Attributing the behavior of low-level clouds in large-scale
models to sub-grid scale parameterizations
R. A. J. Neggers,
1,2Key points:
1. The behavior of low-level clouds in climate models is attributed to parameterizations 2. The resemblance between SCM and GCM results is assessed and quantified
3. Boundary-layer schemes are found to have a unique fingerprint behavior
Abstract. This study explores ways of establishing the characteristic behavior of boundary-layer schemes in representing subtropical marine low level clouds in climate models. To this purpose parameterization schemes are studied in both isolated and interactive mode with the larger-scale circulation. Results of the EUCLIPSE/GASS intercomparison study for single-column models (SCM) on low level cloud transitions are compared to general circulation model (GCM) results from the CFMIP-2 project at selected gridpoints in the subtropical Eastern Pacific. Low cloud characteristics are plotted as a function of key state variables for which large-eddy simulation results suggest a distinct and reasonably tight relation. The typical patterns thus established are compared between SCM and GCM results, and their resemblance is quantified using simple metrics. Good agreement is re-ported between SCM and GCM results, to such a degree that SCM results are found to be uniquely representative of their GCM, and vice versa. This suggests that the sys-tem of parameterized fast boundary-layer physics dominates the model state at any given time, even when interactive with the larger-scale flow. This behavior can be interpreted as a unique “fingerprint” of a boundary-layer scheme, recognisable in both SCM and GCM simulations. The result justifies and advocates the use of SCM simulation for improv-ing weather and climate models, includimprov-ing the attribution of typical responses of low clouds to climate change in a GCM to specific parameterizations.
1. Introduction
Boundary layer clouds play a key role in the Earth’s cli-mate system, given their strong impact on the vertical dis-tribution of heat, moisture, aerosols and radiation. Under-standing their response to global warming is one of the grand challenges in climate science, a problem that has focused re-search efforts on feedback mechanisms between clouds and climate [Bony et al., 2015]. One of the key problems is that boundary layer processes, including low level clouds, remain unresolved at the typical discretizations applied in General Circulation Models (GCMs), and have to be rep-resented through parameterization. Although suspected for some time, recent studies have again emphasized issues with cloud representation in climate models [e.g.Nam et al., 2012;
Stevens and Bony, 2013], and some have linked climate un-certainty to the representation of low level clouds in GCMs [Bony and Dufresne, 2005;Dufresne and Bony, 2008;Vial et al., 2013; Zelinka et al., 2013]. Although these results have been instructive and have focused the research effort, it has proven much more difficult to actually attribute GCM errors to individual parameterizations.
Various techniques have been developed to investigate the behavior of boundary-layer clouds in GCMs. A unique as-pect of these clouds is that they are an integral part of a
1Institute for Geophysics and Meteorology, University of Cologne, Germany.
2Royal Netherlands Meteorological Institute, De Bilt, The Netherlands.
Copyright 2015 by the American Geophysical Union.
tightly coupled system of processes including turbulence, convection, microphysics, radiation and surface exchange. These processes act at time-scales much shorter than the large-scale dynamics. For this reason these processes are sometimes referred to as “fast physics”. Accordingly, one might expect that in a GCM a boundary-layer scheme tends to quickly establish its own unique state. Weather forecast-ing techniques have been successfully applied to investigate this behavior in climate models, such as the initial tendency approach [Rodwell and Palmer, 2007] and the Transpose-AMIP approach [Williams et al., 2013]. The Single Column Model (SCM) technique even goes one step further, in that a single vertical column of the GCM grid is time-integrated in an isolated mode from the larger-scale flow, using pre-scribed large-scale forcings [e.g. Randall et al., 2003]. A benefit of SCM simulation is its low computational cost, which enhances the model transparency and facilitates sen-sitivity studies. Model results can be constrained with ob-servational datasets and with Large-Eddy Simulation (LES) results, configured and driven in exactly the same way.
SCM simulation is actively used as a testing ground for parameterization development and improvement [Neggers et al., 2012], and even to make statements about cloud cli-mate feedbacks in GCMs [e.g.Zhang et al., 2013]. But is it safe to do this? One wonders to what degree the SCM results are representative of the behavior of parameterized physics in a GCM setting. Are SCM results predictive of how a GCM behaves? These critical questions are often implicitly answered positively, but actual proof for these as-sumptions is lacking. It would be helpful to somehow be able to characterize the typical behavior of parameterized physics, so that it could more easily be recognized in GCM evaluations. In other words, to establish their typical finger-print, using a metric that allows us to distinguish between behavior of different boundary-layer schemes.
