Article Global warming: Sun and water Energy & Environment 2017, Vol. 28(4) 468–483 ! The Author(s) 2017 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0958305X17695276 journals.sagepub.com/home/eae Harold J Blaauw Abstract This paper demonstrates that global warming can be explained without recourse to the greenhouse theory. This explanation is based on a simple model of the Earth’s climate system consisting of three layers: the surface, a lower and an upper atmospheric layer. The distinction between the atmospheric layers rests on the assumption that the latent heat from the surface is set free in the lower atmospheric layer only. The varying solar irradiation constitutes the sole input driving the changes in the system’s energy transfers. All variations in the energy exchanges can be expressed in terms of the temperature variations of the layers by means of an energy transfer matrix. It turns out that the latent heat transfer as a function of the temperatures of the surface and the lower layer makes this matrix next to singular. The near singularity reveals a considerable negative feedback in the model which can be identified as the ‘Klimaverstärker’ presumed by Vahrenholt and Lüning. By a suitable, yet realistic choice of the parameters appearing in the energy transfer matrix and of the effective heat capacities of the layers, the model reproduces the global warming: the calculated trend in the surface temperature agrees well with the observational data from AD 1750 up to AD 2000. Keywords Global warming, climate model, climate energetics, hydrological cycle, Klimaverstärker Introduction The mean temperature of the Earth’s surface has gone up over the past 250 years. According to the Intergovernmental Panel on Climate Change (IPCC)1 the temperature rise during 20th century was 0.78  0.07 K. Most people accept the Panel’s view that the warming owes to the so-called greenhouse effect, viz. the increase of the internal energy of the Earth’s climate system (to be defined in ‘Preliminaries’ section) caused, through a complex of processes, by Retired, Leidschendam, The Netherlands Corresponding author: Harold J Blaauw, Oosteinde 16, Leidschendam 2266HK, The Netherlands. Email: h.j.blaauw@casema.nl Blaauw 469 the growing CO2 concentration in the atmosphere. However, a genuine proof of the effect has not been given in spite of many indications brought forward. Maybe the strongest point in favour of the greenhouse idea is the absence of a credible alternative, possibly additional explanation for the global warming. Basically, as there are no other significant energy inputs to the Earth, we can conceive just one alternative: the varying solar irradiation. However, the IPCC has reported that the climate forcing by the solar radiation only accounts for about 10% of the full forcing. The minor role of the Sun is often illustrated by a calculation based on a very simple model of the Earth (e.g. in Beer et al.2). The model treats the Earth as a black body at a temperature of 255 K emitting long-wave radiation the power of which is balanced by the net solar energy input, about 239 W m2. Over the past century the solar irradiation, 1361 W m2, has changed by no more than 1 W m2, hence the net input has changed by about 0.17 W m2. Assuming the balance and using Stefan–Boltzmann’s law we then find a surface temperature rise of roughly 0.05 K. The simple model is just a very crude representation of the Earth. Only the infrared radiation emission determines the response of the system to its energy input. The model does not take into account the heat transfers between the atmosphere and the surface. Inclusion of these transfers may be important as Vahrenholt and Lüning argue in their book Die kalte Sonne: Warum die Klimakatastrophe nicht stattfindet.3 Their point, in brief, is that the greenhouse effect explains only part of the temperature increase. To make up for the deficiency they presume the existence of a ‘Klimaverstärker’, viz. a phenomenon that amplifies the temperature effect of the variable solar energy input (compared to the simple model). The authors suggest that this phenomenon might relate to the latent heat transfer from the surface into the atmosphere. The idea of a Klimaverstärker is taken up here. Preliminaries Global warming is believed to be brought about primarily by the increase of the amount of CO2 in the atmosphere, viz. the greenhouse effect. Here, that proposition is left as it is. Rather the focus is on the varying solar irradiation affecting the temperatures in the Earth’s climate system. It can be studied independently, viz. a possible greenhouse effect and an effect owing to the irradiation can be disentangled. First, it is because the one does not directly influence the other. Second, the effects are quite small (less than 1 K surface temperature change compared to a mean temperature of 288 K) permitting first-order approximations for both effects. Then they can be treated separately. Hence, as the focus is on the irradiation, we might as well take the atmospheric CO2 content fixed. If one so desires he or she can add a greenhouse effect, if any, to the effect of the varying irradiation. As is not uncommon the climate system is represented by a single column of 1 m2 cross section. The properties of this column are averages over the globe and over a suitable running time interval, e.g. one year. We choose the boundaries of the column so that all processes pertaining to the energy transfers within the system and between the system and its surroundings are included. It means the variables determining the system’s state only depend on the altitude in the atmosphere and on the depth in the surface. Lateral energy transfers can be left out. By assumption, the climate system is stable if the amount of atmospheric CO2 does not grow, as in pre-industrial times, and the irradiation is fixed. Stability means the system, initially in a stationary state, responds to a disturbance by re-attaining a stationary state 470 Energy & Environment 28(4) (not necessarily the same as the initial state). The assumption is credible since the Earth’s temperatures do not show a runaway trend, at least not prior to the outset of the anthropogenic CO2 growth. (In general, physics tell us that a system deprived of interactions with its surroundings develops towards a stationary state. Chemists refer to Le Chatelier’s principle.) Obviously, the conditions are hypothetical as the atmospheric CO2 content changes with seasons and the irradiation exhibits small fluctuations. Yet, it makes sense to define a reference state under the indicated steady conditions and describe the real state by making small adjustments to this reference state. Definition of the 3L model As said in the ‘Introduction’ section, inclusion of the heat transfers in modelling the Earth’s system may be important. That is why a simple and transparent model, a three-layer model (3L model), is developed. The model divides the column representing the system into three layers: a surface layer, a lower and an upper layer of the atmosphere. The boundaries of the layers are obvious (cf. the second paragraph in the previous section) except for the boundary between the two atmospheric layers. We define this boundary by the condition that the latent heat transferred from the surface to the atmosphere is fully absorbed by the lower layer, i.e. the latent heat does not reach the upper layer. The boundary can be chosen at an altitude of about 2.3 km where on average the atmospheric temperature is 273 K (0 C). Each layer is attributed a single (mean) temperature and a single heat capacity. Figure 1 schematically displays the Earth’s system and its layers. The caption contains the specification of the energy transfer rates and the relevant properties of each layer. Energy conservation underlies the description of the system’s behaviour. This principle applies to each of the layers at all times. It yields three coupled equations depending on time t. However, the equations are practically unsolvable. The specification of the terms is hard to Figure 1. Schematic representation of the three-layer model including the energy transfers. The system consists of a surface layer, index 1; a lower atmospheric layer, index 2; and an upper atmospheric layer, index 3. J: the absorption rate of solar energy; Jk: the absorption rate of solar energy for layer k; Qk: the sensible heat transfers between the layers; L: the latent heat transfer; Ek: the infrared emission by layer k, except for the surface which emits E1 + E1d, E1d directly to outer space; R: the infrared emission into outer space. The arrows indicate the direction in which the transfers are taken positive. Each layer k is characterized by an average temperature Tk and a heat capacity Ck. Blaauw 471 give and non-linearity presents grave problems. A way out of this situation is to consider variations of the quantities involved. We express the variations as dUk for the internal energies, as dEk for the emission rate of long-wave radiation energy and so on. We define them with respect to the stable reference state of the Earth as introduced in the previous section. Then we can write the energy conservation equations in terms of the variations of the quantities (time t excepted). Of course, it implies we will end up with relative temperature variations. The equations for the variations read d U1 ¼ J1 þ E2  Q1  L  ðE1 þ E1 d Þ dt d U2 ¼ J2 þ E1 þ E3 þ Q1 þ L  Q2  2  E2 dt d U3 ¼ J3 þ E2 þ Q2  2  E3 dt ð1Þ ð2Þ ð3Þ The strategy now is to convert these energy conservation relations into equations relating the temperature variations of the three layers. We can achieve this by making several assumptions. For one, it is assumed first-order variations will do. This is reasonable if the real state is close to the reference state. The variations of the internal energies Uk are expressed as Uk ¼ Ck  Tk , Tk being the temperature of layer k. We assume the heat capacities Ck constant because the composition of the layers does not change significantly (the share of CO2 and H2O in the content of the layers is very small). The layers are treated as grey bodies. This is permitted since the mean free path of photons, viz. the optical depth, is small compared to the dimensions of the bodies. Stefan–Boltzmann’s law, Ek ¼ "    Tk4 provides us with the variations of the long-wave radiation emissions Ek =Ek ¼ 4  Tk =Tk ð4Þ where Ek and Tk are the emission rates and the temperatures in the stable reference state of the Earth. It also applies to Ed1 since the ratio of Ed1 and E1 can be taken fixed. Note that in this way the emissivity e drops out. Yet, we cannot dispense with it because it relates Ek with Tk. In fact, we take e ¼ 0.9 as follows from the Earth’s energy budget as presented by Kiehl and Trenberth4: out of the 390 W m2 the long-wave radiation emitted by the surface carries away per second only 40 W m2 makes it directly into outer space. As to the sensible heat transfers Qk, k ¼ 1, 2, Newton’s law of cooling provides us with Q1 ¼ 1  ðT2  T1 Þ ð5Þ Q2 ¼ 2  ðT3  T2 Þ ð6Þ the convection coefficients j1 and j2 assumed constant (since the composition of the atmosphere is fixed). These equations are particular forms of Fourier’s law which are reasonable because in good an approximation the atmospheric temperature falls linearly with altitude (at least in the troposphere). In general, the latent heat transfer L depends on the temperatures of the surface and the lower atmospheric layer. (More details will be given in ‘Quantification of the heat transfer parameters’ section.) Its variation then reads L ¼ 1  T1 þ 2  T2 1 and 2 being constants. ð7Þ 472 Energy & Environment 28(4) With these specifications the energy conservation equations