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PUBLICATIONS Journal of Advances in Modeling Earth Systems RESEARCH ARTICLE 10.1002/2016MS000659 Key Points:  Nudging can suppress physicsdynamics interaction and cause undesirable effects  Short ensemble simulations can help understand the evolution of model sensitivity

Correspondence to: G. Lin, [email protected] Citation: Lin, G., H. Wan, K. Zhang, Y. Qian, and S. J. Ghan (2016), Can nudging be used to quantify model sensitivities in precipitation and cloud forcing?, J. Adv. Model. Earth Syst., 8, doi:10.1002/ 2016MS000659. Received 21 FEB 2016 Accepted 13 JUN 2016 Accepted article online 16 JUN 2016

Can nudging be used to quantify model sensitivities in precipitation and cloud forcing? Guangxing Lin1, Hui Wan1, Kai Zhang1, Yun Qian1, and Steven J. Ghan1 1

Pacific Northwest National Laboratory, Atmospheric Science and Global Change Division, Richland, Washington, USA

Abstract Efficient simulation strategies are crucial for the development and evaluation of highresolution climate models. This paper evaluates simulations with constrained meteorology for the quantification of parametric sensitivities in the Community Atmosphere Model version 5 (CAM5). Two parameters are perturbed as illustrating examples: the convection relaxation time scale (TAU), and the threshold relative humidity for the formation of low-level stratiform clouds (rhminl). Results suggest that the fidelity of the constrained simulations depends on the detailed implementation of nudging and the mechanism through which the perturbed parameter affects precipitation and cloud. The relative computational costs of nudged and free-running simulations are determined by the magnitude of internal variability in the physical quantities of interest, as well as the magnitude of the parameter perturbation. In the case of a strong perturbation in convection, temperature, and/or wind nudging with a 6 h relaxation time scale leads to nonnegligible side effects due to the distorted interactions between resolved dynamics and parameterized convection, while 1 year free-running simulations can satisfactorily capture the annual mean precipitation and cloud forcing sensitivities. In the case of a relatively weak perturbation in the large-scale condensation scheme, results from 1 year free-running simulations are strongly affected by natural noise, while nudging winds effectively reduces the noise, and reasonably reproduces the sensitivities. These results indicate that caution is needed when using nudged simulations to assess precipitation and cloud forcing sensitivities to parameter changes in general circulation models. We also demonstrate that ensembles of short simulations are useful for understanding the evolution of model sensitivities.

1. Introduction The Community Atmosphere Model version 5 (CAM5), like all other Atmospheric General Circulation Models (AGCMs), contains a large number of uncertain parameters in parameterization schemes that represent processes unresolved by the computational mesh [Qian et al., 2015; Guo et al., 2014, 2015]. Examples of such subgrid-scale processes include cloud and aerosol formation, solar and terrestrial radiation, and turbulence. The parameters used in the subgrid-scale physics parameterizations are usually derived from limited measurements or theoretical or empirical calculations, and cannot always be directly constrained by observational data. For practical purposes, the parameter values are often adjusted (‘‘tuned’’) to improve the agreement between model simulations and observations, which adds extra-uncertainties to future climate projections made with such models.

C 2016. The Authors. V

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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To quantify sensitivities of the simulated climate to variations in the uncertain parameters, sufficiently long simulations are needed to confidently distinguish the impact of parameter changes (‘‘signal’’) and internal variabilities in the climate system (‘‘noise’’). Depending on the quantities of interest, multiple years or decades of simulations might be needed. However, such long simulations can be computationally expensive, or even impractical, for high-resolution models or when many experiments are needed. One such case is the uncertainty quantification (UQ) studies that usually require several hundred or even thousands of simulations [Murphy et al., 2004; Carslaw et al., 2013; Jackson et al., 2008; Zhang et al., 2012; Yang et al., 2012, 2013; Yan et al., 2015; Qian et al., 2015]. Optimizing the simulation strategy to reduce the computational cost but meanwhile retain an accurate characterization of model sensitivity is therefore important for the calibration of models designed for future climate prediction. The nudging technique, namely the Newtonian relaxation of meteorological conditions toward weather reanalysis or a baseline simulation, has been used as a simple data assimilation technique in studies that

