Uncertain parameters in physical parameterizations of
general circulation models (GCMs) greatly impact model performance. In
recent years, automatic parameter optimization has been introduced for
tuning model performance of GCMs, but most of the optimization methods are
unconstrained optimization methods under a given performance indicator.
Therefore, the calibrated model may break through essential constraints that
models have to keep, such as the radiation balance at the top of the model. The
radiation balance is known for its importance in the conservation of model
energy. In this study, an automated and efficient parameter optimization
with the radiation balance constraint is presented and applied in the
Community Atmospheric Model (CAM5) in terms of a synthesized performance
metric using normalized mean square error of radiation, precipitation,
relative humidity, and temperature. The tuned parameters are from the
parameterization schemes of convection and cloud. The radiation constraint
is defined as the absolute difference of the net longwave flux at the top of the model (FLNT) and the net solar flux at the top of the model (FSNT) of less than 1 W m-2. Results show that the synthesized performance under the optimal
parameters is 6.3 % better than the control run (CNTL) and the
radiation imbalance is as low as 0.1 W m-2. The proposed method
provides an insight for physics-guided optimization, and it can be easily
applied to optimization problems with other prerequisite constraints in
GCMs.
Introduction
The subgrid-scale physical processes in general circulation models (GCMs)
are represented by parameterization schemes, which may exist with several
uncertain parameters. Inappropriate parameters can seriously affect the
overall performance of the model. The Intergovernmental Panel on Climate
Change Fifth Assessment Report (IPCC AR5) pointed out that studies on
parameter uncertainty are critical to improve climate simulation
capabilities (Mastrandrea et al., 2011). Bauer et al. (2015) also indicated
that small errors in the physical parameterization schemes could lead to
large-scale systematic errors. Traditionally, to achieve better performance,
the uncertain parameters are tuned based on the experience of model experts
and statistical analysis. This is a labor-intensive job, and the tuning
results make it difficult to achieve local or global optimality in complex
climate models.
To efficiently reduce parameter-introduced uncertainty, quite a few
automated parameter calibration methods have been proposed. These
calibration methods can be categorized into two types. One attempts to
obtain the probability distributions of the parameters by likelihood and
Bayesian estimation methods. Cameron et al. (1999) exploited the generalized
likelihood uncertain estimation to obtain parameter ranges with a specific
confidence level. An adaptive Markov Chain Monte Carlo (MCMC) was used to
calibrate the uncertain parameters in the fifth-generation atmospheric general circulation model (ECHAM5) (Järvinen
et al., 2010). Edwards et al. (2011) proposed a simplified procedure of
Bayesian calibration to make a quantification of uncertainty in climate
forecasting. This type of method has also been successfully applied to the
CAM3.1 model and the third Hadley Centre Climate Model (HadCM3) (Jackson et
al., 2008; Williamson et al., 2013).
The other method is to adjust parameters using optimization methods to
minimize the errors between model simulations and observations, which are
formulated with a given performance indicator. Many intelligent evolutionary
optimization algorithms were applied to model tuning. For example, both
simulated stochastic approximation annealing (SSAA) (Yang et al., 2013) and
multiple very fast simulated annealing (MVFSA) (Zou et al., 2014) were used
for uncertainty quantification and parameter calibration.
Both methods can consider the interaction of parameters, achieve automatic
optimization, and avoid the subjectivity and experientiality of manual
calibration. However, they also share high computation cost challenges due
to the hundreds and thousands of required simulations. This is usually
unacceptable, especially for high-resolution climate models. To overcome the
computational issues, the surrogate model, which is a way to replace the
real climate model with a cheaper statistical model for faster optimization,
has been recently introduced. Applications of these methods in climate
models include the work presented by Neelin et al. (2010) and Wang et al. (2014). However, training a precise surrogate model for a complicated
climate model such as the Community Earth System Model (CESM) is very challenging. Moreover, capturing the
climatic characteristics of extreme events is difficult for the cheap
statistical model. To make it possible to optimize parameters efficiently
and quickly in the complex and highly nonlinear earth system models, an
improved simplex algorithm was presented by Zhang et al. (2015). This method
can overcome the shortcomings of the traditional simplex downhill method,
and the computing efficiency of the algorithm is improved compared with
evolutionary optimization algorithms.
The application of various automatic parameter optimization methods in
climate models has gradually received more attention; however, the optimization algorithms mentioned above are mostly unconstrained, and they lack
emphasis on the physical mechanisms of the model itself. This paper takes
radiation balance as an example. According to the Earth's energy
conservation theory, the absorbed solar radiation is approximately equal to
outgoing longwave radiation at the top of the model. Forster et al. (2007)
proposed that radiative balance is critical to the Earth's system, and the
bias of radiation has a big impact on the change in surface temperature.