turn into a vector equation that is basic for the 3L model C d q ¼ J  ðM  NÞq dt ð8Þ The vector q has the components dT1, dT2 and dT3, whereas the vector dJ consists of dJ1, dJ2 and dJ3. The matrices C, M and N are given by 0  1  4  E1 þ Ed1 =T1 4  E2 =T2 0 B C ð9Þ M ¼ @ 4  E1 =T1 8  E2 =T2 4  E3 =T3 A 0 0 4  E2 =T2 1  2 1  1 B N ¼ @ 1 þ 1 1 þ 2  2 0 2 0 1 0 C1 0 B C C ¼ @ 0 C2 0 A 0 0 C3 8  E3 =T3 1 0 C 2 A 2 ð10Þ ð11Þ The essential elements of the basic equation are the matrix M  N, here called the energy transfer matrix, and the variation of the solar energy absorption dJ. Since the absorption rate can be taken proportional to the solar irradiation (because the amount of molecules absorbing solar radiation does not change), dJ is a function of time following the irradiation variations. Then the properties of M  N determine the general nature of the solution. As the temperatures are required not to run away, the matrix must have eigenvalues with positive real parts.5 As the condition on the eigenvalues is not self-evident, the energy transfer matrix needs special attention when we quantify the 3L model. Quantification of the reference energy transfers We intend to use the data on the Earth’s energy budget as presented by Kiehl and Trenberth4 for quantifying the matrices. To that end we have to decide whether these data adequately describe the energy budget for the Earth in its reference state. Let the differential of the ratio E/T, as a typical element of M (indices omitted), with respect to the stable state be ðE=TÞ. It follows from E=T ¼ "    T3 that ðT=EÞ  ðE=TÞ ¼ 3  T=T. A temperature increase of 0.7 K over the last century and a surface temperature of 288 K yield 0.7% for the right-hand side and hence for the relative error in ðE=TÞ as far as the surface is concerned. Similar estimates can be made for the atmospheric layers. The percentage compares favourably with the uncertainties, a few W m2 at least, in the data on the radiation energy transfers. Since we only consider a first-order approximation the Kiehl and Trenberth data suffice for quantifying the elements of M. The Kiehl and Trenberth data apply to the Earth’s system consisting of the surface and the entire atmosphere. For the construction of a 3L model, some adjustments and additions are in order. In particular, the solar energy absorption rates, Jk, and the sensible heat transfer rate, Q2, from the lower to the upper atmospheric layer have to be determined. They can be estimated by applying Lambert–Beer’s law to the solar energy absorption under Blaauw 473 clear sky conditions followed by a correction for the mean cloudy conditions (the reflection of sunlight by the atmosphere is attributed to the clouds only). We arrive at J2 ¼ 13 W m2 and J3 ¼ 58 W m2 . These values say that in the atmosphere the major portion of the solar radiation is absorbed in the upper layer because of the layer’s depth. This is not unreasonable since the solar radiation comes in from above. The discussion in Kiehl and Trenberth4 on the energy transfers and their uncertainties shows the estimate on the sensible heat transfer, Q1 in the 3L model, and the estimate of the infrared radiation emission rate of the atmosphere back to the surface, E2, are indirect only and, moreover, interrelated. In fact, the authors estimate the emission rate to be 324 W m2 from which the sensible heat transfer rate follows: 24 W m2. They also refer to papers in which the latter rate amounts to 17–18 W m2.6,7 The uncertainty is considerable and that is why we adjust the emission rate as follows. The temperature of the lower layer runs from 288 K at the surface to 273 K at its upper boundary. We take a mean temperature of 280 K which yields an infrared emission rate (with 0.9 for the emissivity) of, rounded, 313 W m2. Then the latent heat transfer rate becomes 14 W m2 and it follows that Q2 ¼ 27 W m2 . This completes the evaluation of the reference energy transfers which we summarize in Table 1. It presents the base case as in the sequel we shall also consider other cases with slightly different data The 3L model attributes a single temperature to each layer. By Stefan–Boltzmann’s law (with emissivity 1 for the surface and 0.9 for the atmospheric layers) the surface temperature reads 288 K, the lower layer temperature is 279.9 K and that of the upper layer is 249.9 K. With these data we can evaluate the radiation energy transfer matrix. In ‘The energy transfer matrix’ section it is included in M  N. Quantification of the heat transfer parameters As to the sensible heat transfer the coefficients j1 and j2 follow since the temperatures of the layers and the sensible heat transfers are known: j1 ¼ 1.722 W m2 K1 and j2 ¼ 0.9013 W m2 K1. (Note: the number of digits does not reflect the level of inaccuracy. They merely serve consistency for the values of the parameters turn out to be quite critical. This note holds for all parameter values in the sequel.) The identification and the quantification of the coefficients 1 and 2 appearing in the expression for the latent heat transfer require some details of the hydrological cycle, in particular of its ascending branch. Elements of the cycle pertaining to the latent heat transfer can be found in Peixoto and Oort8. But as they are insufficient for dealing with the problem at hand, some words are devoted to a simple presentation of the ascending branch, i.e. evaporation followed by condensation. Table 1. The data representing the base case for the energy transfer rates in the reference system for the Earth. They are taken from Kiehl and Trenberth4 with some adjustments and additions. Solar energy absorption: IR energy transfers: Heat transfers: IR: infrared radiation. J1 ¼ 168 W m2 E1 ¼ 350 W m2 Q1 ¼ 14 W m2 J2 ¼ 13 W m2 Ed1 ¼ 40 W m2 Q2 ¼ 27 W m2 J3 ¼ 58 W m2 E2 ¼ 313 W m2 L ¼ 77 W m2 E3 ¼ 199 W m2 474 Energy & Environment 28(4) Evaporation of water occurs by virtue of a gradient of the vapour pressure (which is directly related to the chemical potential since the vapour behaves as a perfect gas). If the vapour would not condense, the vertical vapour pressure distribution would be the barometric distribution with a scale length of about 13 km (slightly depending on the atmospheric temperature). This distribution expresses the balance between buoyancy and gravitation. But water vapour does condense if its pressure is equal or greater than the saturated vapour pressure. We can construct the vertical profile of the saturated vapour pressure from the data in Schmidt9 and the approximately linear fall of the atmospheric temperature with increasing altitude (the lapse rate being about 6.49 K km1; see International Civil Aviation Organization10). This profile and the barometric distribution intersect in the dew point, at and above which the vapour condenses and clouds appear. Above the dew point the vapour pressure follows the saturated vapour profile and the balance represented by the barometric distribution is lost. The natural tendency to restore the balance implies that the difference between the two pressure distributions, at and above the dew point, constitutes the driving force for the water vapour going up to disappear by condensation. The freezing point is at an average altitude of about 2.3 km. It is assumed that no condensate, viz. no liquid water, is present at higher altitudes: all latent heat is set free between the dew point and an altitude of 2.3 km. This explains the choice of the imaginary boundary between the lower and the upper atmospheric layer. In line with the phenomenological equations of thermodynamics11, we take it that the latent heat transfer L, viz. the product of vapour mass transport with the evaporation heat, is proportional to the driving force. This driving force, in turn, is proportional to a (weighted) integral of the difference between the saturated vapour pressure pv,sat and the barometric vapour pressure, pv,bar, i.e. to an averaged difference pv, bar  pv, sat ¼ ð’  1Þ  pv, sat , ’ being the averaged relative humidity. In reasonable approximation the relative humidity is insensitive to changes of the temperature viz. T2, provided these changes are small, of the order of 1 K or less (cf. Buck’s equation12). It means the temperature dependence of the driving force, 9 and hence  of  the latent heat transfer,1is determined by dpv, sat =dT2 . From Schmidt we deduce 1=pv, sat  dpv, sat =dT2 ¼ 0:0686 K for small variations around T2 ¼ 280 K. As the latent heat transfer L, the reference value of which is 77 W m2, varies by the same relative amount it follows dL=dT2 ¼ 5:284 W m2 K1 . Since the surface temperature did not enter the picture, we find 2 ¼ ð@L=@T2 ÞT1 ¼ 5:284 W m2 K1 . The other parameter to be determined is 1 ¼ ð@L=@T1 ÞT2 , viz. the variation of L with the surface temperature T1 whereby T2 is kept fixed. In reality, a rise of the surface temperature makes the air temperature close to the surface increase. It would affect the vapour pressure. However, the condition is that the atmospheric temperature, viz. T2, does not change. To fulfil this condition, we have to consider a process counteracting the air temperature rise or, for that matter, the increase of the local thermal energy right above the surface. As such a process cannot supply or demand energy to or from the surroundings, it must be a change of the vapour mass, viz. condensation. By condensation the energy in a volume right above the surface goes down and that is exactly what we need. A very simple experiment shows it is not just theory. If we pour hot water, say at 70 or 80 C, into a relatively cold, preferably metal sink, we observe that mist, viz. condensed water, immediately appears to disappear again after a few seconds. It appears because the bottom film of the hot water heats up the sink while the air initially remains at the same temperature (because heat transfer is relatively slow). Apparently, the heating of the sink’s surface while the air temperature is constant brings on condensation in accordance with the above argument. As the air temperature rises after a while by heat transfer, the mist disappears. Blaauw 475 To quantify the effect we consider a fixed volume of the atmosphere right above the surface. The focus is on the water vapour. If the surface temperature T1 increases by dT1, the volume’s temperature would follow, through transfer of sensible heat, by, say, dT2. As the vapour behaves as a perfect gas, we know that the vapour pressure pv changes by pv =pv ¼ T2 =T2 . But as the volume temperature is required to be fixed, because of the condition on 1, some of the vapour has to condense whereby the volume’s temperature increase is annulled. The heat that would be supplied from the surface reads (n is the mass in moles and cV is the specific heat capacity): H ¼ n  cV  T2 . For restoring T2 the same amount of energy has to be taken away by condensation: H ¼ n  cV  T2 , n being the amount of vapour that disappears by condensation. It follows that n=n ¼ T=T2 . As no exchange of energy with the surroundings is in play, the condensation process runs adiabatically. Consequently, we have pv =pv ¼   n=n, c being cp =cV , viz. the ratio of the heat capacities at constant pressure and at constant volume, respectively. (This relation is easily deduced from the well-known condition for an adiabatic change at constant volume: p1  T ¼ 1  p  n ¼ 2 , 1 and 2 being constants). Combining the variations we arrive at pv =pv ¼   T2 =T2 . So, we have the same circumstances as those underlying the evaluation of 2 and we can conclude that 1 ¼   2 . The above value for 2 and  ¼ 4=3 (a value commonly used in engineering) yields 1 ¼ 7.045 W m2 K1. The energy transfer matrix This concludes the quantification of the model parameters (the heat capacities will be dealt with in the next section). The matrix M  N turns out to be 0 1 0:0936 0:9116 0:0000 B C M  N ¼ @ 0:4620 6:2868 4:0867 A W m2 K1 ð12Þ 0:0000 5:3751 7:2721 The determinant of this matrix is 5.29 (W m K1)3. Its eigenvalues are 0.24, 1.94 and 11.5 W m2 K1. As the determinant is non-zero and the eigenvalues are real and positive, the system is stable as anticipated. Note the first diagonal element is relatively small compared to the other diagonal elements. It means that if the surface temperature changes, the change of the infrared emission by the surface is almost cancelled by an opposite change in the heat transfer, primarily latent heat transfer, from the surface to the atmosphere. 