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aimed at diagnosing model biases under realistically simulated atmospheric states [e.g., Jeuken et al., 1996; Ghan et al., 2001; Boyle et al., 2005; Schmidt et al., 2006; Subramanian and Zhang, 2014; Ma et al., 2015]. It has also been used to help reduce the effect of natural variability thus making it easier to distinguish signal from noise [e.g., Lohmann and Hoose, 2009; Lohmann and Ferrachat, 2010; Kooperman et al., 2012]. For example, nudging has been shown to help effectively isolate the anthropogenic aerosol indirect effect with simulation lengths that are much shorter than what would otherwise be required for free-running simulations [Kooperman et al., 2012]. On the other hand, as nudging introduces an artificial forcing term to the prognostic equations of the model, it can significantly change the basic characteristics of the model climate, resulting in unintentional impacts on the simulated atmospheric physics and/or chemistry. For example, Lohmann and Hoose [2009] found that ECHAM5-HAM produced more convection and precipitation in the tropics when it was nudged toward the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA40 reanalysis, while Kooperman et al. [2012] and Zhang et al. [2014] noted that when temperature and winds in CAM5 were nudged toward the ERA-Interim reanalysis, changes were seen in the top-ofatmosphere (TOA) energy budget, convective precipitation, and the liquid and ice water paths. These studies suggest that, although nudging can reduce the impact of natural internal variability, it could also potentially cause biases. Even when the meteorological conditions are nudged toward a baseline simulation by the same model, there is the potential for nudging to bias the sensitivity of simulations to external parameters. Kooperman et al. [2012] found little evidence of bias when the external parameter was anthropogenic aerosol emissions, but other parameters that more directly interact with the circulation could introduce biases. One should therefore be cautious of using nudging when estimating model sensitivities to parameterization changes and external forcing. For precipitation, a field strongly affected by circulation, previous studies have noticed potential issues associated with nudging [e.g., Lohmann and Hoose, 2009; Zhang et al., 2014], but the consequences of nudging on parametric sensitivity quantification have not been systematically analyzed. This paper aims to evaluate the fidelity and computational cost of the nudging method in quantifying parametric sensitivities related to convection and clouds in CAM5. The two model parameters, we focus on this paper have been found in earlier studies to be influential on the simulated precipitation characteristics. The objectives of this study are to investigate (1) whether nudged simulations can reproduce the parametric sensitivities obtained in multiyear free-running simulations; and (2) when the answer to the first question is positive, whether the nudged runs can reveal the same signal using substantially shorter simulations than would be required for free-running simulations.

2. Model Description and Simulation Setup The global climate model used in this study is CAM5 with the spectral element dynamical core [Taylor and Fournier, 2010; Dennis et al., 2012] on a cubed sphere grid at NE30 resolution (about 110 km grid spacing) with 30 vertical layers. Deep convection is treated with the mass flux parameterization of Zhang and McFarlane [1995], with further modifications by Richter and Rasch [2008], Neale et al. [2008], and Suhas and Zhang [2014]. Shallow convection is parameterized as in Park and Bretherton [2009]. Large-scale condensation and stratiform cloud fraction are addressed by the parameterization of Park et al. [2014]. The stratiform cloud microphysics in CAM5 is represented by a two-moment parameterization [Morrison and Gettelman, 2008]. The vertical transport of heat, momentum, and moisture by turbulent eddies is represented by the parameterization of Bretherton and Park [2009]. Shortwave and longwave radiative transfer calculations are performed using the RRTMG (Rapid Radiative Transfer Model for General circulation model applications) code [Iacono et al., 2008; Mlawer et al., 1997]. Further details of the model formulation are described in Neale et al. [2010]. In order to illustrate the use of nudging in parametric UQ, we perturbed two parameters in CAM5: the convective relaxation time scale (TAU) used in the deep convection scheme of Zhang and Mcfarlane [1995], and the threshold relative humidity for the formation of low-level stratiform clouds (rhminl) used in the largescale condensation scheme of Park et al. [2014]. TAU has been shown by various studies to have substantial impact on the precipitation characteristics including the global mean precipitation rate [e.g., Yang et al., 2013; Qian et al., 2015], the extreme precipitation events [Williamson, 2013; Qian et al., 2015], and the amplitude of diurnal cycle [Qian et al., 2015]. Rhminl is often tuned to adjust the cloud amount and the energy

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Journal of Advances in Modeling Earth Systems Table 1. Simulation Descriptiona Value of Perturbed Parameter Experiment Name

TAU

rhminl

F_Def F_TAU_H F_TAU_L F_rhminl_H N_UVT_Def N_UVT_TAU_H N_UVT_TAU_L N_UV_Def N_UV_TAU_H N_UV_TAU_L N_UV_rhminl_H S_Def S_TAU_H