Hourdin et al. (2017) pointed out that a 1 W m-2 change in global
energy balance may result in a global mean surface temperature change of 0.5
to 1.5 K in coupled simulations. Additionally, Wild (2008) indicated that
radiation biases in the GCMs may influence climate sensitivity, thus
possibly distorting the prediction of future climate conditions. Lin et al. (2010) showed the importance of climate energy imbalance and stressed that
long-term high-precision measurements of top of the atmosphere (TOA) radiation are necessary.
Radiation balance is critical for GCMs, but its deviation can still exceed 1 W m-2 in some CMIP5 models (Smith et al., 2015). To better understand
this problem, many studies have tried to determine the cause of radiation
deviation by analyzing the influence of uncertain parameters and making
corresponding adjustments. Zhao et al. (2013) concluded that cloud
microphysics and emission-related parameters have statistically important
impacts on the global mean net radiation flux. Qian et al. (2015) indicated
that net radiation flux is very sensitive to some parameters in cloud
microphysics and convection. The improvement of the simulation performance
of the climatology and variability based on the radiation balance is very
meaningful. However, the constrained optimization methods used to calibrate
parameters with physical constraints in climate models remain to be further
studied. Cheng et al. (2018) showed that penalty functions and the separation of
objective and constraint methods are popular for solving constrained
problems. Penalty methods encourage the search toward feasible regions by
increasing the objective function value with a penalty value for the points
that violate the constraints. The exterior penalty method is relatively easy
to implement, and it can be widely used in various algorithms. The
separation of objective and constraint is commonly used by transforming
constraints into objectives, but it is limited by the convergence of the
multi-objective algorithms when the optimization problem has a high
computational cost.
The purpose of this paper is to propose an effective constrained
optimization method and demonstrate its feasibility in the calibration of
uncertain parameters under the premise of ensuring the balance of radiation. This paper is organized as follows. Section 2 describes the details of
the model and experimental design. Section 3 introduces the new constrained
parameter calibration method. Evaluations and analysis of the optimization
results are presented in Sect. 4. The last section contains the conclusion
and discussion.
Parameters description of CAM5. The default, final optimal
values by constrained and unconstrained calibrations, as well as the ranges
of parameters. CAPE means the convective available potential energy.
UnconstrainedConstrainedParameterDescriptionRangeDefaulttunetunezmconv_c0_lndDeep-convection precipitation2.95×10-3–0.00590.003190.00295efficiency over land85×10-3zmconv_c0_ocnDeep-convection precipitation2.25×10-2–0.0450.0250.0225efficiency over ocean6.75×10-2zmconv_tauTimescale for consumption ratedeep CAPE1800–540036001838.8141800cldfrc_rhminhThreshold relative humidity forhigh stable clouds0.6–0.90.800.8970.900cldfrc_rhminlThreshold relative humidity forlow stable clouds0.8–0.950.88750.9300.900cldsed_aiFall speed parameter forcloud ice300–1100700853.207970.613Model and experimentModel description
The model used in this study is CAM5 (release v5.3), which is the
atmospheric component of the CESM 1.2.1. The
dynamical core uses the finite-volume method developed by Lin and Rood (1996) and Lin (2004).
More details on CAM5 can be found in the work of Neale et al. (2010). Deep
convection is handled by a parameterization scheme developed by Zhang and
McFarlane (1995) with the further modifications of Richter and Rasch (2008),
as well as Neale et al. (2008). The original parameterization of stratiform
cloud microphysics is handled by Morrison and Gettelman (2008).
Modifications of ice nucleation and ice supersaturation can be found in
Gettelman et al. (2010). The parameterization of fractional stratiform
condensation is described by Zhang et al. (2003) as well as Park et al. (2014). Radiation scheme uses the rapid radiative transfer method for GCMs (RRTMG) (Mlawer et al., 1997; Iacono et al., 2008).
Experiment design
Table 1 shows the parameters to be adjusted, the ranges, and the default
values. These parameters were identified as sensitive to cloud and
convection processes in previous studies. Qian et al. (2018) showed that deep-convection precipitation efficiency zmconv_c0_lnd and zmconv_ c0_ocn have significant impact
on the variance of shortwave cloud forcing (SWCF) over the land and ocean,
respectively. Thresholds of relative humidity for high and low stable clouds
(cldfrc_rhminh and cldfrc_rhminl) are
regarded as the important parameters for cloud and radiation (Zhang et al.,
2018). In addition, the relative humidity threshold for low clouds is also
one of the strongest parameters impacting the global mean precipitation, and it makes a huge contribution to the TOA net radiative fluxes in CAM5 (Qian et
al., 2015). The timescale for the consumption rate of deep convective available potential energy (CAPE) (zmconv_tau) is identified as the most sensitive parameter to
the convective precipitation in the Zhang–McFarlance scheme by Yang et al. (2013). The
cloud ice sedimentation velocity (cldsed_ai) has a
significant effect on cloud radiative forcing (Mitchell et al., 2008), and
it has been identified as a high-impact parameter in sensitivity experiments
related to temperature, radiation, and precipitation, etc. (Sanderson et
al., 2008). The ranges of these parameters are based on previous
studies (Qian et al., 2015; Zhang et al., 2018).