2 Response to a one-step irradiation increase in the 3L model As a first step in analysing global warming by the 3L model we take the Earth’s reference system and consider a sudden one-step change of the solar irradiation. This change is set equal to the irradiation increase over the 20th century, i.e. 0.06%13, and a lower value of the absolute value was proposed in Kopp and Lean14; both papers agree quite well on the relative irradiance variation. The composition of the Earth’s system remains unaltered. Then, the solar energy absorption rate jumps accordingly by 0.1434 W m2 which is distributed over the layers as 0 1 0:1008 B C Jstep ¼ @ 0:0078 AW m2 ð13Þ 0:0348 476 Energy & Environment 28(4) Since stability is guaranteed, in the limit t ! 1 it holds that C dtd q ¼ 0 and the temperature changes tend to the values q 1 ¼ ðM  NÞ1 Jstep . (Note that the heat capacity is irrelevant for q 1 .) The calculation with the data from the previous section results in the asymptotic temperature changes 0 q1 1 0 1 T1,1 0:49 ¼ @ T2,1 A ¼ @ 0:06 AK T3,1 0:04 ð14Þ While the atmospheric temperatures hardly change, in fact they decrease minutely, the surface temperature has gone up considerably. The increase is about 10 times the increase as derived from the simple model mentioned in ‘Introduction’ section. The results strongly depend on the parameter values used. To get an idea of the sensitivity we vary the sensible heat transfer, Q1. It is taken because its value is not well determined by observations (cf. ‘Quantification of the reference energy transfers’ section). We assume the energy balances remain intact which means E2 and Q2 have to be varied along with Q1 (other energy transfers are kept fixed). The outcomes for the surface temperature are displayed in Figure 2. We see dT1,1 agrees with the temperature increase reported by the IPCC for Q1 between 13.2 and 13.5 W m2. If Q1 is about 12.49 W m2 the energy transfer matrix M  N becomes singular. For smaller values of Q1 one eigenvalue of this matrix is negative which corresponds to an unstable state of the Earth’s system. The energy transfer matrix being next to singular constitutes the Klimaverstärker presumed by Vahrenholt and Lüning3 accounting for the relatively large value of dT1,1. This property of the matrix is connected to the nearly equal but opposite responses of the latent heat transfer and the rate by which the surface sends long-wave radiation into the atmosphere, to a change of, primarily, the surface temperature. Figure 2. Surface temperature rise, dT1,1, as a function of the sensible heat transfer from the surface to the atmosphere, Q1. Included is the temperature rise as reported by the IPCC.1 The grey area, typed n.s., indicates the sensible heat transfer domain in which the Earth’s system is unstable. Blaauw 477 Global warming driven by solar irradiation It isn’t really fair to compare the asymptotic values for the surface temperature with the temperature increase reported by the IPCC. It is because, owing to its heat capacities, the Earth’s system responds to irradiation changes with some delay. To get the picture we have to solve the basic equation. For that we need to specify the heat capacity matrix C and the change of the solar energy absorption over time dJ(t). The heat capacities of the atmospheric layers can be estimated by taking 1.0 kJ kg1 K1 for the specific heat capacity of air, and assuming an exponential density profile of the atmosphere. It follows that C2 ¼ 0.080 Wyr 2 K1 and C3 ¼ 0.22 Wyr m2 K1. The quantification of the surface heat capacity C1 is less straightforward. Its value depends on the average depth of the oceans taken into account since the heat capacity of the oceans greatly dominates the surface heat capacity. Different values circulate in literature. For instance, Schwartz15 reports C1 ¼ 17  7 Wyr m2 K1 in connection with a typical response time of 5  1 year for the Earth’s system. It has invited comments from other researchers.16–18 The subsequent discussion makes clear that different values for C1 can be deduced, and that one single heat capacity for the surface might be insufficient. For instance, although Boer et al.19 in studying the Earth’s response to volcanic events mention heat capacities ranging between 6.4 and 8.4 Wyr m2 K1, they find indications for a smaller heat capacity (in the order of 1 Wyr m2 K1). Given the considerable uncertainty and the lack of unanimity we shall take a single C1 as an adjustable parameter. The absorption of solar energy is derived from the irradiation data provided by Krivova et al.13 These data are considered representative for the total solar irradiation although at present they are subject to discussion.20 We assume the composition of the layers as to solar energy absorbers is constant. It means the absorption is distributed over the layers by 24.268 and 5.439% for the atmosphere and 70.293% for the surface. The absorption rates vary with the solar input rate at a fixed ratio: 0.1756. To keep the calculations simple and transparent, the irradiation variations are approximated by piecewise linear fits to the 11 years running mean of the data as shown in Figure 3. Figure 3. The total solar irradiation from AD 1600 up to AD 2010. It is assumed proportional to the absorption of solar energy which serves as the input to the basic equation. The TSI is approximated by a piecewise linear fit to the 11-year running mean (fat black line). 478 Energy & Environment 28(4) The basic differential equation, dtd q ¼ C1 J  C1 ðM  NÞq , is solved by Euler’s method with sufficiently small step size. As a first case Q1 ¼ 14 W m2 is chosen. For C1 we take 1, 2, 3 and 5 Wyr m2 K1. Figure 4 shows the results in comparison with the temperature data from McIntyre and McKitrick21,22 covering AD 1700 to about AD 1980 and from NASA GISS23 for AD 1880 to AD 2010. These relative observational data have been joined by equating their mean over the first half of the past century. The offset of the solutions has been chosen so that they equal the observations around AD 1880. Several remarks can be made. The calculated temperature anomalies roughly correspond with the structure in the observational data over the time span from AD 1750 to present. We note that the heat capacity C1 has considerable impact on the temperature variations: the smaller C1, the larger the fluctuations. Contrarily, a large heat capacity adversely affects the agreement for times before AD 1750. Another point is that the 3L model does not disclose the finer details of the surface temperature variations. The graphical representations of the solution in Figure 4 show the calculated temperature variations lag behind to the observational data over the past decades. It has to do with the choice for Q1 as indicated by Figure 2. That is why the calculations are repeated for Q1 equal to 13.5 and 13.2 W m2. The results are displayed in Figure 5. Clearly they are significant improvements over the case considered above. In particular, the solution for Q1 ¼ 13.5 W m2 and C1 ¼ 1 Wyr m2 K1 comes close to the actual temperature anomalies. The solutions for larger values of C1 are omitted because their correspondence with the data rapidly deteriorates with increasing C1. Figure 4. Solutions of the basic equation for the case Q1 ¼ 14 W m2. The solutions correspond to the heat capacities C3 as indicated. For comparison the temperature data from McIntyre and McKitrick21,22 (black) and from NASA GISS23 (grey) are included. The relative offsets of the curves are discussed in the main text. Blaauw 479 Figure 5. Same as Figure 4 but for Q1 ¼ 13.2 and 13.5 W m2. The heat capacity C1 is restricted to the given values because higher values yield solutions that do not closely follow the observational data. We can exhibit the finer details the model does not cover, by taking the difference between the observed data and the model’s results on dT1. An example pertaining to Q1 ¼ 13.5 W m2 and C1 ¼ 1 Wyr m2 K1 is shown in Figure 6 where the difference is denoted by D(dT1). Apparently, strong oscillations occur. Other realistic values for Q1 and C1 only affect the amplitude to some extent. Here, no attempt has been made to incorporate these phenomena in the modelling, because much research still is devoted to them. Several explanations have been proposed. The fluctuations might relate to more or less periodic phenomena like decadal oscillations, El Niño and La Niña (ENSO); see https://www.esrl.noaa.gov/psd/enso/.24 Other studies25,26 say that the 60-year cycle might correlate with astronomical phenomena. The input for solving the basic differential equation consisted of the 11-year running mean of the irradiation. However, the irradiation considerably fluctuates with the solar cycles.13,14,20 We can take the fluctuations into account by superimposing them on the input. It turns out that the effect on the surface temperature is moderate: the temperature oscillations are about  0.15 K maximum, the largest value for the smallest heat capacity and for the last century (since the solar cycle fluctuations tend to get larger over this era). Such oscillations submerge in the overall oscillations shown in Figure 6. Precipitation rate in the 3L model A point of interest is the globally averaged precipitation rate. In the construction of the 3L model the variation of this rate is taken directly proportional to that of the latent heat transfer rate. From the results of the model calculations, we infer that over the 20th century 480 Energy & Environment 28(4) Figure 6. The difference between the observational data (black: McIntyre, McKitrick; grey: NASA GISS) and the model calculations for Q1 ¼ 13.5 W m2 and C1 ¼ 1 Wyr m2 K1. It is indicative for oscillatory phenomena in the Earth’s climate system. Figure 7. The trend of the globally averaged annual precipitation rate from AD 1950 up to AD 2008. The black line presents the data as given by the IPCC, whereas the blue line shows the results of the 3L model (Q1 ¼ 13.5 W m2, C1 ¼ 1 Wyr m2 K1). the latent heat transfer falls by 4.9% in case Q1 ¼ 14 W m2, by 7.3% for Q1 ¼ 13.5 W m2 and by 10.5% for Q1 ¼ 13.2 W m2. (These percentages owe to the large value of 1, i.e. to the negative feedback.) The precipitation rate then must decrease by the same relative amount. This seems to disagree with the position quite commonly held that the precipitation rate has not significantly changed over the past two centuries.27 Indeed the EPA data29 support this view although the data are valid for land only. However, if we consider the post-war era the IPCC data and the model results do agree, cf. Figure 7. As both data sets are of a relative nature, their averages have been set equal over the time interval. The correspondence for times prior to AD 1950 is not really satisfactory but that might relate to the reliability of the data. In fact, the measurements of the precipitation rate may suffer from systematic errors, the more so in the old days. (Some words on the uncertainties in Blaauw 481 measuring precipitation rates can be found at: http://mynasadata.larc.nasa.gov/global-pre cipitation/; see also IPCC fourth assessment report.27) Another indication for the trend of the precipitation rate can be derived from the change in the Earth’s cloud coverage. The relation between the precipitation and the clouds is simple though not trivial. When the evaporation diminishes, so does the amount of water in the clouds because the precipitation responds with some delay (the residence time of atmospheric water, which may be affected by the evaporation rate, is a little over a week). Hence, the cloud cover goes down. The 3L model says the precipitation has decreased slowly over the past century (7.3% over 100 years). It is slow compared to the response time and, hence, we can assume quasi-equilibrium conditions. Then the changes in precipitation and in cloud cover relate positively, i.e. less precipitation means less cloud coverage. Since AD 1983 the International Satellite Cloud Climatology Project (ISCCP) monitors the average cloud coverage. (Data obtained by the ISCCP can be found at: http://isccp.giss.nasa.gov/ products, and graphs of the cloud coverage are found in http://climate4you.com). The observations show that from that day to the present the cloud coverage has gone down by about 3.5%. In particular, the low-level cloud cover accounts for the decrease. Accordingly, the evaporation and the precipitation must have dropped which is in line with the 3L model reconstruction. The 3L model and the Milankovič cycles From the model we can estimate the variability of the surface temperature along with the irradiation, i.e. dT1/dI. The result is roughly 0.1 K (W m2)1. The Milankovič cycles indicate that the full irradiation oscillations, viz. twice the amplitude, are of the order of 100 W m2.30 It follows that the temperature variations are about 10 K which is close to the data derived from the Vostok ice cores31 commonly taken as a proxy for the average global temperatures. Hence, the model constitutes a direct explanation for the glacial and interglacial eras without recourse to other phenomena. Conclusion It has been demonstrated that by using a simple model of the Earth’s climate system with realistic values for the energy transfers involved, the varying solar irradiation and the system’s response fully explain the global warming over the past 250 years even without any greenhouse effect. The model surely is open for expansion, e.g. for introducing more layers. Still, the revealed main trends as to the Earth’s surface temperature and the precipitation will not seriously be affected by such adjustments. The pivotal element in the model is a strong negative feedback brought on by the response of the latent heat transfer to the surface temperature variations. This feedback constitutes the ‘Klimaverstärker’, viz. the mechanism amplifying the effect of the irradiation, as presumed by Vahrenholt and Lüning.3 The results may be helpful for further research into climate forcing, the precipitation rate and the climatic oscillations. As to the first issue the forcing by the solar irradiation turns out to be grossly underestimated nowadays. Second, the variation of the globally averaged precipitation rate is shown to be inversely related to the irradiation variation due to the negative feedback. And finally, the residuals from the comparison of the temperature data with the model results may constitute additional input for studies on the decadal oscillations. 482 Energy & Environment 28(4) Acknowledgements The author wishes to express his gratitude to Dr Sebastian Lüning for useful comments, for pointing out valuable references and for encouragement. Also, he is indebted to one of the reviewers for bringing up additional research information. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) received no financial support for the research, authorship, and/or publication of this article. References 1. IPCC fourth assessment report: climate change 2007, the AR4 synthesis report, 2007. Geneva: IPCC. 2. Beer J, Wender W and Stellmacher R. The role of the sun in climate forcing. Q Sci Rev 2000; 19: 403–415. 3. Vahrenholt F and Lüning S. Die kalte Sonne: warum die Klimakatastrophe nicht stattfindet. Hamburg: Hoffmann und Campe, 2012. 4. Kiehl JT and Trenberth KE. Earth’s annual global mean energy budget. Bull Am Meteorol Soc 1997; 78: 197–208. 5. Arnol’d VI. Ordinary differential equations. Berlin: Springer-Verlag, 1992. 6. Sellers WD. Physical climatology. New York: University of Chicago Press, 1965. 7. Budyko MI. The earth’s climate: past and future. New York: Academic Press, 1982. 8. Peixoto JP and Oort AH. Physics of climate. New York: Springer-Verlag, 1992. 9. Schmidt E (ed.) Verein Deutscher Ingenieure-Wasserdampftafeln. Berlin: Springer-Verlag, 1968. 10. International Civil Aviation Organization. Manual of the ICAO standard Atmosphere (extended to 80 kilometres (262 500 feet)), Doc 7488-CD, 3rd ed. Montreal (Can.): International Civil Aviation Organization, 1993. 11. De Groot SR and Mazur P. Non-equilibrium thermodynamics. Amsterdam: North-Holland Pub. Co, 1962. 12. Buck AL. New equations for computing vapor pressure and enhancement factor. J Appl Meteorol 1981; 20: 1527–1532. 13. Krivova NA, Balmaceda L and Solanki SK. Reconstruction of solar total irradiance since 1700 from the surface magnetic flux. Astron Astrophys 2007; 467: 335–346. 14. Kopp G, Lean JL (eds) A new, lower value of total solar irradiance: evidence and climate significance. A new, lower value of total solar irradiance: evidence and climate significance. Geophys Res Lett 2011; 38: L01706. 15. Schwartz SE. Heat capacity, time constant, and sensitivity of earth’s climate system. J Geophys Res 2007; 112: D24505. 16. Scafetta N. Comment on ‘‘Heat capacity, time constant, and sensitivity of earth’s climate system’’ by Schwartz SE. J Geophys Res 2008; 113: D15104. 17. Knutti R, Krähen-mann S, Frame DJ, et al.. Comment on ‘‘Heat capacity, time constant, and sensitivity of earth’s climate system’’ by Schwartz SE. J Geophys Res 2008; 113: D15103. 18. Schwartz SE. Response to comment on ‘‘Heat capacity, time constant, and sensitivity of earth’s climate system’’, http://www.ecd.bnl.gov/steve/pubs/HeatCap CommentResponse.pdf (accessed January 2017). Blaauw 483 19. Boer GJ, Stowasser M and Hamilton K. Inferring climate sensitivity from volcanic events. Clim Dyn 2007; 28: 481–502. 20. Kopp G, Krivova N, Wu CJ, et al. The impact of the revised sunspot record on solar irradiance reconstructions. Solar Phys 2016; 2951–2965. Epub ahead of print 2016. DOI: 10.1007/s11207-0160853-x. 21. McIntyre S and McKitrick R. Corrections to the Mann (1998) proxy data base and Northern hemisphere average temperature series. Energy Environ 2003; 14: 751–771. 22. McIntyre S and McKitrick R. The M&M critique of the MBH98 northern hemisphere climate index; update and implications. Energy Environ 2005; 16: 69–100. 23. National Aeronautics and Space Administration (NASA), Earth Science Division. Recent temperature data, http://data.giss.nasa.gov/gistemp/tabledata_vs/GLB.Ts+dSST.txt (accessed 2013). 24. Climate decadal oscillations, https://climate.ncsu.edu/climate/patterns/PDO.html (accessed September 2016). 25. Scafetta N. Multi-scale dynamical analysis (MSDA) of sea level records versus PDO, AMO, and NAO indexes. Climate Dyn 2014; 43: 175–192. 26. Scafetta N. Discussion on climate oscillations: CMIP5 general circulation models versus a semiempirical harmonic based on astronomical cycles. Earth-Sci Rev 2013; 126: 321–357. 27. IPCC fourth assessment report: Climate change 2007, the AR4 synthesis report, 2007, section 9.5.4.2. Geneva: IPCC. 28. Dai A, Fung IY and Del Genio A. Surface observed global land precipitation variations during 1900–1988. J Climate 1997; 10: 2943–2962. 29. US Environmental Protection Agency, Precipitation Worldwide 1901–2013, https://www3.epa.gov/ climatechange/science/indicators/weather-climate/precipitation.html (2016, accessed September 2016). 30. Berger A and Loutre MF. Insolation values for the climate over the last 10 million years. Q Sci Rev 1991; 10: 297–317. 31. Petit JR, Jouzel J, Raynaud D, et al. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature 1999; 399: 429–436. Harold J Blaauw holds a PhD in physics from the University of Amsterdam/AMOLF. He has worked in the energy policy field first within the Ministry of Economic Affairs and then as Secretary of the former Advisory Council for Energy Research, prior to joining the Science Policy Department of the Ministry of Education and Science. After being acting director of the former Foundation for Biophysics (NWO) till his retirement he has been an independent consultant on science management and energy. Copyright of Energy & Environment is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. Global warming benefits the small in aquatic ecosystems Martin Daufresnea,b,1, Kathrin Lengfellnera, and Ulrich Sommera aFB3–Marine Ökologie, Leibniz-Institut für Meereswissenschaften (IFM-GEOMAR), 24105 Kiel, Germany; and bHYAX–Lake Ecosystems Laboratory, Cemagref, 13182 Aix-en-Provence, France Edited by Stephen R. Carpenter, University of Wisconsin, Madison, WI, and approved June 3, 2009 (received for review February 25, 2009) Understanding the ecological impacts of climate change is a crucial challenge of the twenty-first century. There is a clear lack of general rules regarding the impacts of global warming on biota. Here, we present a metaanalysis of the effect of climate change on body size of ectothermic aquatic organisms (bacteria, phyto- and zooplankton, and fish) from the community to the individual level. Using long-term surveys, experimental data and published results, we show a significant increase in the proportion of small-sized species and young age classes and a decrease in size-at-age. These results are in accordance with the ecological rules dealing with the temperature–size relationships (i.e., Bergmann’s rule, James’ rule and Temperature–Size Rule). Our study provides evidence that reduced body size is the third universal ecological response to global warming in aquatic systems besides the shift of species ranges toward higher altitudes and latitudes and the seasonal shifts in life cycle events. biological scale 兩 body size 兩 climate change 兩 ectotherms 兩 metaanalysis A t the biogeographical scale, the most noticeable ecological impact of global warming is a shift of species’ ranges toward higher altitudes and latitudes in accordance with their thermal preferences (1–3). This observation has been used extensively to forecast the effect of climate change on biota by modeling future species distributions according to climate-change scenarios (4). However, such patterns and pattern-related predictions do not elaborate specific underlying ecological mechanisms. As a consequence, our understanding and, in turn, our ability to forecast the impacts of climate change on biota remains limited (e.g., it seems possible to forecast species’ ranges, but it remains difficult to predict the relative abundances of species within a community). Besides the shifts in species’ ranges, the second well-known ecological response to global warming is a change in phenology (3). Such patterns could lead to a decoupling of the dynamics of predators and prey (5). This mechanism-oriented hypothesis, generally referred to as the match–mismatch hypothesis (6), offers perspectives in forecasting the ecological impacts of climate change (5, 7, 8). Nevertheless, all of the components of the food web can be affected by dissimilar changes in phenology, leading to complex dynamics that are difficult to predict (5). The match–mismatch hypothesis and the shifts of species’ ranges are key tools when evaluating the ecological consequences of global warming, but they are thus far insufficient to provide clear views on future ecological changes. Further general rules dealing with the impacts of a global rise in temperature on biota are needed. Body size is a fundamental biological characteristic that scales with many ecological properties (e.g., fecundity, population growth rate, competitive interactions) (9, 10). Surprisingly, few studies have dealt with changes in body size with global warming (10), especially for ectotherms, although they represent ⬇99.9% of species on Earth (11). Furthermore, the biological scales (individual, population, community) at which global warming should act on body size have not been studied. Three rules concerning ecogeographical and ecothermal gradients (10) are relevant in this context. First, Bergmann’s rule (12), states that warm regions tend to be inhabited by small-sized species. 