1h 8h 0.5 h 1h 1h 8h 0.5 h 1h 8h 0.5 h 1h 1h 8h

0.8875 0.8875 0.8875 0.99 0.8875 0.8875 0.8875 0.8875 0.8875 0.8875 0.99 0.8875 0.8875

Simulation Length

Simulation Type

30 years

Free-running

5 years

Nudged UVT

5 years

Nudged UV

60 days

Short ensembles

a TAU is the convective relaxation time scale used in the deep convection scheme developed by Zhang and Mcfarlane [1995], and rhminl is the threshold relative humidity for the formation of low stratiform clouds used in the parameterization of liquid stratus cloud fraction [Park et al., 2014]. Nudged UVT stands for the nudged UVT simulations; nudged UV stands for the nudged UV simulations.

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balance of the global atmosphere, and also has been shown by many studies to have important impact on the global mean precipitation rate [e.g., Qian et al., 2015]. For the purpose of evaluation, we first performed a 30 year free-running control simulation with the default parameter values, as well as one 30 year freerunning simulation for each parameter perturbation. Each 30 year simulation started with a 1 month spin-up that was not included in the analysis shown later in the paper. The model sensitivity was obtained as the difference of 30 year averaged fields between the perturbed and control simulations. Hereafter, these 30 year free-running simulations are considered reference simulations.

For each parameter perturbation, we also carried out pairs of control and perturbed simulations that were nudged toward the first 5 years of the free-running control simulation. The nudged simulations also had a 1 month spin-up that was not included in the analysis. As in Kooperman et al. [2009], a 6 h nudging relaxation time was employed. In this paper, two nudging strategies are evaluated: constraining both horizontal winds and temperature (refereed to as ‘‘nudged UVT simulations’’) and constraining only the horizontal winds (refereed to as ‘‘nudged UV simulations’’). To better understand the behaviors of the free-running simulations and nudged runs, we also carried out ensembles of short free-running simulations. The basic strategy of this method is to replace the traditional serial-in-time long-term climate integrations by representative ensembles of shorter simulations. For certain model sensitivities related to clouds, it has been shown that this method can be used to obtain equally robust signals but at substantially lower computational cost compared to the multiyear continuous simulations [Wan et al., 2014]. Ensembles of short simulations were performed with the default model parameters and with increased TAU. Each ensemble contained 12 members. The simulations were started on the first day of each month using initial conditions sampled from a previously performed free-running climate simulation. The same sets of initial conditions were used for the control and perturbed simulations. All ensemble members were run for 60 days. In summary, we carried out 11 multiyear simulations and two 60-day ensembles (Table 1). All simulations were driven by prescribed climatological seasonal cycles of sea-surface temperature (SST) and sea-ice cover. Emissions of aerosols and reactive gases were prescribed by their values in the year 2000 following Lamarque et al. [2010]. In free-running simulations, we first ran the control simulation (F_def), with the default value of TAU (1 h) and rhminl (0.8875). We then changed TAU to 8 h or 0.5 h, the high and low ends of the range of TAU identified in Qian et al. [2015], in simulations of F_TAU_H or F_TAU_L, respectively. Likewise, we perturbed TAU to 8 and 0.5 h in nudged UVT and nudged UV simulations as well (N_UVT_H, N_UVT_L, N_UV_H, and N_UV_L). In addition, we examined the perturbation of TAU from 1 to 8 h in ensembles of short simulations (S_Def and S_TAU_H). Finally, we perturbed rhminl to a high value (0.99) [Qian et al., 2015] in free-running mode (F_rhminl_H) and in UV nudging mode (N_UV_rhminl_H).

3. Results In this section, we start the evaluation of nudging by examining the model’s response to perturbation of TAU from the default value of 1 to 8 h, followed by exploring the case with a decrease of TAU from 1 h to half-an-hour. Different perturbations of TAU allow us to test the impact of signal strength on the nudging effect. Results are then presented for simulations in which rhminl is changed from the default value of

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Journal of Advances in Modeling Earth Systems (a) Free (30 yrs)

(c) Nudged UVT (1 yr)

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(b) Free (1 yr)

(d) Nudged UV (1 yr)

Figure 1. Spatial distribution of annual mean convective precipitation change (mm/d) in response to a perturbation of TAU from 1 to 8 h. (a) 30 year average of the reference (free-running) simulations; other plots: the first year of (b) the free-running, (c) nudged UVT, and (d) nudged UV simulations. Stippling in (a) indicates where the signal is significant at the 95% confidence interval according to the Student’s t-test.