The output variables used to evaluate performance metric
index and the source of the corresponding observations.
VariableFull nameObservation (OBS)LWCFLongwave cloud forcingCERES-EBAFSWCFShortwave cloud forcingCERES-EBAFPRECTTotal precipitation rateGPCPQ850Specific humidity at 850 hPaERA-InterimT850Temperature at 850 hPaERA-Interim
The output variables used to synthesize a performance indicator are longwave
cloud forcing (LWCF), SWCF, precipitation (PRECT), humidity at 850 hPa
(Q850), and temperature at 850 hPa (T850), shown in Table 2. The observations
of LWCF and SWCF are from CERES-EBAF (Clouds and the Earth's Radiant Energy
System-Energy Balanced and Filled; Loeb et al., 2014). PRECT is from
GPCP (Global Precipitation Climatology Project; Adler et al., 2003), and
Q850 and T850 are from ERA-Interim, which was produced by the ECMWF (Dee et
al., 2011).
In this study, we use 1.9∘ latitude × 2.5∘ longitude
resolution CAM5 with 30 vertical layers. Each simulation is a 5-year atmospheric model intercomparison project (AMIP) from 2000 to 2004 with the observed climatological sea surface temperature
(SST) and sea ice (Rayner et al., 2003). The simulations in the last 3 years
are used to evaluate the synthesized performance metric and constraint.
Method
A constrained automatic optimization method is proposed based on Zhang et
al. (2015). The synthesized metrics used to evaluate the performance of
overall simulation skills are shown in Eq. ():
1σmF2=∑i=1Iw(i)xmF(i)-xoF(i)2,2σrF2=∑i=1Iw(i)xrF(i)-xoF(i)2,3χ2=1NF∑F=1NFσmFσrF2.(σmF)2 represents a criterion for the
simulation skill of the models with modified parameters; (σrF)2 is an evaluation of the default
experiment simulation skill. If the indicator χ2 is less than 1,
this means that the simulation with tuned parameters is better than the
control run (CNTL). The smaller the index, the better performance of model. The model
outputs are represented by xmF(i), and
xoF(i) denotes the corresponding reanalysis or
observation data. The expression xrF(i) represents model outputs from the CNTL. The weight of the different grids on the sphere is represented by ω. I denotes the total
number of grids in the
model. The number of the output variables in the
performance index is represented by NF.
The radiation balance is defined as the absolute value of the difference
between net solar flux (FSNT) and net longwave flux (FLNT) in climatology at
the top of the model of less than 1 W m-2, which is the maximum deviation
of radiation observations in the decade before 2014 (Trenberth et al.,
2014).
Coupled with the radiation balance constraint, the optimization problem of
this study can be expressed as Eqs. () and ():
4minχ2,5subjecttoABSFSNTm-FLNTm<1.
Converting the unconstrained problem into a constrained problem using the
penalty function method, it can be transformed into the augmentation
function as Eq. ():
F(x)=χ2+β×ABSFSNTm-FLNTm.
The penalty factor β for the constraint in Eq. () is chosen to be 10 000 if the constraint in Eq. () is not satisfied; otherwise it is equal to 0. The purpose of this choice is to optimize the search space to avoid the possibility of radiation imbalance. This penalty function method is easy and effective when dealing with this tightly constrained optimization.
We use the improved simplex downhill method, proposed by Zhang et al. (2015), to optimize the augment function. Firstly, the single-parameter
perturbation sample method (SPP) is used to obtain several better initial
values, while ensuring that the initial geometry of simplex downhill is
well-conditioned. The initial value preprocessing mechanism ensures that the algorithm starts from a good basis. This is important for the simplex
algorithm, which may easily fall into local optimum. Next, the simplex
downhill algorithm is applied to search for better performance.
The change in augmentation function F(x) across the
optimization iterations. The x axis is the number of iterations.
The y axis is the value of F(x) in Eq. (6). The black line shows the value of F(x) in a given iteration step, while the red line shows the best F(x)
value up to the current iteration step.
Comparison of results between the constrained optimization
algorithm and the unconstrained optimization algorithm. The 15 red squares
and 15 black triangles are optimized solutions found by the unconstrained
optimization algorithm and constrained algorithms, respectively. The blue
diamond is the result of the CNTL experiment. The x axis is the synthesized
metric index in Eq. (3). The y axis is the radiation bias at the top of the model.
Taylor diagram of the climate mean state of each output
variable from 2002 to 2004 between the model run with optimal parameters and
the CNTL run. The number (1) in the diagram stands for EXP, and (2) stands for
CNTL.