A unique opportunity for comparing GCMs to SCMs has recently been created by the combination of two interna-tional research projects. The first project is the second phase of the Cloud Feedback Model Intercomparison Project (CFMIP-2, http://cfmip.metoffice.com/), which is an ex-tension to phase 5 of the Coupled Model Intercomparison Project [CMIP5 Taylor et al., 2012]. One of the key tar-gets of CFMIP-2 is to make high-resolution, high-frequency data from the CMIP5 simulations available at a set of se-lected gridpoints that are of interest to the research com-munity [Webb et al., 2015]. The aim is to facilitate process-model development and improvement. The set of locations is chosen to reflect areas where GCMs are known to have problems in cloud representation [e.g.Lin et al., 2014], and includes the subtropical marine subsidence zones that are associated with high cloud cover and cloud amount [Klein and Hartmann, 1993]. The second project is the combined EUCLIPSE/GASS model intercomparison project on low-level cloud transitions, in which cases based on observational data in the subtropical marine subsidence zones are simu-lated with LES and SCM [van der Dussen et al., 2013; Neg-gers et al., 2015]. The aim is to assess the performance of boundary-layer schemes in reproducing the transition from stratocumulus to shallow cumulus.
This study is dedicated to exploring ways of character-izing the typical behavior of boundary layer schemes in the subtropical marine subsidence regime, making use of both SCM and GCM output. Four GCMs participating in CFMIP-2 also participated in the EUCLIPSE/GASS inter-comparison project for SCM models - using exactly the same system of parameterizations. In addition, there is also unity of location, with many of the CFMIP-2 selected gridpoints located in the subtropical Eastern Pacific region that also hosts the composite transition cases [Sandu et al., 2010]. In other words, an opportunity is created for a fair comparison of the behavior of parameterized low clouds in both isolated and interactive mode with the larger-scale circulation. The purpose of this study is twofold:
• To establish the typical behavior of boundary-layer clouds in both SCM and GCM realizations as a function of key state variables; and
• To cross-compare these patterns, quantify their resem-blance, and attempt to thus attribute behavior of low clouds in GCMs to parameterization schemes.
Achieving these goals comes down to demonstrating that boundary-layer schemes behave in a unique and recognisable way, be it in SCM or GCM context. If the result is that typ-ical patterns as established in SCM simulations can not be recognized in GCM output, this puts in question the use of the SCM technique in improving GCM parameterizations, simply because they do no represent the GCM context well enough. However, if significant correlations exist between SCM and GCM behavior this would build confidence in the use of SCMs as a research tool. A positive result would mean that GCM behavior can be attributed to specific parameter-izations, and would advocate the use of SCM in addressing uncertainties in numerical predictions of future climate re-lated to boundary-layer clouds.
Section 2 describes the setup of the GCM, SCM and LES experiments of which data is used in this study, gives an overview of the subset of CFMIP-2 selected gridpoints, and introduces the participating SCM and GCM codes. Section 3 defines three measures of inversion strength, and explores their use in establishing fingerprint behavior of parameter-ized boundary-layer physics, making use of LES results. The main results of this study are presented in Section 4, while the general conclusions and their implications are further discussed in Section 5.
2. Dataset description
2.1. GCM output at selected gridpoints
The GCM data from the 5th Coupled Model Intercom-parison Project (CMIP5) used in this study concerns ex-periments that follow the configuration of the Atmospheric
Model Intercomparison Project [AMIP,Gates et al., 1999], featuring a prescribed sea surface temperature (SST) while the atmosphere is allowed to run freely. In the CFMIP-2 ex-tension to CMIP5 model output was generated for the above AMIP runs at a range of selected gridpoints at high, unaver-aged time- and height discretizations. Many variables are in-cluded in the model output, which is designed to allow eval-uation of the model and its parametric components at pro-cess level and at integration timestep. More information on the locations of all selected sites and the available variables is provided on the CFMIP website (http://www.cfmip.net). The GCM data used in this study is available through the Earth System Grid data-portal that is part of CMIP5.