0.8875 to 0.99. The analysis focuses on the response of precipitation (convective and large-scale precipitation) and cloud forcing. 3.1. Strong Perturbation in Convection 3.1.1. Free-Running Simulations Figures 1a and 2a present the 30 year mean annual mean convective and large-scale precipitation change caused by the increase in TAU (from 1 to 8 h) in the free-running simulations. Stippling in the figures shows the grid points where the signal is significant at the 95% confidence level. Clearly, most of the signals in the 30 year free run are statistically significant. Over most of the regions, convective precipitation rates decrease, but large-scale precipitation rates increase. This is expected, because the increase in TAU reduces the magnitude of cumulus cloud base mass flux, leading to less convective precipitations [Mishra et al., 2010]. The weaker convection causes an accumulation of convective instability and moisture content in the atmosphere, which thus increases large-scale precipitation [Mishra et al., 2010]. Strong decreases of convective precipitation occur over the equatorial belts of the Pacific Ocean and the East Asian Monsoon region, while strong increases in the large-scale precipitation are evident over the equatorial regions, south of the equator over the Indian Ocean and the West Pacific Ocean, and near the East coast of North America and East Asia. In contrast, the convective precipitation increases over the tropical eastern Pacific and northern Indian Ocean region, and the large-scale precipitation decreases over the Indian subcontinent and the oceanic regions nearby. The increases of convective precipitation over the tropical Indian Ocean and to the

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Figure 2. As in Figure 1 but for the large-scale precipitation rate (mm/d).

east of Central America are associated with responses of the resolved-scale circulation, which we will discuss in the next section (cf. Figure 5). The longer TAU results in stronger convergence near the surface, and provides more favorable conditions for convection to occur. The geographical distributions of changes in the shortwave cloud forcing (SWCF) and longwave cloud forcing (LWCF) are shown in Figures A1a and A2a, respectively. The cloud forcing responses reflect primarily the weakening of the convective activities: both SWCF and LWCF are considerably weakened in the ITCZ and the tropical monsoon regions, but are slightly enhanced in some small areas. To evaluate the magnitude of internal variability and provide a basis for the assessment of the nudged simulations, the precipitation rate changes seen in the first year of the 30 year simulations are shown in Figures 1b and 2b. In addition, the global mean, pattern correlation, and spatial root-mean-square error (RMSE) of 1 year averages are shown in Figure 3. The pattern correlations and RMSEs were calculated with respect to the 30 year averages. We view each 1 year average as a separate estimate of the long-term average. The solid-filled light blue bars indicate the mean (global mean, pattern correlation, or RMSE) of the 30 estimates, and the black vertical line associated to the end of each bar indicates the 6r range where r denotes the standard deviation. Similar statistics are shown for the 3 and 5 year averages with solid-filled light green and yellow bars, respectively. Figure 3 indicates that the interannual variability of precipitation response is small in this set of simulations. The global mean convective and large-scale precipitation responses vary only by a few percent from year to year. The pattern correlations between 1 and 30 year averages are typically 0.9 or higher. Indeed, the geographical distributions of the 1 year mean precipitation rates shown in Figures 1b and 2b resemble the corresponding 30 year averages (Figures 1a and 2a) quite well.

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Figure 3. (top row) Global mean, (middle row) pattern correlation, and (RMSE, bottom row) root-mean-square error of the model sensitivity to an increase of TAU from 1 to 8 h. The pattern correlation and RMSE were calculated against the model sensitivity derived from the 30 year free-running simulations. The four columns correspond to results for the difference of convective precipitation, large-scale precipitation, shortwave cloud forcing, and longwave cloud forcing (from left to right). The black vertical lines attached to the solid filled bars indicate the standard deviation of the metrics (global mean, pattern correlation, and RMSE) of 5 year, 3 year, or 1 year averages. Details of the simulation setup are explained in section 2 and Table 1.

