Earth's balanced climates in view of their energy budgets

Earth’s well-known energy budget scheme is subjected to variations representing changes of insolation and atmospheric absorption. The Charney Report variability cases of doubled atmospheric CO 2 concentration and insolation increase by 2 % are found reproducible. The planetary emissivity is revealed linear to surface temperature, conformant with measurements. Atmospheric water vapor with its characteristic concentration-temperature dependency appears as a major component in Earth’s energy balancing mechanisms. From this, shift towards fewer and stronger rainfall events is prescribed for rising temperatures.


Introduction
A major aim of the present studies is the search for reproducibility on the results from sophisticated scienti c research. Inherently, nature and climate are complex systems. Their understanding requires consideration of numerous aspects, each bound to coherently re ect the same system.
Earth's energy budget sorts the underlying processes by a rather transparent set of rules. The master rule is given by the observation that at any condition through history, Earth has managed to establish an energy-equilibrated state, thus avoiding endless runaway paths. Climate equilibrium states are characterized by balanced energy budgets, the entering energy ux equaling the emerging ux. This applies to the planetary Earth-space system (shortwave insolation entering, longwave radiation emerging to space) as well as to the subsystems of atmosphere and surface.
The energy budget appears like an accounting scheme.
i. The energy ux received on Earth originates from the shortwave insolation at the top of the atmosphere (TOA), reduced by the re ections from the planetary The emitted energy ux is composed of the radiation from clouds, the (cloud-atmosphere, and the surface in the atmospheric window.
ii. The atmosphere receives energy from insolation absorption and from the surface via longwave absorption, evapotranspiration, and sensible heat; it emits radiation to the surface and into space from clouds and at clear sky.
iii. The surface absorbs a fraction of the insolation and receives radiation from the atmosphere; it loses energy by radiation into space (in the atmospheric and into the atmosphere as well as by evapotranspiration and sensible In addition, the surface (in this exchanges energy with the oceans; in an equilibrium state, the exchange is balanced, i.the ocean heat uptake is Earth surface emissivity is less than For simplicity when translating between radiation and temperature, ideal black-body with emissivity equal 1 is assumed through the present study.

Earth's Energy Budget -Variability Studies
The rst three columns of Table 1 summarize the current energy budget [1]. Based on this reference data set, three variations are explored. In this procedure, three parameters are treated as t variables: the longwave radiation from the atmosphere to the surface, the evapotranspiration & sensible heat component, and the longwave emittance to space from the clouds.
In variability case 1, the insolation at the top of the atmosphere is raised by 2 %. In case 2, the longwave atmospheric absorption is increased such that the surface temperature is raised by 3°C. In case 3, an additional longwave radiation of 3.2 W/m 2 is assumed to enter the atmosphere from below. The rst two cases relate to variabilities studied earlier ( [2] with further references): the rst case addressing an insolation increase, the second case an increase in atmospheric CO 2 concentration. The third case relates to the anthropogenic energy consumption. The energy budget values of the three variability cases are computed from the reference data set as described in column 2 of Table 1. The solutions for the free parameter values (italics in Table 1) are non-unique. At rst, their choice follows rather intuitive perception. At second, they may be adapted for consistency reasons, particularly related to the separately elaborated absorber density scheme [3]). Markable consistency is noted between the present energy budget and the absorber density scheme with water vapor as its dominant player.
Discussion on the variability cases: Variability case 1, insolation increase by 2 %. The temperature increase as given by the energy budget values is 3°C, the same as in [2] when applying there a sensitivity of 0.75°C/(W/m 2 ). -The sensitivity de ned as the ratio of surface temperature change to the TOA (longwave) emittance change, the same as the change in planetary shortwave absorption, hence S = ΔT S / ΔLW space = ΔT S /ΔSW Abs , the energy budget values of case 1 in Table 1   For all variability cases, variations to the algorithms of Table 1 -i.e. altering albedo and atmospheric shortwave absorption in dependence on surface temperature -leaves the described results unchanged (details not shown).

Conclusion
The Charney Report variabilities, i.e. insolation and CO 2 concentration change, can be reproduced within the energy budget. Equilibrium requires TOA longwave emittance to change with absorbed shortwave irradiation in case of insolation change, and TOA longwave emittance to remain constant in case of absorber change (e.g. of CO 2 concentration). -Already inferring from case 1, emissivity is decreasing with increasing insolation and in turn increasing surface temperature. This indicates that water vapor is predominantly regulating emissivity with temperature, in view of water vapor being the major longwave absorber and at the same time, its concentration relatively strongly dependent on temperature.