Figure 1 shows a map of the Eastern Pacific, including the subset of 29 selected gridpoints that are used in this study. The selection of this subset reflects the cloud regime of interest as well as the necessity to overlap with the SCM intercomparison study. Subtropical marine boundary layer clouds occur persistently in the low level Tradewind flow in the Eastern part of the oceanic basins [Klein and Hartmann, 1993]. At some point in the Easterly flow the low level cloud deck experiences a transition from stratocumulus to shallow cumulus, associated with a sharp decrease in cloud cover and cloud amount. The set of selected gridpoints constitute two transects through the NE and SE subsidence zones, and have been defined in previous research projects. The loca-tions in the NE Pacfic make up the GPCI transect [Teixeira et al., 2011], while the points in the SE Pacific form the VOCALS transect [Mechoso et al., 2014].
2.2. SCM intercomparison on cloud transitions
An overview of the setup of the four subtropical marine low-level cloud transition cases that together make up the EUCLIPSE/GASS intercomparison study is given by Neg-gers et al. [2015]. Three of the four cases are situated in the NE Pacific, with one case is situated in the NE Atlantic just south of the Azores islands. What the four cases share is their Lagrangian setup, so that the advective forcings of temperature, humidity and momentum disappear from the associated budget equations. Similar to the GCM AMIP runs the time-development of the SST is prescribed; the same holds for the time-development and vertical structure of the large-scale subsidence. In all four cases the low level cloud deck transitions from stratocumulus to shallow cumu-lus during the time-period of simulation.
SCM and LES runs were generated for these cases. An extensive treatise on the creation of the four cases from ob-servational and reanalysis data, as well as a detailed report on the LES results, is given byvan der Dussen et al.[2013] for the ASTEX case and bySandu et al. [2010] andSandu and Stevens[2011] for the three composite cases. The SCM results are intercompared and discussed in great detail by
Neggers et al.[2015]. The data used in this study is sampled from the database of model output that was created during the EUCLIPSE/GASS intercomparison case.
The geographic location of the SCM cases only partially matches the set of 29 CFMIP-2 locations. For example, the ASTEX case is not located in the NE Pacific. In addition, the VOCALS area is not covered by any SCM case. The main motivation for expanding the SCM and GCM datasets with points outside the core area is to increase the statistical significance of their comparison. The additional locations are all selected to match the cloud regime of interest (sub-tropical marine boundary-layer clouds in subsidence zones). A sensitivity test is included in this study to give the reader
insight into the impact of including the ASTEX and VO-CALS points on the main results. As will be shown, the results are reasonably robust for the selection of points.
2.3. Participating codes
Table 1 lists the four participating GCM codes and their associated SCMs. The participating models are all operational climate models, and include CNRM-CM5 (ARPEGE-CLIMAT), HadGEM2-A (MetOffice), IPSL-CM5A-LR (LMDZ-AR4) and MPI-ESM-LR (ECHAM6), with the associated SCMs mentioned between brackets. The names of the SCMs deviate from the associated GCMs, in or-der to stay consistent with the SCM intercomparison study [Neggers et al., 2015]. As stated earlier, the SCM simulations were performed with the identical system of parameteriza-tion as used in the CMIP simulaparameteriza-tions.
3. Evaluation strategy
3.1. Measures of inversion strength
One goal of this study is to establish the typical behav-ior of boundary-layer clouds in models. To this purpose key state variables will first be defined in terms of which cloud behavior can be expressed. The idea is that this dependence should be unique for each model; in other words, in the space set up by the selected key state variables a parameterization scheme should be identifiable by a unique fingerprint or pat-tern.
Weak relations have been suggested between boundary-layer cloud cover and the strength of the capping inversion. Figure 2 is a schematic overview of the thermodynamic and cloud structure of the marine boundary layer in transition. As thermodynamic state variables are chosen the liquid wa-ter potential temperatureθland the total specific humidity qt, because they are conserved for moist adiabatic motions.