F(x) gradually converges as shown in Fig. 1. There are some
cases in which the radiation balance is not satisfied at the beginning of
optimization. However, as the iteration step increases, the search space of
the algorithm is constrained within the feasible range. The goal is then to
make the synthesized performance metric smaller. In addition, a comparative
experiment with unconstrained algorithms is done to verify our doubts about
unconstrained methods. Figure 2 shows the performance indices and radiation
deviations corresponding to the first 15 solutions after the two algorithms
converge. The constrained optimization algorithm can find
solutions that are more radiation-balanced; however, the final solution
metrics are not as good as the unconstrained optimization algorithm.
Compared to the CNTL experiment, we can find quite a few solutions with
better metrics and smaller radiation biases.
ResultThe optimal model
The best uncertainty parameters obtained by the unconstrained optimization
method optimize the overall performance of the simulation by 10.1 %, but
they have a radiation deviation of up to 3.8 W m-2. When considering the
converged constrained optimization algorithm, the optimal parameters can
improve the model performance by 6.3 %, and the radiation imbalance is as
low as 0.1 W m-2. The corresponding results of the optimal solutions
with the two methods are shown in Table 3. Both unconstrained optimization
and constrained optimization can further improve the simulation performance,
but unconstrained optimization may encounter an optimal solution that does
not satisfy the radiation balance, thus leading to meaningless optimization.
The optimization results discussed below are based on the proposed
constrained optimization method.
Synthesized performance metric index and radiation bias in
the CNTL run and the optimal model run with unconstrained and constrained
methods.
Meridional distribution of the difference between EXP/CNTL
and observed data of (a) LWCF, (b) SWCF, (c) PRECT, (d) Q850, and (e) T850.
The position of the dark blue line is 0; the red and black
solid lines represent the difference between EXP / CNTL and the observations.
Performance metric index of each variable in the optimal
model run with unconstrained and constrained methods.
The optimization of each output variable is shown in Table 4. In addition, a
Taylor diagram is used to estimate the model performance through the
standard deviation and correlation (Fig. 3). By combining the results of
Table 4 and Fig. 3, it can be concluded that SWCF and Q850 receive most
optimization, as they achieve a better performance index. Also, compared to
the default experiment, their standard deviations have improved. Table 5
shows the standard deviations of the variables, which are important for the
model but not used as evaluation criteria. It is noteworthy that they are
also close to the default experiment.
The percentage of standard deviation of the eight fields between
the CNTL run and the optimal model run with constrained optimization
according to the corresponding observations.
The spatial distribution of TOA SW cloud forcing of (a) observation, (b) CNTL–observation, (c) EXP, (d) EXP–observation, (e) CNTL, and (f) EXP–CNTL.
For a more comprehensive analysis of the spatial variation of the output
variables, the zonal distribution of the difference between the control (labeled as CNTL)/the optimized (labeled as EXP) simulations and
observations of all metric variables are shown in Fig. 4. SWCF and Q850 have
been obviously improved over low and middle latitudes, but the changes in
PRECT and T850 are not particularly notable. Further, LWCF only showed
significant improvement near the Equator, and it slightly deteriorated over
the middle and high latitudes.
Interpretation of the results
The optimized parameters values are provided in the “Constrained tune”
column of Table 1. The deep-convection precipitation efficiency over land
and ocean is reduced relative to the default values. The timescale for the consumption rate of CAPE for deep convection is smaller than the default
value, and both relative humidity thresholds for high and low clouds are
increased. Additionally, the sedimentation velocity of cloud ice is larger.
Next, we will explain how the changes in these parameters are related to the
results of the simulations.
The spatial distribution of specific humidity at
850 hPa of (a) observation, (b) CNTL–observation, (c) EXP, (d) EXP–observation, (e) CNTL, and (f) EXP–CNTL.
The relative humidity threshold for low clouds is larger in optimization
experiments than the default value, which will obviously lead to the
decrease in low-cloud fraction. The decreased low-cloud fraction is
consistent with the increase in SWCF. The CNTL experiment has excelled at
simulating the spatial distribution of SWCF (Fig. 5c), but it has a negative
bias over the ocean in the low latitudes, where the improvement is
significant in the optimal experiment.
The zonal mean specific humidity at 850 hPa is significantly improved, and
its spatial distribution is presented in Fig. 6. In the optimal experiment,
the atmosphere is drier in the tropics and middle latitudes, which is closer to
the observation than the CNTL experiment. Meanwhile, the middle to low
troposphere is also slightly drier in these areas (Fig. 7), which may be
related to the increased convective precipitation. A quasi-equilibrium
closure is used in the deep-convection scheme in CAM5, which is based on
CAPE. The adjustment timescale represents the denominator of the cloud
bottom convective mass flux. When the timescale is shorter with less
changed CAPE, the increased cloud-base mass flux would help to enhance the
convective precipitation. Additionally, compared to the CNTL experiment, the
lower troposphere gets warmer and the middle troposphere is colder, which
exacerbates the instability of the temperature structure (Fig. 8) and leads
to more convective precipitation. The spatial distribution of convective
precipitation over the tropics where convection occurs most frequently can
be seen in Fig. 9. The increase in convective precipitation may be related
to the decrease in specific humidity at 850 hPa. However, the increase in
total precipitation is not particularly significant and is dominated by
the changes in convective precipitation. The main reason is likely
associated with the decreased precipitation efficiency parameters, which
could reduce the convective precipitation as compensation. Therefore, the
decreases in precipitation efficiency partially offset the precipitation
change caused by tau and temperature structure.