12788 –12793 兩 PNAS 兩 August 4, 2009 兩 vol. 106 兩 no. 31 Second, James’ rule (13) states that, within a species, populations with smaller body size are generally found in warmer environments. Third, the temperature–size rule (TSR) states that the individual body size of ectotherms tends to decrease with increasing temperature (14). Combining these rules, we can build a set of 5 hierarchical and nonmutually exclusive hypotheses concerning the potential effect of climate change on size structures from the individual to the community scales (Fig. 1). The first hypothesis predicts a decrease in mean body size at the community scale under warming whatever the underlying mechanisms (community body size shift hypothesis). If there is a decrease in the mean body size at the community scale under warming, there are 4 subsequent hypotheses that could explain this decrease. According to Bergmann’s rule, the first mechanism acts at the community scale is an increase in the proportion of small size species (species shift hypothesis) in terms of abundances of individuals and/or number of species. Second, according to James’ rule, the decrease in size at the community scale could also be due to a decrease in mean body size at the population scale (population body size shift hypothesis). In turn, such a size decrease at the population scale could be due to 2 mechanisms. First, according to the TSR, the size-at-age (or size-at-stage; individual scale) should decrease with increasing temperature (size-at-age shift hypothesis). Note, however, that this decrease should not be observed for early ages or stages because the TSR predict a higher growth rate but a lower final size at higher temperature. In addition to this decrease in size-at-age/stage, an increase in the proportion of juveniles (population age-structure shift hypothesis) could also be expected at the population scale. The latter hypothesis does not correspond to the above-cited ecogeographical or ecothermal rules, but it is the default explanation if the population body size shift hypothesis applies whereas the size-at-age shift hypothesis does not apply. Note that, due to compensatory effects, the invalidation of a hypothesis does not imply that both subsequent hypotheses do not apply. For instance, no changes in mean size at the community scale can be due to a decrease in mean body size at the population scale and an increase in proportion of large species. In this article, we studied changes in body size from individuals to communities under climate warming by testing the 5 hypotheses described above. The tests of the hypotheses were based on (i) the analysis of the effects of increasing temperature on long-term fish data sampled in French rivers and in the Baltic Sea, (ii) the analysis of experimental plankton data (bacteria, phyto- and zooplankton) collected in light- and temperaturecontrolled mesocosms (15), and (iii) on a review of related published work based on data collected in mesocosms and in the Author contributions: M.D. and U.S. designed research; M.D., K.L., and U.S. performed research; M.D. analyzed data; and M.D. wrote the article. The authors declare no conflict of interest. This article is a PNAS Direct Submission. 1To whom correspondence should be addressed. E-mail: martin.daufresne@cemagref.fr. This article contains supporting information online at www.pnas.org/cgi/content/full/ 0902080106/DCSupplemental. www.pnas.org兾cgi兾doi兾10.1073兾pnas.0902080106 Decrease in mean body size Population body size shift hypothesis Decrease in mean body size Community body size shift hypothesis Individual Decrease in individual body sizes Size-at-age shift hypothesis Increase in proportion of juveniles Population age-structure shift hypothesis Increase in proportion of small species Species shift hypothesis Fig. 1. The tested hypotheses regarding the impact of warming on body size at different biological scales. Prop. small sp. 300 200 150 Prop. juveniles 100 50 0 Mean size Ab. Mean sp. size Mean size at age SR -50 -100 F F -150 -200 M (/2) -250 -300 North Sea (Fig. 2). Impacts of potential confounding factors, and especially of fisheries, were considered. Our results support the hypothesis that reduced body size is a third universal or very general ecological response to global warming among ectotherms in aquatic systems, besides the shift of species ranges toward higher altitudes and latitudes and the seasonal shifts in life-cycle events. Results We found that increased temperature acts on communities, populations and individuals through changes in species composition, growth and reproduction. Community Body Size Shift. A metaanalysis revealed that the mean temporal trend (S) of mean body size of fish in large French rivers was significantly negative during the last 2–3 decades under gradual warming (Fig. 3). A decrease in mean body size with increasing temperature was also observed for bacteria in temperature-controlled mesocosms [extended linear mixedeffect (LME) model, coefficient estimate ⫽ ⫺1.06 ⫻ 10⫺3, t value ⫽ ⫺5.51, number of observations ⫽ 68, P ⫽ 3.1 ⫻ 10⫺2; . .. .. Fig. 2. Location of the study areas. 1– 4: Long-term survey of freshwater fish communities in large rivers. 5–7: Long-term survey of brown trout populations. 8: Long term survey of North Sea fish community. 9 –10: Long term survey of herring and sprat populations in the Baltic Sea. 11–13: Sampling of bacteria and phytoplankton communities and of Pseudocalanus sp. (zooplankton) in temperature-controlled mesocosms. Numbers in brackets refer to published climate–size relationships reviewed in this article (16, 17). Daufresne et al. M Community body size shift hyp. Species shift hyp. Population body size shift hyp. Population age-struct. shift hyp. Size-at-age shift hyp. Fig. 3. Mean effect sizes (i.e., mean weighted temporal trend statistic S; ⫾95% confidence intervals). Negative or positive trend values indicate temporal decrease or increase, respectively. Mean temporal trends are significant if their 95% confidence intervals did not contain 0. Community body size shift and species shift hypotheses were tested by using 4 freshwater fish communities. To test the species shift hypothesis, small species were defined as species with a maximum size below the first quartile of the maximum size of all of the species in the community. Proportions of small species are calculated in terms of species richness (SR) and abundances (Ab.). Population body size shift and population age-structure shift hypotheses were tested by using 28 and 18 fish populations, respectively. Size-at-age shift hypothesis was tested by using 28 age classes. Significantly different means for marine (M) vs. freshwater (F) populations are represented. To increase readability some effect sizes are divided by a factor x (indicated in the figure as /x). Fig. 4A]. The mean cell size of phytoplankton also tended to decrease with increasing temperature in the same mesocosms (16) (Fig. 4B). Species Shift. Supporting the species-shift hypothesis, the proportion of small-sized species significantly increased in communities of large French rivers (Fig. 3) both in terms of species richness and abundance. Similar patterns were also observed for the fish community of the North Sea where the geographical ranges of small species expanded, whereas those of large species shrank due to warming (17) (Fig. 4C). In this way, the more even distribution of small species and the patchier distribution of large species should result locally in an average temporal increase in the number of small species and an average decrease in the number of large species. Finally, because the same size si was attributed to all individuals from a given phytoplankton taxon i in ref. 16, the observed decrease in mean size described above (community body size shift; Fig. 4B) is entirely due to an increase in proportion of abundances of small-sized taxa. Population Body Size Shift. Besides interspecific patterns, our metaanalysis revealed a negative temporal trend in the mean body size of individual fish populations under global warming (Fig. 3). Herring and sprat populations in the Baltic Sea showed merely significant stronger decrease in mean size than freshwater species populations (coefficient Qb ⫽ 2.67, P ⫽ 0.10), underlining the potential additive effect of fisheries. Population Age-Structure Shift. The decrease in fish mean body size at the population scale was partially due to a significant PNAS 兩 August 4, 2009 兩 vol. 106 兩 no. 31 兩 12789 ECOLOGY Population Trend statistic S Community B 0.040 60 50 3 Cell Volume (µm ) A 40 pg C cell -1 0.030 0.020 30 64% Io 20 0.010 32% Io 16% Io 10 0 0 2 4 6 0 2 dT (°C) 6 4 6 D 0.10 1.2 Length (mm) Trend in size of the distribution area C 4 dT (°C) 0.05 0.00 1.1 1.0 0.9 −0.05 0.8 0 50 100 150 200 Maximum length of fish species 0 2 dT (°C) Fig. 4. Change in size structures under warming. (A) Cell size of bacteria subjected to different level of warming (⫹0, ⫹2, ⫹4, and ⫹6 °C) compare to a reference thermal regime (dT) [means (open and closed circles), standard errors (gray lines), and raw data (closed rectangles) in the different replicates are represented]. (B) Mean cell size of phytoplankton at different level of warming (dT) and different light conditions [percentage of the natural light intensity above cloud cover (Io); 16% Io: hanging triangles; 32% Io: circles; 64% Io: standing triangles] (after figure 3c of ref. 16). (C) Effect of maximum length on distribution trends (expansion or shrinkage) of fish species in the North Sea during the past 20 y (after figure 4b of ref. 17). (D) Size of female adult Pseudocalanus sp. at different level of warming (dT) (symbols as for A). increase in proportion of juveniles (Fig. 3), emphasizing the change in age structure of the populations. No specific response of herring and sprat populations was found (coefficient Qb ⫽ 2.1, P ⫽ 0.15). Size-At-Age Shift. Finally, long-term analysis of fish populations highlighted a significant decrease in size-at-age (Fig. 3) with a significantly stronger effect for herring and sprat populations in the Baltic Sea (coefficient Qb ⫽ 20.4, P ⫽ 6.34 ⫻ 10⫺6). The decrease in size-at-age was also detected in experimental data. We observed a decrease in size of adult females of Pseudocalanus sp. with temperature in the temperature-controlled mesocosms (extended LME model, coefficient estimate ⫽ ⫺13.46, t value ⫽ ⫺8.41, number of observations ⫽ 807, P ⫽ 4.00 ⫻ 10⫺4; Fig. 4D). Discussion Observed patterns are consistent with our hypotheses, emphasizing a negative effect of global warming on the body size of aquatic ectotherms from the individual to community structure levels. Given that the biota and ecosystems considered in this study were diverse with regard to the potential confounding factors affecting body size, our results suggest that a common mechanism (or set of