A first, rough measure of inversion strength is the Lower Tropospheric Stability [LTS, Klein and Hartmann, 1993], defined as
LTS =θ700l −θsf cl , (1)
with 700 referring to the 700 hPa pressure level. The con-venience of this measure is that it can easily be diagnosed from models with a low vertical resolution; a downside is that it does not take boundary-layer internal structure into account. This motivates defining the strength of the in-version more accurately by means of the jumps in thermo-dynamic state variables across the capping inversion layer. One measure of inversion strength that makes use of theθl
jump is the Estimated Inversion Strength [EIS,Wood and Bretherton, 2006], defined as
EIS = ∆θl, (2)
where ∆ indicates the change in value across the inver-sion, betweenz+
topandz
−
top. An alternative, more complex
parameter to define inversion strength is the Cloud Top Entrainment Instability parameter [CTEI, e.g. Deardorff, 1980; Randall, 1980;Kuo and Schubert, 1988;Lock, 2009], which depends on both jumps
κ= 1 + ∆θl (L/cp)∆qt
. (3)
When interpreting κ it should be noted that the humid-ity jump is always negative while the potential temperature jump is always positive (see also Fig. 2). To calculate EIS andκinformation is needed on the position and depth of the capping inversion layer. The exact method used to diagnose inversion properties from the vertical grid of the SCM and LES results is described in detail in Appendix A.
3.2. Scatterplots
The behavior of total cloud cover (TCC) as a function of LTS, EIS andκis now briefly investigated using Large-Eddy Simulation (LES) results. Figure 3 shows LES results for all four transition cases. LES results for a well-documented fair-weather Cumulus case [Rain in Cumulus over the Ocean, or RICO;vanZanten et al., 2011] are included to further ex-pand the parameter space, because in three of the four cases the transition to fair-weather cumulus is not complete.
In all three diagrams the pdf of collective LES results shows a distinctive pattern. The diagrams using LTS and EIS show multiple modes on the ordinate for a substantially broad range of values on the abcissa. This means that for a given value of LTS or EIS more than one solution of TCC is possible, implying that that these measures are not useful for separating between states in cloud cover. The spread in TCC increases when moving from high to low LTS and EIS values. It is interesting to interpret this in terms of the findings ofWood and Bretherton [2006]. They used re-analysis data to find a much better relation between EIS and TCC, as indicated in Fig. 3b. It is hypothesized that the difference is mainly explained by i) the use of LES re-sults at much higher temporal and spatial resolutions, ii) the absence of time-averaging, and iii) the limitation to only four cases. Indeed theWood and Bretherton[2006] fit seems commensurate with the increasing probability of lower cloud covers at lower EIS that is visible in Fig. 3c. In that sense, the LES results presented here do not necessarily contradict their findings. What is clear though is that the EIS-TCC relation should not be applied at process-level time-scales to parameterize TCC.
An important result is that of all three measures of in-version strength theκparameter yields the tightest pdf in the transition from high to low cloud cover (see Fig. 3c). In addition, even though the width of the pdf in the tran-sition zone is not zero, at least multiple modes (i.e. more than one maxima for a given value on the x-axis) are ab-sent. Theκ parameter was formulated in order to explain the break-up of the capping cloud layer in stratocumulus-topped boundary-layers. The results presented here support the general relation between total cloud cover andκas re-ported byLock [2009] using LES results. However, they are also commensurate with the results ofSandu and Stevens
[2011], who argue that significant spread still exists, and that this spread is too significant to allow the parameteri-zation of cloud cover as a one-to-one function ofκ.
The aim of this study is not to contribute to this discus-sion, or to further investigate the underlying science ques-tions. Instead, the idea is to make use of the apparent tight-ness of the pdf in (κ,TCC) space; the cloud transition from high to low values takes place within a reasonably narrow
κ-range (between about 0.2-0.4, see Fig. 3c). The key ques-tion is if SCMs are able to reproduce this tightness - they might produce much more scatter. If so, then the tight pdf in (κ,TCC) space as diagnosed from the LES can be used as a reference in the evaluation of parameterization schemes. Taking this one step further, the next question is if the pdf in (κ,TCC)-space as established by an SCM simulation can be considered as typical or unique for a certain boundary-layer scheme. Answering this science question is the central objective of this study.