Pressure–latitude distributions of specific humidity of
(a) EXP–OBS, (b) CNTL–OBS, and (c) EXP–CNTL.
Pressure–latitude distributions of temperature of (a) EXP–OBS, (b) CNTL–OBS, and (c) EXP–CNTL.
The spatial distribution of convective precipitation over
the tropics of EXP (a), CNTL (b), and EXP–CNTL (c).
Pressure–latitude distributions of cloud fraction of EXP (a), CNTL (b), and EXP–CNTL (c).
It is difficult for all variables to be optimized, due to the strong
interaction among parameters and the complex relationship among output
variables. The simulations of T850 between optimal and CNTL experiments are
very similar. It is likely the result of the combined effects of all
relevant parameterizations. In the optimal experiment, LWCF is closer to the
observation in the tropics, but it becomes slightly smaller at middle to
high latitudes compared to the CNTL experiment, which implies the larger
bias. The relative humidity threshold for high clouds and the sedimentation
velocity of ice crystals are correspondingly increased, and both of them
would lead to the reduction in high clouds. High-cloud fraction changes
compared to the CNTL experiment can be seen in Fig. 10c. The reduced high
cloud is consistent with the reduction in LWCF. Cloud changes also
inevitably affect SWCF. It can be seen that the middle cloud has increased
relative to the default experiment (Fig. 10c), and the increase in the
middle cloud may be related to the decrease in precipitation efficiency over the ocean.
Note that three of six parameters hit their lowest allowable limit with the
TOA balance constraint. We found that the incoming shortwave radiation flux
is more sensitive to tuning parameters than the outgoing longwave radiation
flux. Thus, to reduce the TOA imbalance and keep the reasonable
model performance, the shortwave radiation flux should be reduced largely
via increasing low-cloud fraction and liquid water content. These three
variables can help achieve this by setting to the lowest bounds. This
suggests that getting both the TOA balance and reasonable model performance
is a relatively complex and difficult problem due to model structure
problems, as pointed out by Qian et al. (2018) and Yang et al. (2019).
Meanwhile, finding out how to pick parameters with a similar sensitivity to both
longwave and shortwave radiation flux might be a potential approach to
overcome the bound limit and it warrants further studies.
In conclusion, the increase in SWCF is consistent with the decrease in cloud
fraction for the sake of a larger relative humidity threshold of low clouds.
Changes in the Q850 are related to increased convective precipitation.
Precipitation only slightly increases in the tropics, and the global total
precipitation has changed very little, which is related to the comprehensive
effect of the changes in the convection adjustment timescale, the
precipitation efficiency parameter, and the vertical temperature structure.
T850 simulated by the optimization experiment is similar to the default
experiment. The reduced LWCF is related to the decreased high clouds caused
by the increased relative humidity threshold for high clouds and the
increased sedimentation velocity of ice crystals.
Conclusion and discussion
Radiation balance is a crucial factor for the long-term energy balance of
GCMs, but it has not received enough attention in automatic parameter
optimization. First of all, this paper points out that the previous
parameter optimization algorithms do not consider radiation balance a
necessary condition, and the obtained optimization parameters are likely to
break this important physical constraint, which may lead to unacceptable
calibrated parameters. Thus we propose an efficient constrained automatic
optimization algorithm to calibrate the uncertainty parameters in CAM5 with
the constraint of the absolute value of the difference of net solar flux and
net longwave flux at the top of the model (less than 1 W m-2). In the
parameter calibration, we use the comprehensive performance with the five fields
of LWCF, SWCF, PRECT, Q850, and T850 as the performance indicators. We choose
the uncertain parameters in cloud and convection parameterizations,
including the deep-convection precipitation efficiency over land and ocean,
thresholds of relative humidity for stable high and low clouds, the
timescale for consumption rate deep CAPE, and the ice falling speed. Each
simulation in our optimization experiments is a 5-year AMIP experiment
forced with prescribed seasonal climatology of SST and sea ice.
The optimal parameters found by our method can increase the overall
performance of the model by 6.3 %, and the radiation imbalance is as low
as 0.1 W m-2. The most optimized variables are SWCF and Q850. The
increase in SWCF is consistent with the decrease in cloud water due to
a larger relative humidity threshold value for low clouds. The reduction in
the Q850 in the troposphere may be related to the increase in convective
precipitation. The change in global total precipitation is not particularly
obvious, which is likely the comprehensive effect of the changes in the convection adjustment timescale, the precipitation efficiency parameter, and
the structure of temperature over the troposphere. The change in T850 is very
small, and the result is slightly better than that of the default
experiment. Meanwhile, under the constraint of energy balance, LWCF has
deteriorated in the middle and high latitudes. This also reflects some
issues that may exist in the structure of the model.