mechanisms) links size structure and thermal energy at all biological scales considered. Of course, other factors may have additive or multiplicative effects on size. For instance, it has been shown that body size of fish decreases with fishery activities (18, 19). By targeting large individuals, fisheries are considered as a selective pressure favoring early 12790 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0902080106 maturation at smaller size. Thus, fishery activities could explain the observed decrease in size of herring and sprat in the Baltic Sea. On the other hand, regarding freshwater ecosystems, recreational fishing tended to decrease over the study periods in France (e.g., ⫺38,703 fishermen/year from 1993 to 2008; data source: Federation Nationale de la Peche en France et de la Protection du Milieu Aquatique, www.federationpeche.fr). In addition, the species considered in our study (mostly cyprinid species) are not specially targeted by fishermen who prefer top predators. Similarly, the commercial fishing mostly concerns migratory species, eels, and top predators that accounted together for 79% of the total catches over the 1999–2001 period (data source: Suivi National de la Peche aux Engins/Resultats Professionnels; Conseil Superieur de la Peche/Office National de l’Eau et des Milieux Aquatiques, www.onema.fr). Finally, the number of professional fisherman was low at our study areas (e.g., on average 4, 3, 0, and 3 in the vicinity of site 1, 2, 3, and 4, respectively, over the 1999–2002 period; data source: Suivi National de la Peche aux Engins/Resultats Professionnels). Therefore, fishery pressure can be considered of minor impact in the freshwater areas studied in this article. Thus, the impact of fisheries cannot fully explain the decrease in size observed in rivers. In addition, obviously, fisheries cannot explain the patterns observed in the mesocosms. As a consequence, the overall consistency of the observed patterns emphasizes the role of temperature. Such results underline the importance of taking into account thermal constraints as potential confounding factors when studying changes in size structures. Indeed, early Daufresne et al. Daufresne et al. mechanism exists, it should be linked to general theories in ecology. For instance the metabolic theory of ecology [MTE (33)] could help to understand at least part of the involved mechanisms. Indeed, according to this theory, the equilibrium number of individuals in a population (K) is predicted to vary as K ⬀ [R]M⫺3/4eE/kT, where R is the supply rate of the limiting resource, M is the mean mass of an individual, E is the activation energy of metabolism, k the Boltzmann’s constant and T is the Kelvin temperature. Thus, KM3/4 varies as KM3/4 ⬀ [R]eE/kT. As a consequence, warming should lead to a decrease in the mean body mass and/or a decrease in abundance at equilibrium if [R] does not concomitantly increase. In this way, the MTE could explain the population body size shift hypothesis and/or the species shift hypothesis. Further analyses of the relative sensitivity of the decreases in abundance and size to the species maximum size should help to evaluate the extent to which the MTE explains both hypotheses. Finally, we want to point out that it is critical to assess the evolutionary nature of the observed changes. Indeed, evolutionary responses to disturbances can be difficult (or impossible) to reverse and can lead to loss of genetic diversity (19). From this viewpoint, it would be important to distinguish evolutionary responses from plastic changes for conservation and management purposes (18, 19). Overall, knowing the triggers of changes in size with temperature from individual to community could greatly increase our understanding of ecosystem structuring and our ability to forecast impacts of anthropogenic pressures on biota. Materials and Methods Long-Term Data. Large river fish communities. We used data that were collected each year from 4 different study areas located on large French rivers (the Rhône and the Seine rivers) and over periods ranging from 14 to 27 years (22, 34). Fish were sampled 1– 4 times per year [supporting information (SI) Table S1], from a boat, along banks and by using electrofishing techniques. Electrofished individuals were identified to species, measured and released. All study areas experienced a significant increase in temperature due to climate change (22, 34) (Table S2). We used yearly mean size (all individuals included) to test the community body size shift hypothesis. To test the species shift hypothesis, we used time series of proportion of small species in terms of (i) number of individuals (abundance) and (ii) number of species (species richness). For each study area, small species were defined as species with a maximum size (35) below the first quartile of the maximum size of all of the species in the community. The yearly mean sizes of the most abundant species were used to test the population body size shift hypothesis. At each study area, the most abundant species were defined as the species accounting for ⬎5% of the total abundance. We used time series of the proportion of juveniles (young-of-the-year individuals) to test the population age-structure shift hypothesis. Each year, young-of-the-year individuals were identified by analysis of size-class frequencies. Finally, we used the yearly mean size of youngof-the-year individuals of the most abundant species to test the size-at-age shift hypothesis. We only considered the most abundant species having high juvenile numbers (i.e., on average ⬎50 young-of-the-year individuals per year) to test the population age-structure shift hypothesis and the size-at-age shift hypothesis. For all time series, values were calculated for biological (i.e., not calendar) years fitted on the biological cycle of cyprinids. This enabled comparison of similar year class individual among sites (22, 34). Times series are provided in Table S3. Brown trout populations. We used data that were collected yearly over 15 years from 3 French streams. The sites experienced a significant increase in water temperature during the 1985–2005 period (Table S2, Mann–Kendall trend tests, n ⫽ 21 for each test, P values ranging from 2.6 ⫻ 10⫺6 to 1.7 ⫻ 10⫺2). Each site consisted of a stream section of 140 –200 m closed by upstream and downstream nets. Trout were sampled by using 2-pass removal electrofishing, and each individual was measured and weighed before being released. For each sample, young-of-the-year individuals were identified by analysis of size-class frequencies. We used the time series of yearly mean individual size in the 3 populations to test the population body size shift hypothesis. The population age-structure shift hypothesis was tested by using the yearly proportions of young-of-the-year fish. Times series are provided in Table S4. Herring and sprat populations. We used fishery data provided by the International Council for the Exploration of the Sea (ICES; available online at www. ices.dk/reports/ACFM/2005/WGBFAS/directory.asp). Data consisted of time sePNAS 兩 August 4, 2009 兩 vol. 106 兩 no. 31 兩 12791 ECOLOGY maturation at smaller size has systematically been attributed to fishery activities in marine ecosystems (18, 19), although this pattern perfectly fits the TSR in environments that have been subjected to gradual warming. Although not underestimating the impact of fisheries, our results stressed that fishery pressure cannot be considered as the unique trigger of observed changes in size structures in marine ecosystems. Further analyses would be needed to evaluate the relative merit of global warming and fisheries in explaining changes in body size of marine fish. The TSR predicts a negative effect of warming on size at maturity but a positive effect on growth rate. As a consequence, warming leads to smaller sizes late in the ontogeny but to larger sizes early in the ontogeny. Thus, by only considering young-of-the-year individuals fish in rivers when testing the size-at-age shift hypothesis, we probably underestimated the impact of climate change on individual body size under no or low fishery pressure. Cascading effects could also contribute to the changes in size. For instance, we cannot exclude that the decrease in size of Pseudocalanus sp. is partially due to low food quality of smallsized phytoplankton in warmer mesocosms (Fig. 4B). However, this effect can, again, not fully explain the observed changes because the other decreases in size (e.g., for freshwater fish or for phytoplankton) were not observed under decreasing food quality. Regarding fish communities, top-down constraints can also influence size structures. In particular, change in the abundance of predators can influence the abundance of smaller prey (20, 21). Nevertheless, in the large rivers studied, no special change in the predator abundance was observed (22, 23). Thus, we can safely conclude that temperature clearly negatively impacts body sizes at all biological scales. One of the most surprising results of our analysis is the increase in proportion of young age classes under warming. Actually, to our knowledge, such a pattern has never been suggested before to explain the decrease in mean body size at the population scale under warming. However, it is important to note that this hypothesis has been mostly tested by using European freshwater fish populations where cyprinidae was the dominant family. The positive effect of high temperature and/or low flow conditions on recruitment is well known for many cyprinidae (24–30). Even though the underlying mechanisms are unclear, we cannot exclude that this effect is specific to cyprinids. From this viewpoint, we may agree that it is necessary to test the population age-structure shift hypothesis with other biota to consider it as a rule. We have shown that ecological rules represent important tools when evaluating the ecological impacts of climate change. Symmetrically, climate change provides a good opportunity to test for the relative contribution of temperature in explaining ecogeographical rules. Explanations of Bergmann’s and James’ rules have invoked also latitude-related factors other than temperature, e.g., food availability, predation risk, distance from lowlatitude refuges during ice ages, migration availability, and resistance to starvation (31). Although not negating the role of other factors, our study provides strong evidence that temperature actually plays a major role in driving changes in the size structure of populations and communities. More generally, it would be interesting to consider the impacts of global warming when studying any ecological rules based on size variability. For instance, according to Elton’s rule [which states that body size decreases with decreasing trophic levels (32)], our results suggest that upper trophic levels could be more sensitive to climate warming than lower ones. To conclude, we provide evidence that reduced body size is the third universal ecological response to global warming besides the shift of species ranges toward higher altitudes and latitudes and the seasonal shifts in life-cycle events. Further analyses would be necessary to identify the possible mechanism linking temperature and size across the different biological scales. If such a ries of yearly total catch in numbers and mean weight in the catch for different age classes (1 y old to ⬎8 y old) over 31 years in the Baltic Sea. Sprat data were available for the whole Baltic Sea except the Kattegat area (i.e., for ICES subdivisions 22–32). Herring data were available for the whole Baltic Sea except zones located to the east of ⬇15°05⬘00⬙ E (i.e., for ICES subdivisions 25–32 and Gulf of Riga). Baltic Sea surface