4. Results
4.1. GCM results at single gridpoints
To give the reader an idea of the cloud regime of in-terest, Fig. 4 shows example time-height contour plots of
the cloud fraction as sampled from the HadGEM2-A GCM for the period JJA 2006 at three selected gridpoints on the GPCI Transect in the NE Pacific. These points are also in-dicated in Fig. 1, for reference. Gridpoint 18 is still in the StCu range, showing a shallow boundary layer of about 1km depth that is frequently covered completely by clouds. At Gridpoint 22 the boundary-layer has deepened significantly to about 2km, with the cloud layer similarly deepened and frequently featuring a capping cloud layer. In this sense this regime resembles the ”cumulus rising into stratocumulus” regime as observed during the ATEX campaign [Augstein et al., 1973, 1974;Stevens et al., 2001]. Finally Gridpoint 24 shows fair weather cumulus associated with much lower cloud fractions and a yet deeper cloud layer, with cloud tops sometimes even reaching 4 to 5 km during the final month. A striking feature visible at all three gridpoints is that within the JJA 2006 period significant variability exists in boundary-layer depth, cloud cover and cloud vertical struc-ture. This means that many different boundary-layer states are encountered, which creates some confidence in the rep-resentativeness of the (κ-TCC) diagrams that can be con-structed from this data. In other words, the distribution of cloud-inversion states in the GCM can be expected to be reasonably well sampled.
4.2. SCM results for four transition cases
Figure 5 shows scatter plots in (κ,TCC) space of the re-sults of four SCM simulations for all four transition cases. Each panel contains results of a single SCM. It should be noted that the statistical quality of these Lagrangian SCM simulations differs from the fixed-point GCM analy-ses, mainly in the shorter duration of the sampling period (3 days vs 3 months). This reflects the typical simulation times of previous model intercomparison studies for SCM and LES, which were limited by the computational demand of LES simulations. However, due to the transience of the four cases perhaps a sufficient number of states is visited to already allow a fair comparison with the GCM results.
Significant differences exist among SCM codes in (κ,TCC) space, both in the position and the width of the
κ-range in which the cloud transition takes place, if at all. Each code exhibits some unique features. For exam-ple, the ARPEGE-CLIMAT model reproduces the LES to some degree, in that the transition takes place in the range
κ∈ {0.3,0.4}(see also Fig. 3c). However, it seems to pre-fer two modes for a given intermediate TCC. The ECHAM6 model seems not to transition at all, preferring a well-defined mode at (κ,TCC) = (0.6,100%). The LMDZ-AR4 model has a distinctive maximum at (κ,TCC) = (0.6,80%), and transitions to low cover regime at higherκvalues compared to the LES. The MetOffice model also reproduces the LES structure to a reasonable degree, even reproducing the tight PDF during the transition as seen in the LES.
It is intriguing to establish that these patterns differ so much among the SCMs. At many points they also deviate substantially from the LES results. The question now arises how typical these patterns are. Can they be interpreted as fingerprints of the system of parameterizations that together establish this behavior? And can these patterns still be rec-ognized in GCM runs? As noted before, the pdfs as sampled from SCM runs might not be “complete”; areas in (κ,TCC) space might not yet have been visited, yielding sub-sampled or unsaturated pdfs. The question to what degree these pat-terns as established during four short SCM cases can still be recognized in GCM data is addressed in the next section.
4.3. Comparing GCM and SCM results
Figure 6 shows contour plots in (κ,TCC) space of the GCM results at the 29 selected gridpoints for the period JJA 2006, overplotted with the results of the associated SCM as
shown in 5. The GCM results are shown as contour plots while the SCM results are shown as symbols. This is a con-venient way of combining both datasets in one frame, while still allowing their visual comparison. The GCM distribu-tion is calculated using a 25x25 two-dimensional histogram in the visualized ranges, with bin-sizes of.072 and 4% on the abscissa and ordinate respectively.
The results suggest that the unique behavior established in the SCM results reappears in the GCM results. For exam-ple, the transition zone from high to low cloud fraction in the ARPEGE-CLIMAT SCM matches that of its native CNRM-CM5 GCM pretty well. The persistent mode at (κ,TCC) = (0.6,100%) as diagnosed in the ECHAM6 results reappears in the MPI-ESM-LR results at the same position. The same is true for the peculiar mode at (κ,TCC) = (0.6,80%) in the IPSL-CM5A-LR results, and the position and width of the transition zone in the HADGEM2-A results. However, some differences also exist; these do not concern mismatches in location, but mainly in GCM modes not being covered by SCM points. As discussed earlier, it is speculated that these areas represent conditions that are simply not visited during the four transition cases.