Cloud forcing results are also included in Figures A1, A2, and 3, which are shown separately for SWCF and LWCF. Like what we have seen for precipitation, the interannual variabilities are relatively small, and the 1 year averages are already good approximations to 30 year averages. 3.1.2. Nudged Simulations The UVT-nudging, in contrast, changes the precipitation and cloud forcing responses substantially. As can be seen in Figures 1c, 2c, and 3, while the decreases (increases) in convective (large-scale) rainfall are qualitatively reproduced in most regions, the magnitudes of the responses are substantially smaller than those in the reference simulations. Substantially weaker responses can also been seen in SWCF and LWCF (Figures A1c, A2c, and 3). The global mean responses are 20.46 mm/d (with UVT-nudging) versus 20.62 mm/d (without nudging) for convective precipitation, and 0.46 mm/d (with UVT-nudging) versus 0.72 mm/d (without nudging) for large-scale precipitation when comparing 1 year UVT-nudging runs with the 30 year freerunning simulations (Figure 3 and Table A1). The global mean SWCF and LWCF changes are about 0.5 and

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22 W/m2 in the UVT-nudging simulations, in contrast to about 3.5 and 23 W/m2 in the free-running simulations (Figure 3 and Table A1). In addition, the increase of convective precipitation in the tropical eastern Pacific and decrease of large-scale precipitation near the Indian subcontinent are not reproduced by the UVT-nudged simulations (Figures 1 and 2), resulting in a lower global pattern correlation coefficient of 0.81 (0.80) for the convective (large-scale) precipitation responses, and 0.40 (0.79) for SWCF (LWCF) (Figure 3 and Table A1). Allowing the temperature field to evolve freely by nudging only winds helps to improve the results. The simulated global mean responses are closer to the reference simulations, and the pattern correlations are higher (Figure 3 and Table A1). But the regional responses in the eastern tropical Pacific and in the Asian monsoon region are still not correctly captured (Figures 1d and 2d). While the improvements obtained by removing the constraint on temperature are consistent with earlier findings of Zhang et al. [2014], the substantial side effects of wind-only nudging were not fully expected. To better understand the results, we conducted and analyzed the ensembles of short free-running simulations. In Figure 4, convective precipitation responses to the increase of TAU are shown for the first 5 model days. Notice that the results shown here are the average of 12 ensemble members; for each member, the pair of simulations with TAU 5 1 h and TAU 5 8 h were initialized using the same atmosphere and land model states. The expected decreases in convective precipitation occur globally at the first time step when the interactions between winds and the convection have not yet emerged. By day 2, however, the precipitation responses become very inhomogeneous in space, while corresponding small-scale responses are seen in horizontal winds (Figure 5). Although it was expected that the parameterized convection would interact with the resolved dynamics, the strength of the wind responses contradicts our original expectation that winds in the control and perturbed simulations would not diverge much in the first few days. Prior to this work, we have conducted several studies that used short ensembles to quantify model sensitivities to parameter perturbation or model time step change [e.g., Wan et al., 2014]. In those simulations, noisy responses in tropical precipitation and cloud forcing (as indicated by small-scale positive and negative responses occurring next to each other) were not visible until day 5 or 6. For example, the SWCF responses at day 3 caused by model time step change are shown in Figure 6 of Wan et al. [2014], and we have verified that the results are similar when the ensemble size is reduced to 12 members. In a recent and not yet published study where multiple parameters in the shallow convection and turbulence schemes were perturbed, we also saw clear responses in the tropical precipitation, but the spatial patterns were rather smooth in the first 5 days, and the wind responses were substantially smaller than those shown in Figure 5 in this paper. Because of the contrast between the earlier experiences and the results shown in Figures 4 and 5, we infer that in the case of strong perturbation of TAU from 1 to 8 h, the interaction between convection and circulation is too strong for the wind nudging with a 6 h time scale to sufficiently preserve the characteristics of the parametric sensitivities. 3.1.3. Computational Cost We have shown earlier in section 3.1.1 that in the absence of interannual variability in external forcing (e.g., SST), the impacts of perturbing TAU from 1 to 8 h can be well captured by averaging just 1 year of the freerunning simulations. When assessing the computational cost, an additional aspect to consider is how long a spin-up phase one needs to discard from the simulations before taking the 1 year average. To answer this question, Figure 6 presents the geographical distribution of 12-member mean convective precipitation responses from the short simulations, averaged from day 2 to day 15 in the left plot and from day 16 to day 31 in the right plot. While the general decrease of convective precipitation can already be seen in the first 15 days, the responses associated with circulation changes in the eastern tropical Pacific and Asian monsoon regions are not captured until a later stage. By contrast, ensemble averages in the second half-months show a close resemblance with the reference results presented earlier in Figure 1. This suggests that the response of convective precipitation is well developed within a month. Therefore, for the perturbation of TAU from 1 to 8 h, a pair of continuous 13 month simulations are sufficient to reveal the response in the annual mean precipitation. Constraining the meteorology does not bring an appreciable reduction in computational cost, but causes side effects in the assessment of model sensitivity. As an aside, we note that if one were to use the short ensembles to quantify precipitation sensitivity, the simulation length would need to exceed 15 days in order for the circulation responses to develop (Figure 6). Since the geographical distribution of convective rainfall has strong day-to-day variability, a sufficient number of daily samples are needed to reveal the characteristic spatial distribution of the annual mean precipitation response. This means the total integration time (with all members summed together) would be close to 1 year. Therefore, in this particular case, the short ensembles would not lead to appreciable reduction in the total simulation length, either.

