrut transition if the adiabatic cooling is not comensating for the latent heat release. Thus their argument is based on the assumtion that most of the energy from latent heat release is consumed by adiabatic cooling. While we are obviously aware of the existence of the hysical rocess of adiabatic cooling (and show below that it is imlicitly accounted for in our model), it is not a valid assumtion that most of the latent heat release is consumed by this rocess. To the contrary, the monsoon circulation over the continent is redominantly sustained by the release of latent heat and subsequent warming of the atmosheric column over land as stated in a number of classic studies as for examle (Webster et al. 1998). 43 44 For that reason we deliberately addressed in our minimalistic model (and we clearly declared this in the article) the simlest, but fundamentally imortant cases with 2
45 46 47 48 49 redominantly advective character of the low-atmoshere circulations in the main monsoon regions. These situations are illustrated by Figure S2 from our article, where we showed mas of the low-trooshere winds over these regions, with dominant contribution from the advective comonent. It is further shown in our Figure 2 which comares the latent heat release to other energy comonents for different regions. 50 51 Adiabatic cooling in the Levermann et al. (2009) model 52 53 54 55 56 57 58 59 A very secific incororation of adiabatic cooling into our concetual model let Boos and Storelvmo (2015) to their central result of a vanishing of the threshold in monsoon rainfall. The secific reresentation they choose is based on an aroximation of the second horizontal derivative of the temerature by a linear function of its first horizontal derivative (horizontal velocity), dividing the velocity scale by the horizontal length scale (their equations (1)-(3) and (S1) and (S2)). This aroximation is very crude. Here we show that our model imlicitly incororates adiabatic cooling without eliminating the ossibility of abrut monsoon transitions as seen in aleo-records: 60 61 62 Levermann et al. 2009 aer is based on the classical equations and conventional assumtions. In that article we start with the equation for the secific entroy (see, e.g., (Lorenz 1967, age 13)) in z-coordinate: 63 ds dt Q = T m, (1) 3
64 65 66 67 where s = c lnϑ is the secific entroy of the air, c and ϑ are the secific heat at constant ressure and the otential temerature of the air, t is time, Qm is the net heating rate er unit mass, and T is kinetic temerature. Multilying the left hand side of equation (1) by the air density ρ and using the continuity equation yields: 68 ds ρ s ρ = dt t + ( ρ sv ), (2) 69 70 71 72 73 74 75 where / t is the artial derivative with resect to time, is the three-dimensional gradient vector, V is the three-dimensional vector of atmosheric velocity, and is a scalar multilication sign. Integrating equation (2) with resect to z vertically from the earth's surface to the trooause and horizontally over the monsoon land region, assuming quasi-stationarity of the rocess and imosing zero boundary conditions on the vertical velocity w at the surface and at the trooause, z tr, using equation (2) one obtains 76 c z tr ztr ϑ ztr ϑ ( H ρϑvh dz) dσ = (, ) (, 0 QV Pdz dσ + 0 QV T 0 T dz) dσ, (3) 77 where H is the horizontal gradient vector, V H is the vector of the horizontal velocity, 78 is the total area of the monsoon land region, while Q V, P V and Q, are, resectively 79 80 81 82 the net heating rate er unit volume due to the condensation and radiation. In our simle monsoon model we neglected the sensible heat flux at the land surface. The condensation heating rate is ositive throughout the entire trooshere. The radiation heating rate is non-ositive throughout the entire trooshere in the monsoon land 4
83 84 regions (McFarlane et al. 2007). The factor ϑ / T is ositive in the trooshere. Thereby one can bring this factor outside the integrals in the right side of equation (3), 85 reresenting it by constant arameters S P, and S, resectively, in the first and 86 87 88 89 second terms in the right hand side of equation (3). We can denote S P, and S integral static stability arameters of the monsoon land system, associated with the condensation and radiation rocesses. This way, the deviation of as the ϑ / T from 1 is the indicator of the contribution from the vertical motions to the atmoshere heat balance: in 90 the adiabatic (i.e., with T = ϑ ) atmoshere the vertical motions could not contribute to 91 92 93 94 95 96 the heat balance. Equating condensation to reciitation rate over the monsoon land region and rescribing as the arameter the ratio ε = H / L, where H and L are resectively, the vertical extent of the lower branch of the monsoon inflow to the land and the horizontal scale (distance between the coast line and the remote boundary of the monsoon region, see Levermann et al. 2009), we get the equation whose general structure is identical to Eq. (1) from that aer, namely 97 LPS ε c W T + S = 0, (4) P 98 99 where L is the latent heat of condensation, P and are the averaged over the entire monsoon land region reciitation and radiation rates er unit square, and 100 W = α T, (5) 101 102 where α is a constant arameter and T = T L T > 0 is atmosheric temerature difference between land and ocean. O 5
103 104 105 When deriving equation (4) we use a conventional reresentation of the otential temerature ϑ T + γ z within the trooshere, where γ A is the constant adiabatic A lase rate, so that the horizontal derivatives of ϑ and T match u in that case. 106 107 108 109 110 111 112 113 114 A conservation law for the water vaor mass laces a condition that an overall influx of the water vaor into the system should be equal to zero, for the steady states. This means, in our case, that in the absence of the land evaoration and under the condition that the vertical velocity is zeroed at the surface and at the trooause, an overall (integrated over the entire side surface of the monsoon land region) income of water vaor at the lateral boundaries of the system should be balanced by the outcome of water vaor due to reciitation rate integrated over the entire lower surface of the monsoon land region. Going this way we get the equation for the atmosheric humidity that is identical to the equation (3) from Levermann et al. 2009: 115 ε Wρ ( q q ) P = 0, (6) O L 116 where q O and q L are the secific humidity over ocean and land, resectively. 117 We further reresent P as follows (see Levermann et al. 2009): 118 P = β q L, (7) 119 where β is constant arameter. Finally, combining equations (4) - (7) one can get 120 W β α αβ ( LS Pβ qo + S ) W 2 ε c ε ρc 3 2 + W S ερ = 0, (8) 6
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