Planetary Emissivity From The Energy Budget Variability Studies
In view of all variability cases, the planetary emissivity ε p appears to well correlate with the surface temperature via T s = (-161 • ε p + 386) K, as summarized in Fig. 1. The zonal conditions (orange dotted) exhibit energy ux imbalances, while balances are given in all other cases. The linear relationship appears independent of the driving force (atmospheric longwave absorption and insolation examined here) and applies to a wide range of climate conditions (between − 10 and + 20°C from today's temperature). The relationship is revealed as an intrinsic property of the energy balancing mechanisms, largely originating from the atmospheric water vapor which is temperature-dependent in amount, itself signi cantly determining the surface temperature, and leaving the emittance to space rather slowly varying. Also clear-sky measurements reveal a linear relationship between outgoing longwave radiation (OLR) and near-surface temperature [6]. This is consistent with the present linear emissivity-temperature relationship if clouds contribute positively to OLR at cold and negatively at warm surface temperatures, of the order + 25 and − 55 W/m 2 at 200 and 300 K, respectively. This translates into a could feedback parameter of 0.8 W/m 2 /K.
For equilibrium states, the predominant role of water vapor demands its atmospheric residence time to roughly scale with the concentration dependence on the surface temperature. This is necessary to bring the relatively high concentration variability (exponential on temperature according to the Clausius-Clapeyron relation) in line with the relatively stable evapotranspiration and precipitation energy contributions (amounting to ca. 83 % of ES in Table 1; changing by the order of 0.5 %/°C in the energy budget estimates, details not shown). As a result, mean precipitation remains rather unchanged. On the other hand, a simultaneous increase of water vapor concentration and residence time prescribes increase of low-e ciency rainfall and frequency decrease of higher-intensity rainfall with rising intensity per event.

Conclusion
The natural temperature-regulated provisioning of water vapor to the atmosphere is a major component in Earth's maintenance of the energy ux balance. Prerequisite is the residence time of atmospheric water vapor to roughly scale with its concentration temperature dependency, from the energy budget estimates with ca. 8 %/°C (details not shown). Consequently, mean precipitation remains rather temperatureindependent while rainfall shifts to fewer and more intense events with increasing temperatures. -Emissivity to space is prescribed to inverse-linearly vary with the surface temperature. -The simple energy budget estimates support the absorption-density relationship of [3].

Discussion
It appears interesting that the simple energy budget consideration reveals important intrinsic characteristics of nature: emissivity inverse-linearly following surface temperature, this independent of the temperature-driving agent; water vapor as a dominant component in Earth's energy balancing mechanism, controlled by the characteristic temperature dependency of its concentration; the strongly varying water vapor concentration in combination with the weakly varying evapotranspiration prescribing rainfall pattern changes with temperature. The prominent role of water vapor, with CO 2 in conjunction, is con rmed by a density-based description [3].
The energy budget study is viewed complementary to the radiative forcing-concept. For completed transitions between equilibrium states, it avoids situations where the feedback parameter (in its typical de nition) is predetermined to zero (in case of longwave absorber change: TOA radiation constant while surface temperature changing), which is equivalent to in nite sensitivity and unde ned temperature change in the frequently presented formalism. Within the transitions between equilibrium states (transient climate), potential (TOA) radiation imbalance is supposed to be dominated by the ocean heat uptake (perceived as common knowledge).
The forcing concept's starting point of TOA longwave radiation changing with surface temperature by T 3 (Planck feedback) is put into perspective. For equilibrium states, the energy budget reveals an intrinsic linear behavior, i.e. changing via a constant instead of T 3 , in line with observations. This is fundamentally attributed to atmospheric water vapor with its absorption and concentration-temperature properties. For the transient regime, a rst look is to be directed at the atmosphere-ocean interplay.
The energy budget scheme may serve as shortcut to cumbersome regression analysis of sophisticated simulation results. A handy tool is provided for quick insight in appropriate cases.

Supplementary Materials
. Koll D.D.B., Cronin T.W. Earth's outgoing longwave radiation linear due to H 2 O greenhouse effect.