temperature during the sampling period significantly increased (36) (Table S2). We used yearly mean weights to test the population body size shift hypothesis. Mean weights were calculated as the ratio of total biomass to total catch per year. Total biomasses were estimated as the product of weights-at-age and catches in numbers per age, summed over all ages. The population age-structure shift hypothesis was tested by using the yearly proportions of fish ⬍3 years old. Time series of weight-at-age were used to test the size-at-age shift hypothesis. Published data. To test the species shift hypothesis, we used observed changes in fish community structure in the North Sea under global warming (17). The study was based on the North Sea IBTS (International Bottom Trawl Survey) fishery data from DATRAS (Database of Trawl Surveys) and were provided by the ICES to the authors. Experimental Data. Experimental data were obtained by sampling female adults of the copepod Pseudocalanus sp., bacteria, and phytoplankton communities in indoor mesocosms that simulated early spring (February–April) environmental conditions in the Kiel Bight (Baltic Sea) under different climatic scenarios (15, 16). Eight mesocosms were exposed to 4 temperature regimes (i.e., 2 mesocosms per chamber). The reference regime (⫹0 °C) corresponded to the 1993–2002 average temperature regime observed in the Kiel Bight, whereas the ⫹2, ⫹4, and ⫹6 °C regimes corresponded to different levels of warming. Percentage of the natural light intensity above cloud cover (Io) was controlled to simulate different cloud cover and underwater light attenuation. Phytoplankton was sampled at 16%, 64%, and 32% Io (2005, 2006, and 2007 experiments). Pseudocalanus sp. and bacteria were only sampled at 64% and 16% Io, respectively. Bacteria communities. Data were collected in the ⫹0 and ⫹6 °C mesocosms during the 2005 experiment (37). Bacteria were sampled on average 1.33 times a week in the reference mesocosms and on average 1.5 times a week in the ⫹6 °C mesocosms. For each sample, mean cell volume of the community was derived from length and width cell measurements. Measurements were assessed by means of a new Porton grid—G12 after DAPI staining in an epiflu- 1. Parmesan C, Yohe G (2003) A globally coherent fingerprint of climate change impacts across natural systems. Nature 421:37– 42. 2. Root TL, et al. (2003) Fingerprints of global warming on wild animals and plants. Nature 421:57– 60. 3. Walther GR, et al. (2002) Ecological responses to recent climate change. Nature 416:389 –395. 4. Pearman PB, et al. 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Olsen EM, et al. (2004) Maturation trends indicative of rapid evolution preceded the collapse of northern cod. Nature 428:932–935. 12792 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0902080106 orescence microscope by vision. We used mean cell volume in the different mesocosms to test the community body size shift hypothesis. Times series are provided in Table S5. Pseudocalanus sp. individuals. Female adults of Pseudocalanus sp. were sampled and individually measured at the end of the 2006 experiment. The size-at-age shift hypothesis was tested by using mean length of individuals in the different mesocosms. Copepods are particularly suitable for testing this hypothesis because they do not increase in length after having molted to the adult stage. Times series are provided in Table S6. Published data. We used a study dealing with changes in size structure of phytoplankton communities in Kiel mesocosms (16) to test the community body size hypothesis and the species shift hypothesis. Statistical Analysis. Hypotheses were tested with the time series data by using a weighted metaanalysis (38). The ‘‘effect sizes’’ in the metaanalysis were S statistics from Mann–Kendall trend tests (39) (see Fig. S1, SI Text, and Table S7 and S8). Variances of S were corrected for temporal autocorrelation when they occurred (40). Mean temporal trends were considered significant if their 95% confidence intervals did not contain 0 (38). To test whether fishery pressure on herring and sprat populations can influence the response of organisms to warming (population body size shift, population age-structure shift, and size-at-age shift hypotheses), we defined a categorical variable that discriminated marine vs. freshwater populations. Fishery effect was evaluated by checking for significant between-group heterogeneity (Qb) in the effect size (38). For experimental data, we used LME models (41) to evaluate the effect of temperature on the dependent variables (see Fig. S1, SI Text, and Table S7 and Table S8). This allowed the potential differences in variance among mesocosms to be considered when evaluating the coefficients of the models and their confidence intervals. All statistical analyses were performed by using R (42). ACKNOWLEDGMENTS. We thank Électricité de France, Cemagref (and especially H. Capra), H. G. Hoppe, R. Koppe, P. Breithaupt (Leibniz-Institut für Meereswissenschaften–GEOMAR), and ICES for providing data. English has been edited by T. Snelder. We thank D. Atkinson for his helpful comments on the early drafts of the manuscript and C. Bonenfant for statistical advice. This work was partially supported by the Deutsche Forschungsgemeinschaftfunded priority program 1162 ‘‘AQUASHIFT’’ and by Électricité de France. 19. Kuparinen A, Merila J (2007) Detecting and managing fisheries-induced evolution. 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Grenouillet G, Hugueny B, Carrel G, Olivier J, Pont D (2001) Large-scale synchrony and interannual variability in roach recruitment in the Rhône River: The relative role of climatic factors and density-dependent processes. Freshw Biol 46:11–26. 31. Blackburn T, Gaston KJ, Loder N (1999) Geographic gradients in body size: A clarification of Bergmann’s rule. Divers Distrib 5:165–174. 32. Elton C (1927) Animal Ecology (Sidwick and Jackson, London). 33. Brown JH, Gillooly JF, Allen AP, Savage VM, West GB (2004) Toward a metabolic theory of ecology. Ecology 85:1771–1789. 34. Daufresne M, Boët P (2007) Climate change impacts on structure and diversity of fish communities in rivers. Glob Change Biol 13:2467–2478. 35. Froese R, Pauly D, eds (2009) FishBase available at www.fishbase.org, ver 03/2009. 36. Mackenzie BR, Schiedek D (2007) Daily ocean monitoring since the 1860s shows record warming of northern European seas. Glob Change Biol 13:1335–1347. Daufresne et al. 40. Hamed K, Rao A (1998) A modified Mann–Kendall trend test for autocorrelated data. J Hydrol 204:182–196. 41. Pinheiro J, Bates D (2004) Mixed-Effects Models in S and S-PLUS (Springer, New York). 42. R Development Core Team (2008) R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, Austria). ECOLOGY 37. Hoppe HG, et al. (2008) Climate warming in winter affects the coupling between phytoplankton and bacteria during the spring bloom: A mesocosm study. Aquat Microb Ecol 51:105–115. 38. Gurevitch J, Hedges V (1993) in Design and Analysis of Ecological Experiments, eds Scheiner M, Gurevitch J (Chapman and Hall, New York), pp 378 –398. 39. Kendall M (1955) Rank Correlation Methods (Griffin, London), 2nd Ed. Daufresne et al. PNAS 兩 August 4, 2009 兩 vol. 106 兩 no. 31 兩 12793 Clim Dyn (2014) 43:2607–2627 DOI 10.1007/s00382-014-2075-y Global warming and 21st century drying Benjamin I. Cook • Jason E. Smerdon Richard Seager • Sloan Coats • Received: 19 August 2013 / Accepted: 27 January 2014 / Published online: 6 March 2014 Ó Springer-Verlag (outside the USA) 2014 Abstract Global warming is expected to increase the frequency and intensity of droughts in the twenty-first century, but the relative contributions from changes in moisture supply (precipitation) versus evaporative demand (potential evapotranspiration; PET) have not been comprehensively assessed. Using output from a suite of general circulation model (GCM) simulations from phase 5 of the Coupled Model Intercomparison Project, projected twentyfirst century drying and wetting trends are investigated using two offline indices of surface moisture balance: the Palmer Drought Severity Index (PDSI) and the Standardized Precipitation Evapotranspiration Index (SPEI). PDSI and SPEI projections using precipitation and PenmanMonteith based PET changes from the GCMs generally agree, showing robust cross-model drying in western North America, Central America, the Mediterranean, southern Africa, and the Amazon and robust wetting occurring in the Northern Hemisphere high latitudes and east Africa (PDSI only). The SPEI is more sensitive to PET changes than the PDSI, especially in arid regions such as the Sahara and Middle East. Regional drying and wetting patterns largely mirror the spatially heterogeneous response of precipitation in the models, although drying in the PDSI and SPEI calculations extends beyond the regions of reduced precipitation. This expansion of drying areas is attributed to globally widespread increases in PET, caused by increases in surface net radiation and the vapor pressure deficit. B. I. Cook (&) NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025, USA e-mail: benjamin.i.cook@nasa.gov J. E. Smerdon  R. Seager  S. Coats Lamont-Doherty Earth Observatory, 61 Route 9W, Palisades, NY 10964, USA Increased PET not only intensifies drying in areas where precipitation is already reduced, it also drives areas into drought that would otherwise experience little drying or even wetting from precipitation trends alone. This PET amplification effect is largest in the Northern Hemisphere mid-latitudes, and is especially pronounced in western North America, Europe, and southeast China. Compared to PDSI projections using precipitation changes only, the projections incorporating both precipitation and PET changes increase the percentage of global land area projected to experience at least moderate drying (PDSI standard deviation of B-1) by the end of the twenty-first century from 12 to 30 %. PET induced moderate drying is even more severe in the SPEI projections (SPEI standard deviation of B-1; 11 to 44 %), although this is likely less meaningful because much of the PET induced drying in the SPEI occurs in the aforementioned arid regions. Integrated accounting of both the supply and demand sides of the surface moisture balance is therefore critical for characterizing the full range of projected drought risks tied to increasing greenhouse gases and associated warming of the climate system. 