The unconstrained optimization methods calibrate the uncertain parameters in
climate models without a consideration of the principles that model have to hold,
this creates challenges in maintaining the physics constraints and improving
the structure of models. Perhaps a more physics-guided optimization is a
better way to understand the principles of climate systems and to best use
these principles in tuning processes. In the future, we will apply this
method to coupled models, where the radiation imbalance has a more
significant impact on long-term simulation stability. In addition, we will
also try to introduce more constraints, such as the surface energy balance,
into automatic parameter calibration.
Code and data availability
The code of our algorithm, the observations, and the related scripts can be found at 10.5281/zenodo.3405619 (Wu, 2019). The source code of CAM5.3 is available from http://www.cesm.ucar.edu/models/cesm1.2/ (last access: 14 December 2019, NCAR, 2018).
If you have any problems, please feel free to contact us (wulitianyi@gmail.com).
Author contributions
LW and TZ proposed the tuning method. LW, YQ, and WX designed the metrics and the
constraint. YQ and LW evaluated the optimal results. LW, TZ, WX, and YQ wrote
the paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This work is partially supported by the National Key R&D Program of China
(grant nos. 2017YFA0604500 and 2016YFA0602100) and the Center for High
Performance Computing and System Simulation of Pilot National Laboratory for
Marine Science and Technology (Qingdao).
Financial support
This work is partially supported by the National Key R&D Program of China
(grant nos. 2017YFA0604500 and 2016YFA0602100) and the Center for High
Performance Computing and System Simulation of Pilot National Laboratory for
Marine Science and Technology (Qingdao).
Review statement
This paper was edited by Andrea Stenke and reviewed by two anonymous referees.
References
Adler, R. F., Huffman, G. J., Chang, A., Ferraro, R., Xie, P. P., Janowiak,
J., and Gruber, A.: The version-2 global precipitation climatology project
(GPCP) monthly precipitation analysis (1979–present), J. Hydrol., 4,
1147–1167, 2003.
Bauer, P., Thorpe, A., and Brunet, G.: The quiet revolution of numerical
weather prediction, Nature, 525, 47–55, 2015.
Cameron, D., Beven, K. J., Tawn, J., Blazkova, S., and Naden, P.: Flood
frequency estimation by continuous simulation for a
gauged upland catchment (with uncertainty), J. Hydrol., 219, 169–187, 1999.Cheng, G. H., Gjernes, T., and Wang, G. G.: An Adaptive Aggregation-Based
Approach for Expensively Constrained Black-Box Optimization Problems, J.
Mech. Design., 140, 091402, 10.1115/1.4040485, 2018.
Dee, D. P., Uppala, S. M., Simmons, A. J., Berrisford, P., Poli, P.,
Kobayashi, S., and Bechtold, P.: The ERA-Interim reanalysis: Configuration
and performance of the data assimilation system, Q. J. Roy. Meteor. Soc.,
137, 553–597, 2011.
Edwards, N. R., Cameron, D., and Rougier, J.: Precalibrating an intermediate
complexity climate model, Clim. Dynam., 37, 1469–1482, 2011.
Forster, P., Ramaswamy, V., Artaxo, P., Berntsen, T., Betts, R., Fa- hey, D.
W., Haywood, J., Lean, J., Lowe, D. C., Myhre, G., Nganga, J., Prinn, R.,
Raga, G., Schulz, M., and Van Dorland, R.: Radiative Forcing of Climate Change,
in Climate Change 2007 – The Physical Science Basis: Working Group I
Contribution to the Fourth Assessment Report of the Intergovernmental Panel
on Climate Change, Cambridge University Press, UK, 129–234, 2007.Gettelman, A., Liu, X., Ghan, S. J., Morrison, H., Park, S., Conley, A.,
Klein,S. A., Boyle, J., Mitchell, D., and Li, J.-L.: Global simulations of
ice nucle-ation and ice supersaturation with an improved cloud scheme in the
Com-munity Atmosphere Model, J. Geophys. Res.-Atmos., 115, D18216, 10.1029/2009JD013797, 2010.
Hourdin, F., Mauritsen, T., Gettelman, A., Golaz, J. C., Balaji, V., Duan,
Q., Folini, D., Ji, D., Klocke, D., Qian, Y., Rauser, F., Rio, C.,
Tomassini, L., Watanabe, M., and Williamson, D.: The art and science of
climate model tuning, B. Am. Meteorol. Soc., 98, 589–602, 2017.Iacono, M. J., Delamere, J. S., Mlawer, E. J., Shephard, M. W., Clough, S.
A., and Collins, W. D.: Radiative forcing by long-lived greenhouse gases:
Calculations with the AER radiative transfer models, J. Geophys.
Res.-Atmos., 113, D13103, 10.1029/2008JD009944, 2008.