4.4. Quantifying resemblance
The results so far suggest that the behavior of boundary-layer schemes in (κ,TCC)-space as established with SCM re-alizations reappears in GCM experiments. But how can this resemblance between two pdfs be quantified? Many methods can be thought of, however a complication is that the SCM pdf is under-sampled, or incomplete. Such missing modes do not necessarily reflect a lack of model performance, but could also be due to the fact that the associated conditions are simply not encountered during the SCM simulations. A solution is to focus on the key features of the pdf that i) reflect the resemblance as established by eye and ii) can be expected to already be captured by a few SCM simulations. The most important variable in the evaluation of the ca-pacity of a process-model to represent the low level cloud transition is arguably the position on theκ axis at which this process effectively takes place. This point of transition corresponds to the modeµof the pdf, defined as the value on the abscissa at which the pdf is maximum, for a given TCC. The modes for a range of TCC values yield an axis in (κ,TCC) space, as shown in Fig. 7. A root-mean-square (RMS) of the difference between an SCM and GCM axis can then be defined as follows,
RMS = v u u t 1 NI N X i=1 (µS i −µGi) 2 Ii, (4)
where N is the total number of bins on the TCC axis, i
the associated bin-index, and superscriptsSandGindicate the SCM and GCM, respectively.Iiis an indicator function
reflecting if a TCC-bin contains SCM and GCM points or not,
Ii=
= 1 ifµSi andµGi both exist,
= 0 if not. (5)
As a result, the total number of binsNI can be written as
NI= N
X
i=1
Ii. (6)
The RMS thus quantifies the resemblance between an SCM and GCM concerning the maximum in the pdf; the lower the RMS, the better the resemblance. A useful benefit is that
it can also be applied to incomplete pdfs, for example with TCC bins where the SCM pdf has no entries. In practice this does occur, even though the four SCM cases have been designed to cover a transition.
The RMS as discussed above can be calculated for any SCM-GCM combination; so not only for the SCM with its native GCM, but for all possible SCM-GCM combinations. The four GCMs and four SCMs at the centre of this study then yield a 4x4 “resemblance-matrix” containing 16 RMS values, as shown in Fig. 8a. For clarification Fig. 8b shows horizontal cross-sections through this matrix, allowing as-sessment of the absolute RMS values. The first intriguing result is that a distinct minimum exists on the diagonal. This suggests that the pdf of an SCM in (κ,TCC) space al-ways best resembles that of its associated GCM. Another feature is that the matrix is reasonably, but not perfectly, symmetric. This suggests that reversing the SCM-GCM combination still gives, to some degree, the same resem-blance. Phrased alternatively, a certain SCM labeled “A” resembles a certain GCM labeled “B” to the same degree as GCM “A” resembles SCM “B”.
The powerful implication of these results is that the shape of the pdf in (κ,TCC) space really can be interpreted as a “fingerprint” of the underlying fast physics, in this case the boundary-layer scheme. Note that various aspects of the comparison could still be improved; for example, the time and location of the SCM and GCM simulations do not ex-actly match. To create more confidence in the results the sensitivity to the number of included points and the time-period of the GCM data is assessed in Fig. 9. Excluding the VOCALS points does not significantly alter the gen-eral shape of the resemblence matrix; the same holds for extending the time-period from JJA 2006 to two full years, although the minimum on the diagonal does get somewhat more pronounced. Accordingly, the general conclusion that the behavior in (κ,TCC) is unique for a boundary layer scheme is robust.
This study was fortunate in the fact that the four partic-ipating GCMs have very different boundary-layer schemes. This yields a resemblance matrix with the lowest RMS val-ues on the diagnonal, which was successful in demonstrat-ing the principle that each scheme gives a unique represen-tation of low clouds. But what if two GCMs would have identical, say perfect, physics? In that case the associated pdfs in (κ,TCC) space would be identical, and thus indistin-guishable. Also note that the MPI-ESM-LR GCM already behaves pretty similarly to the ARPEGECLIMAT SCM -which illustrates that only comparing the position of the pdf axis is perhaps not stringent enough a test for fully charac-terizing the pdf.
5. Discussion and conclusions
The main conclusion of this study is that the impact of the collective of parameterized fast physics that is responsible for the representation of subtropical marine low-level clouds in GCMs is so strong that it dominates the model state at any given time, even when interactive with the larger-scale flow. This is evident in (κ,TCC) space, where results of a particular physics package exhibit a unique, distinguish-able pattern, with quantifidistinguish-able resemblance between SCM and GCM results. This behavior can be therefore be inter-preted as a typical “fingerprint” of a parameterization pack-age. The conclusion is that SCM simulations of low clouds in the subtropical marine subsidence regime are indicative, or predictive, of their behavior in a GCM, and vice versa.