1 Introduction Extreme climate and weather events have caused significant disruptions to modern and past societies (Coumou and Rahmstorf 2012; Ross and Lott 2003; Lubchenco and Karl 2012), and there is concern that anthropogenic climate change will increase the occurrence, magnitude, or impact of these events in the future (e.g., Meehl et al. 2000; e.g., Rahmstorf and Coumou 2011). Drought is one such extreme phenomenon, and is of particular interest because 123 2608 of its often long-term impacts on critical water resources, agricultural production, and economic activity (e.g., Li et al. 2011; e.g., Ding et al. 2011; e.g., Ross and Lott 2003). Focus on drought vulnerabilities has increased due to a series of recent and severe droughts in regions as diverse as the United States (Hoerling et al. 2012, 2013; Karl et al. 2012), east Africa (Lyon and DeWitt 2012), Australia (McGrath et al. 2012), and the Sahel (Giannini et al. 2003). Recent work further suggests that global aridity has increased in step with observed warming trends, and that this drying will worsen for many regions as global temperatures continue to rise with increasing anthropogenic greenhouse gas emissions (Burke et al. 2006; Dai 2013; Sheffield and Wood 2008). There are significant uncertainties, however, in recent and projected future drought trends, especially regarding the extent to which these trends will be forced by changes in precipitation versus evaporative demand (Hoerling et al. 2012; Sheffield et al. 2012). Drought is generally defined as a deficit in soil moisture (agricultural) or streamflow (hydrologic); as such, it can be caused by declines in precipitation, increases in evapotranspiration, or a combination of the two. In the global mean, both precipitation and evapotranspiration are expected to increase with warming, a consequence of an intensified hydrologic cycle in a warmer world (Allen and Ingram 2002; Huntington 2006). Regional changes in precipitation and evapotranspiration, and the dynamics that drive such changes, are nevertheless more uncertain, despite the fact that these changes are perhaps of greatest relevance to on-the-ground stakeholders. Precipitation projections in general circulation models (GCMs) have large uncertainties compared to other model variables, such as temperature (e.g., Knutti and Sedlacek 2013). The most confident estimates indicate that precipitation will increase in mesic areas (e.g., the wet tropics, the mid- to high latitudes of the Northern Hemisphere, etc) and decrease in semi-arid regions (e.g., the subtropics). This is generally referred to as the ‘rich-get-richer/poor-getpoorer’ mechanism, and is attributed to thermodynamic (warming and moistening of the atmosphere) and dynamic (circulation) processes (Chou et al. 2009, 2013; Held and Soden 2006; Neelin et al. 2003; Seager et al. 2010). Evapotranspiration includes both the physical (evaporation) and biological (transpiration) fluxes of moisture from the surface to the atmosphere and can be viewed in terms of actual evapotranspiration (latent heat flux) or evaporative demand (potential evapotranspiration; PET). PET is expected to increase in the future (Scheff and Frierson 2013), forced by increases in both total energy availability at the surface (surface net radiation) and the vapor pressure deficit (the difference between saturation and actual vapor pressure; VPD). Increased radiative 123 B. I. Cook et al. forcing from anthropogenic greenhouse gases (GHG) will increase surface net radiation in most areas by inhibiting longwave cooling, while GHG-induced warming of the atmosphere will increase the VPD. Importantly, VPD increases with warming, even at constant relative humidity (e.g., Anderson 1936). Actual evapotranspiration is expected to increase less than PET in areas where latent heat fluxes are, or will become, limited by moisture supply. Indeed, declines in global actual evapotranspiration have been documented over the last two decades (Jung et al. 2010), attributed primarily to soil moisture drying in the Southern Hemisphere. The idea that increased evaporative demand in a warmer world will enhance drought is not new (e.g., Dai 2011), but it is important to understand where precipitation or evaporation changes will be dominant individual drivers of drought and where they will work in concert to intensify drought. To date, however, little has been done to quantify and explicitly separate the relative contribution of changes in precipitation versus evaporative demand to the magnitude and extent of global warming-induced drying. To address this question, we use output from a suite of twentieth and twenty-first century GCM simulations, available through the Coupled Model Intercomparison Project phase 5 (CMIP5, Taylor et al. 2012), to calculate two offline indices of surface moisture balance: the Palmer Drought Severity Index (PDSI; Palmer 1965) and the Standardized Precipitation Evapotranspiration Index (SPEI; Vicente-Serrano et al. 2009). Both indices provide ideal and flexible estimations of surface moisture balance, allowing us to vary inputs such as model precipitation, temperature, and surface energy availability in order to separate and quantify the influence of specific variables on future drought projections. Our analysis thus addresses three questions: (1) What are the relative contributions of changes in precipitation and evaporative demand to global and regional drying patterns?, (2) Where do the combined effects of changes in precipitation and evaporative demand enhance drying?, and (3) In which regions, if any, are increases in evaporative demand sufficient to shift the climate towards drought when precipitation changes would otherwise force wetter conditions? 2 Data and methods 2.1 CMIP5 model output We use GCM output available from the CMIP5 archive, the suite of model experiments organized and contributed from various modeling centers in support of the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC). Output from the historical and Global warming and 21st century drying RCP8.5 model scenarios is used. The historical experiments are run for the years 1850–2005 and are forced with observations of transient climate forcings (e.g., solar variability, land use change, GHG concentrations, etc). These experiments are initialized in 1850 using output from long, unforced control runs with fixed pre-industrial climate forcings. The RCP8.5 scenario (2006–2099) is one of a suite of future GHG forcing scenarios; RCP8.5 is designed so that the top of the atmosphere radiative imbalance will equal approximately ?8.5 W m-2 by the end of the twentyfirst century, relative to pre-industrial conditions. The RCP8.5 scenario runs are initialized using the end of the historical runs. Our analysis is restricted to those models (Table 1) with continuous ensemble members spanning the historical through RCP8.5 time periods. 2.2 Drought indices We are interested in long-term (decadal to centennial) trends and changes in moisture availability, rather than shorter-term (month to month) drought events. For this reason, our analysis uses two drought indices that integrate over longer timescales: the PDSI and 12-month SPEI. Understanding the causes, inception, and termination of discrete (and often short and intense) drought events (e.g., Hoerling et al. 2012, 2013) is an important scientific goal. Our focus, however, is on the longer-term drying and wetting responses to GHG warming, the hydroclimatic baseline within which seasonal or annual events will occur in the future. Simulated soil moisture within the GCMs is not easily separated into contributions from precipitation or PET, making it difficult to identify the extent to which soil moisture trends in the models are driven by changes in supply and/ or demand. Moreover, each GCM employs soil models that vary widely in their sophistication (e.g., soil depth, number of layers, etc), tunings, and parameterizations (e.g., soil texture, rooting depths, vegetation types, etc), complicating the meaningful comparison of soil moisture and drought responses across GCMs. PDSI and SPEI provide a flexible framework that allows GCM output to be modified (e.g., detrended) as a means of isolating drought contributions from specific changes, such as trends in precipitation or net radiation. A common offline metric, such as PDSI or SPEI, also provides a standard comparison of soil moisture balance, thus controlling for differences in soil models across the ensemble of CMIP5 GCMs. The PDSI (Palmer 1965) is a normalized index of drought using a simplified soil moisture balance model calculated from inputs of precipitation and losses from evapotranspiration. PDSI is locally normalized, with negative values indicating drier than normal conditions (droughts) and positive values indicating wetter than normal conditions (pluvials), relative to a baseline calibration period 2609 Table 1 Continuous model ensembles from the CMIP5 experiments (historical?RCP8.5) used in this analysis, including the modeling center or group that supplied the output, the number of ensemble members that met our criteria for inclusion, and the approximate spatial resolution Model Modeling center (or Group) # Runs CanESM2 CCCMAa 5 2.8° 9 2.8° 6 0.94° 9 1.25° b Lat/Lon resolution CCSM4 NCAR CNRM-CM5 CNRM-CERFACSc 4 1.4° 9 1.4° CSIRO-MK3.6.0 CSIRO-QCCCEd 5 1.87° 9 1.87° GFDL-CM3 NOAA GFDLe 1 2.0° 9 2.5° GFDL-ESM2G GFDL-ESM2M NOAA GFDLe NOAA GFDLe 1 1 2.0° 9 2.5° 2.0° 9 2.5° GISS-E2-R NASA GISSf 1 2.0° 9 2.5° INMCM4.0 INMg 1 1.5° 9 2.0° IPSL-CM5A-LR IPSLh 4 1.9° 9 3.75° MIROC5 MIROCi 1 1.4° 9 1.4° MIROC-ESM MIROCj 1 2.8° 9 2.8° j MIROC-ESM-CHEM MIROC 1 2.8° 9 2.8° MRI-CGCM3 MRIk 1 1.1° 9 1.1° NorESM1-M NCCl 1 1.9° 9 2.5° a Canadian Centre for Climate Modelling and Analysis b National Center for Atmospheric Research Centre National de Recherches Météorologiques / Centre Européen de Recherche et Formation Avancée en Calcul Scientifique c d Commonwealth Scientific and Industrial Research Organization in collaboration with Queensland Climate Change Centre of Excellence e NOAA Geophysical Fluid Dynamics Laboratory f NASA Goddard Institute for Space Studies g Institute for Numerical Mathematics hInstitut Pierre-Simon Laplace Atmosphere and Ocean Research Institute (The University of Tokyo), National Institute for Environmental Studies, and Japan Agency for Marine-Earth Science and Technology i j Japan Agency for Marine-Earth Science and Technology, Atmosphere and Ocean Research Institute (The University of Tokyo), and National Institute for Environmental Studies k Meteorological Research Institute l Norwegian Climate Centre Table 2 Description of different versions of the PDSI and SPEI calculations, and the model diagnostics used in their calculation PDSI/SPEI Transient Variables Detrended Variables PDSI-ALL, SPEI-ALL tsurf, prec, q, rnet none PDSI-PRE, SPEI-PRE prec tsurf, q, rnet PDSI-PET, SPEI-PET tsurf, q, rnet prec Variables are: tsurf 2-m surface air temperature, prec precipitation, q specific humidity, rnet surface net radiation. Detrended variables have the trend from 2000–2099 removed and replaced with mean conditions for 1980–1999 123 2610 B. I. Cook et al. Fig. 1 Pearson’s correlation coefficients calculated between PDSI (a,c) and SPEI (b,d) and annual average model soil moisture from the approximate top 30 cm of the soil column: CanESM2 (a,b) and CCSM4 (c,d). Maps represent average correlations across a five member ensemble for each model; the comparison interval is 1901–2099 for a given location. PDSI has persistence on the order of 12–18 months (Guttman 1998; Vicente-Serrano et al. 2010), integrating moisture gains and losses throughout the calendar year, and providing a useful metric to describe longer term trends and variability in hydroclimate. PDSI has been widely used as a metric to quantify drought using climate model simulations (e.g., Bonsal et al. 2013; Burke and Brown 2008; Coats et al. 2013; Cook et al. 2010, 2013; Dai 2011, 2013; Rosenzweig and Hillel 1993; Seager et al. 2008; Taylor et al. 2013). Because recent work has suggested that PDSI may be intrinsically too sensitive to changes in PET (e.g., Burke 2011; Seneviratne 2012), we repeat our analysis using an alternative drought index, the SPEI. Like PDSI, SPEI (Vicente-Serrano et al. 2009) is a normalized index of drought, developed from the original Standardized Precipitation Index (SPI, McKee et al. 1993). Whereas the SPI is based on normalized accumulations of precipitation surpluses and deficits over some user-defined interval (typically 1, 3, or 12 months), SPEI uses accumulations of precipitation minus PET. Therefore, SPEI includes in its accounting both supply and demand changes in moisture variability, and can be interpreted similarly to PDSI (i.e., positive values of SPEI indicate wetter than average conditions, negative values indicate drier than average conditions). Unlike PDSI, SPEI does not include an explicit soil moisture balance accounting, a...
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