Jackson, C. S., Sen, M. K., Huerta, G., Deng, Y., and Bowman, K. P.: Error
reduction and convergence in climate prediction, J. Climate, 21, 6698–6709,
2008.Järvinen, H., Räisänen, P., Laine, M., Tamminen, J., Ilin, A., Oja, E., Solonen, A., and Haario, H.: Estimation of ECHAM5 climate model closure parameters with adaptive MCMC, Atmos. Chem. Phys., 10, 9993–10002, 10.5194/acp-10-9993-2010, 2010.Lin, B., Chambers, L., P. Stackhouse Jr., Wielicki, B., Hu, Y., Minnis, P., Loeb, N., Sun, W., Potter, G., Min, Q., Schuster, G., and Fan, T.-F.: Estimations of climate sensitivity based on top-of-atmosphere radiation imbalance, Atmos. Chem. Phys., 10, 1923–1930, 10.5194/acp-10-1923-2010, 2010.
Lin, S.-J.: A “vertically Lagrangian” finite-volume dynamical core for global models, Mon. Weather Rev., 132, 2293–2307, 2004.
Lin, S.-J. and Rood, R. B.: Multidimensional flux-form semi-Lagrangian transport schemes, Mon. Weather Rev., 124, 2046–2070, 1996.Loeb, N. and National Center for Atmospheric Research
Staff (Eds.): The Climate Data Guide: CERES EBAF:
Clouds and Earth’s Radiant Energy Systems (CERES)
Energy Balanced and Filled (EBAF), available at:
https://climatedataguide.ucar.edu/climate-data/ceres-ebafcloudsand-earths-radiant-energy-systems-ceres-energybalanced-andfilled, last access: 14 December 2019.
Mastrandrea, M. D., Mach, K. J., Plattner, G. K., Edenhofer, O., Stocker, T.
F., Field, C. B., Ebi, K. L., and Matschoss, P. R.: The IPCC AR5 guidance
note on consistent treatment of uncertainties: a common approach across the
working groups, Clim. Change, 108, 675, 2011.Mitchell, D. L., Rasch, P., Ivanova, D., McFarquhar, G., and Nousiainen,
T.: Impact of small ice crystal assumptions on ice sedi- mentation rates in
cirrus clouds and GCM simulations, Geophys. Res. Lett., 35, L09806,
10.1029/2008GL033552, 2008.
Mlawer, E. J., Taubman, S. J., Brown, P. D., Iacono, M. J., and Clough, S.
A.: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated
correlated-k model for the longwave, J. Geophys. Res.-Atmos., 102,
16663–16682, 1997.Morrison, H. and Gettelman, A.: A new two-moment bulk stratiform cloud
microphysics scheme in the community atmosphere model, version 3 (CAM3).
Part I: Description and numerical tests, J. Climate, 21, 3642–3659,
10.1175/2008jcli2105.1, 2008.NCAR: CESM1.2 SERIES PUBLIC RELEASE, available at: http://www.cesm.ucar.edu/models/cesm1.2/, last access: 14 December 2018.Neale, R. B., Richter, J. H., Conley, A. J., Park, S., Lauritzen, P. H.,
Gettelman, A., Williamson, D. L., Rasch, P. J., Vavrus, S. J., Taylor, M.
A., Collins, W. D., Zhang, M., and Lin, S. J.: Description of the NCAR
Community Atmosphere Model (CAM5.0), Technical Report NCAR/TN-486+STR,
National Center for Atmospheric Research, Boulder, CO, USA, 2010.
Neelin, J. D., Bracco, A., Luo, H., McWilliams, J. C., and Meyerson, J. E.:
Considerations for parameter optimization and sensitivity in climate models,
P. Natl. Acad. Sci. USA, 107, 21349–21354, 2010.
Park, S., Bretherton, C. S., and Rasch, P. J.: Integrating cloud processes
in the Community Atmosphere Model, version 5, J. Climate, 27, 6821–6856,
2014.
Qian, Y., Wan, H., Yang, B., Golaz, J. C., Harrop, B., Hou, Z., Larson, V.
E., Leung, L, R., Lin, G., Lin, W., Ma, P. L., Ma, H. Y., Rasch, P., Singh,
B., Wang, H., Xie, S., Zhang, K.: Parametric Sensitivity and Uncertainty
Quantification in the Version 1 of E3SM Atmosphere Model Based on Short
Perturbed Parameter Ensemble Simulations, J. Geophys. Res.-Atmos., 123,
13046–13073, 2018.
Qian, Y., Yan, H., Hou, Z., Johannesson, G., Klein, S., Lucas, D., Neale,
R., Rasch, P., Swiler, L., Tannahill, J., and Wang, H.: Parametric
sensitivity analysis of precipitation at global and local scales in the
Community Atmosphere Model CAM5, J. Adv. Model. Earth Sy., 7, 382–411,
2015.