The applied method is shown to function for model re-sults plotted in (κ,TCC) space, where LES results exhibit a weak but distinct and reasonably tight relation between
boundary-layer cloud cover and the cloud top entrainment instability parameter. The method might not work so well for other variables, or for other cloud regimes, where such relation is meaningless or is not expected. Including more GCMs might also change the results, as discussed earlier. The method should therefore be used with caution. This study also refrains from attempting to explain why indi-vidual codes look or behave different; such efforts are best conducted by experts on a particular implementation of a boundary-layer scheme in an operational weather- or climate model, and are therefore considered beyond the scope of this study.
The reciprocality between SCM and GCM results con-cerning subtropical marine low clouds as established in this study has some broader implications for climate science. The first implication is that it justifies and advocates the use of SCM studies in evaluating and improving weather and climate models [e.g.Jakob, 2010;Neggers et al., 2012]. Provided that a sufficiently broad range of situations is sim-ulated so that representativeness and statistical significance is ensured, the SCM results on low clouds at a certain loca-tion of interest, such as a meteorological supersite, should carry over to its associated GCM.
The second implication is that opportunities exist for us-ing SCM studies in the investigation of the response of low clouds and related phenomena to climate change [e.g.Zhang et al., 2013; Gesso et al., 2014]. Based on the results of this study, one speculates that such responses of low clouds in GCM simulations of future climate are similarly domi-nated by the associated parameterizations. In a changing climate, the modes of a pdf in (κ,TCC) space would proba-bly shift, reflecting the changes in the large-scale setting that affect the frequency of occurrence of a certain boundary-layer state, including low clouds. Nevertheless the structure or pattern would probably be preserved, as it is controlled by the underlying parameterizations. This way, SCM sim-ulation can be a useful tool in getting insight into why low clouds in a climate model behave the way they do in fu-ture climate. This could be of help in understanding and perhaps reducing climate uncertainty related to low cloud representation in models.
Appendix A: Diagnosing inversion properties
In this study properties of the boundary-layer inversion are diagnosed in realizations by numerical models that rely on a discretized vertical dimension. The first step is then to define the inversion. In this study the inversion is associated with the height where the vertical gradient in liquid water potential temperatureθlis maximum. In nature inversions
can cover layers of significant depth; typically in shallow cumulus regimes the inversion layer is deeper compared to the stratocumulus regime, in which strong large-scale subsi-dence is effective in reducing the depth of the inversion. To reflect these characteristics the inversion is defined here as the layer around the height of maximumθlgradient where
• theθlgradient is still significant (larger than 10 % of
its maximum value), and
• theθlgradient decreases in the direction away from the
height of its maximum.
Many more methods can be thought of to define the inver-sion. An advantage of this definition, however, is that it can easily be applied in a vertical grid. For example, after calculating the vertical gradient at every level, and identify-ing the level of its maximum, upward and downward scans then yield the depth of the inversion layer. Relying onθl
has the advantage that it is conserved for moist adiabatic motions, thus perhaps reducing sensitivity to cloud param-eterizations. In addition,θlcan easily be constructed from
variables that are standard output in most GCMs; defini-tions relying on fluxes do not have that benefit. Finally,
this definition is capable of diagnosing inversions that poten-tially cover multiple model levels, which reduces sensitivity to vertical resolution. This makes the definition applicable to both finely discretized models such as LES and coarsely discretized models such as SCMs.
In numerical practice the inversion layer is defined as the set of adjacent model levels that meet the conditions de-scribed above. This is illustrated in Fig. 10. The properties with subscripts + and − in the definition of κ in (3) are taken at the model levels immediately above and below the set of inversion levels, respectively. Note that with inter-polation one could correct the + properties for the impact of the free tropospheric lapse rate, which can be significant. However, after initial trials it was decided to refrain from this correction, as it is sensitive to resolution and led to significant artificial scatter (not shown).