Rayner, N., Parker, D. E., Horton, E., Folland, C., Alexander, L., Rowell,
D., Kent, E., and Kaplan, A.: Global analyses of sea surface temperature,
sea ice, and night marine air temperature since the late nineteenth century,
J. Geophys. Res.-Atmos., 108, 1871–2000, 2003.Richter, J. H. and Rasch, P. J.: Effects of convective momentum transport
on the atmospheric circulation in the community atmosphere model, version 3,
J. Climate, 21, 1487–1499, 10.1175/2007jcli1789.1, 2008.
Sanderson, B. M., Piani, C., Ingram, W. J., Stone, D. A., and Allen, M. R.:
Towards constraining climate sensitivity by linear analysis of feedback
patterns in thousands of perturbed-physics GCM simulations, Clim. Dynam., 30,
175–190, 2008.
Smith, D. M., Allan, R. P., Coward, A. C., Eade, R., Hyder, P., Liu, C.,
Loeb, N. G., Palmer, M. D., Roberts, C.D., and Scaife, A. A.: Earth's energy
imbalance since 1960 in observations and CMIP5 models, Geophys. Res. Lett.,
42, 1205–1213, 2015.
Trenberth, K. E., Fasullo, J. T. and Balmaseda, M. A.: Earth's energy
imbalance, J. Climate, 27, 3129–3144, 2014.
Wang, C., Duan, Q., Gong, W., Ye, A., Di, Z., and Miao, C.: An evaluation of
adaptive surrogate modeling based optimization with two benchmark problems, Environ. Model. Softw., 60, 167–179, 2014.
Wild, M.: Short-wave and long-wave surface radiation budgets in GCMs: a
review based on the IPCC-AR4/CMIP3 models, Tellus A., 60, 932–945, 2008.Williamson, D., Goldstein, M., Allison, L., Blaker, A., Challenor, P.,
Jackson, L., and Yamazaki, K.: History matching for exploring and reducing
climate model parameter space using observations and a large perturbed
physics ensemble, Clim. Dynam., 41, 1703–1729, 10.1007/s00382-013-1896-4,
2013.Wu, L.: Constrained-tuning-in-CAM5 v1.0.0 (Version v1.0.0), Zenod, 10.5281/zenodo.3405619, 2019.
Yang, B., Qian, Y., Lin, G., Leung, L. R., Rasch, P. J., Zhang, G. J.,
McFarlane, S. A., Zhao, C., Zhang, Y., Wang, H., Wang, M., and Liu, X.:
Uncertainty quantification and parameter tuning in the CAM5 Zhang-McFarlane
convection scheme and impact of improved convection on the global
circulation and climate, J. Geophys. Res.–Atmos., 118, 395–415, 2013.
Yang, B., Berg, L. K., Qian, Y., Wang, C., Hou, Z., Liu, Y., and Pekour, M.
S.: Parametric and Structural Sensitivities of Turbine Height Wind Speeds
in the Boundary Layer Parameterizations in the Weather Research and
Forecasting Model, J. Geophys. Res.-Atmos., 124, 5951–5969, 2019.
Zhang, G. J. and McFarlane, N. A.: Sensitivity of climate simulations to the
parameterization of cumulus convection in the Canadian Climate Centre
general circulation model, Atmos. Ocean, 33, 407–446, 1995.Zhang, M., Lin, W., Bretherton, C. S., Hack, J. J., and Rasch, P. J.: A
modified formulation of fractional stratiform
condensation rate in the NCAR Community Atmospheric Model (CAM2), J.
Geophys. Res.-Atmos., 108, 4035, 10.1029/2002JD002523, 2003.Zhang, T., Li, L., Lin, Y., Xue, W., Xie, F., Xu, H., and Huang, X.: An automatic and effective parameter optimization method for model tuning, Geosci. Model Dev., 8, 3579–3591, 10.5194/gmd-8-3579-2015, 2015.Zhang, T., Zhang, M., Lin, W., Lin, Y., Xue, W., Yu, H., He, J., Xin, X., Ma, H.-Y., Xie, S., and Zheng, W.: Automatic tuning of the Community Atmospheric Model (CAM5) by using short-term hindcasts with an improved downhill simplex optimization method, Geosci. Model Dev., 11, 5189–5201, 10.5194/gmd-11-5189-2018, 2018.Zhao, C., Liu, X., Qian, Y., Yoon, J., Hou, Z., Lin, G., McFarlane, S., Wang, H., Yang, B., Ma, P.-L., Yan, H., and Bao, J.: A sensitivity study of radiative fluxes at the top of atmosphere to cloud-microphysics and aerosol parameters in the community atmosphere model CAM5, Atmos. Chem. Phys., 13, 10969–10987, 10.5194/acp-13-10969-2013, 2013.
Zou, L., Qian, Y., Zhou, T., and Yang, B.: Parameter tuning and calibration
of RegCM3 with MIT–Emanuel cumulus parameterization scheme over CORDEX East
Asia domain, J. Climate, 27, 7687–7701, 2014.