Acknowledgments. The research presented in this paper has received funding from the European Union, Seventh Frame-work Programme (FP7/2007-2013) under grant agreement no. 244067. Thanks go out to Isabelle Beau, Ian Boutle, Suvarchal Kumar and Marie-Pierre Lefebvre for providing the SCM results for the GASS/EUCLIPSE intercomparison case that are used in this study, and to Johan van der Dussen, Andy Ackerman, Adrian Lock, Peter Blossey and Irina Sandu for the LES results. The CFMIP-2 data used in this study is freely accessible through the Earth System Grid as part of CMIP5, instructions can be found at http://www.cfmip.net. The data from the EUCLIPSE/GASS intercomparison study for SCM and LES is scheduled to be made available online soon, but for now can be obtained from the au-thor upon request.
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Figure 1. Map of the (sub)tropical Eastern Pacific showing the 29 locations at which CFMIP-2 model out-put is used. The three locations on the GPCI transect in the NE Pacific as shown in Fig. 4 are indicated in red.
Table 1. Names and acronyms of the coupled GCMs and their associated SCM.a
Centre National de Recherches M´et´eorologiques (CNRM)-CERFACS / CNRM-Coupled Global Climate Model, version 5
GCM: CNRM-CM5 [Voldoire et al., 2013] SCM: ARPEGE-CLIMAT
Met Office/Hadley Centre Global Environmental Model, version 2Atmosphere only GCM: HadGEM2-A [Martin et al., 2011]
SCM: MetOffice
L’Institut Pierre-Simon Laplace (IPSL)/IPSL Coupled Model, version 5A-LR GCM: IPSL-CM5A-LR (http://icmc.ipsl.fr)
SCM: LMDZ-AR4 MPI Earth System Model
GCM: MPI-ESM-LR [Giorgetta et al., 2013] SCM: ECHAM6 [Stevens et al., 2013]
a GCM names as used in CMIP data archive, SCM names as used in the GASS/EUCLIPSE intercomparison study on cloud transitions.
q
t
l
q
t
lz
topz
baseh
capq
t,0q
t(z
top -)
q
t(z
top +)
l(z
top +)
l(z
top -)
l,0Figure 2. Schematic of the thermodynamic vertical structure of the marine boundary-layer in transition. Fig-ure inspired byWood and Bretherton[2004].
a) b)
c)
Figure 3. Scatter-plot of TCC as a function of a) the LTS, b) the EIS and c) the κ parameter as diagnosed during five LES realizations of the four transition cases. Each case is indicated with a different symbol, with each LES code indicated by a different color. DALES results for the RICO shallow cumulus case are also included to add points in the weak inversion, low cloud cover regime. The dotted line in panel b) represent the fit proposed by
a)
b)
c)
Figure 4. Time-height raster plots of GCM cloud frac-tion of the HADGEM model at three selected gridpoints in the NE Pacific, situated on the GPCI transect. Each panel represents a different phase in the low-level cloud transition, including a) stratocumulus, b) shallow cumu-lus with capping outflow and c) fair-weather cumucumu-lus. Each model gridbox is homogeneously shaded. The time-period shown covers JJA 2006.
a) b)
c) d)
Figure 5. Scatter-plots in (κ,TCC) space of the SCM re-sults for the four transition cases. Each case is indicated with a different symbol, as in Fig. 3.
a) b)
c) d)
Figure 6. Contour-plots in (κ,TCC) space of the GCM results for the 29 selected gridpoints for the period JJA 2006. The associated SCM results shown in Fig. 5 are overplotted for reference (black symbols).
a) b)
c) d)
a) b)
Figure 8. a) Two-dimensional matrix of the resemblence of SCMs and GCMs, as expressed by the RMS reflecting the position of the maximum in the PDF of kappa. b) Horizontal cross-sections through the resemblance ma-trix shown in panel a), yielding lines of RMS values as a function of the GCM for a particular SCM. The minimum value is indicated by the dotted line.
a) b)
Figure 9. Sensitivity test of the SCM-GCM resemblance matrix as shown in Fig. 8a to various aspects of the comparison, including a) excluding the VOCALS points and b) extending the time-period of the GCM data to two full years.
l+ level
- level
level of maximum gradient
Figure 10. Schematic illustration of the method to de-fine the inversion layer in a vertical grid as discussed in Appendix A. The numerical grid is visualized as a col-umn of boxes, with the set of inversion levels shaded blue. The black dots indicate the gridbox midpoints.