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Figure 4. The change in convective precipitation (mm/d) in response to the perturbation of TAU from 1 to 8 h, evolving from day 1 to day 5 predicted in ensembles of short simulations.

3.2. Weak Perturbation in Convection We now compare the nudged and free-running simulations for a case with a weaker parameter perturbation in convection (TAU 5 0.5 h instead of 1 h). Similar to the previous case, temperature nudging substantially alters the global mean response in precipitation and cloud forcing (Figure 7, first row). Wind nudging leads to underestimated convective rainfall responses in the Indian Ocean and over the Western Pacific

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Day 1

First time step

Day 2

Day 3

Day 4

Day 5

Figure 5. The change in near surface wind (m/s) in response to the perturbation of TAU from 1 to 8 h, evolving from day 1 to day 5 predicted in ensembles of short simulations.

Warm Pool (Figures 8a and 8d). Unlike the previous case, however, the 1 year free-running simulations start to show regional responses that are not seen in the 30 year averages (Figure 8b). This is consistent with what are shown in the free-running simulations in the first row of Figure 7: the precipitation and cloud forcing in this case show relatively large interannual variability. Compared to the nudged runs, the 1 year freerunning simulations have significantly lower pattern correlations and higher RMSEs for both the precipitation rates and the cloud forcing (Figure 7, second and third rows), while the 3 and 5 year mean results obtained in the free-running mode agree considerably better with the reference results. These results suggest that this set of simulations, the 1 year free-running simulations and nudged runs both have limitations, although for different reasons. 3.3. Perturbation in Large-Scale Condensation Next, we analyze a case with a parameter (rhminl) perturbation in the large-scale condensation scheme. The precipitation and cloud forcing responses to an increase of rhminl from 0.8875 to 0.99 are shown in Figures 9a, 9b, A3a, and A3b as 30 year averages. It is worth noting that while rhminl is a parameter in the

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b)

Figure 6. The spatial distribution of convective precipitation change (mm/d) in response to the perturbation of TAU from 1 to 8 h averaged for (a) day 2 to day 15 and (b) day 16 to day 31 ensembles of short simulations.

stratiform low-cloud fraction parameterization, the precipitation responses are seen mainly in the convective rainfall, suggesting that this parameter affects precipitation by indirectly changing the stability of the low atmosphere hence affecting convection, rather than directly impacting the stratiform cloud microphysics. The weakening of convective activities over the ocean (Figure 9a) results in weakening in both SWCF and LWCF (Figures A3a and A3b), while the strengthening of convection over the tropical land regions leads to enhanced LWCF (Figure A3b). Results shown in Figures 9c–9f, A3c–A3f, and 10 indicate that the relative merits between the nudged and free-running simulations in this set of experiments are very different from the case of strongly perturbed convection. In fact, the 1 year averaged precipitation responses from the free-running simulations are dominated by noise (Figures 9c and 9d), while the simulations with constrained winds very reasonably reproduce the decreases (increases) of convective rainfall in the low-latitude ocean (land) areas (Figures 9e and 9f). In terms of cloud forcing, the signal in SWCF is reasonably well captured by the 1 year free-running simulation (Figure A3c). For the longwave part, the results calculated from 1 year free-running simulations appear to be noisy (Figure A3d), while the responses revealed by 1 year UV-nudged simulations agree well with the reference results (Figure A3f). The pattern correlations and RMSEs of both precipitation and cloud forcing responses shown in Figure 10 suggest that the 1 year nudged simulations have comparable fidelity of the 5 year free-running simulations, with a substantial reduction of computational cost.

4. Conclusions and Discussion In this study, we evaluated the fidelity and computational cost of nudged simulations for the quantification of parametric sensitivities in precipitation and clouds in CAM5. Two parameters were perturbed, and three sets of simulations were conducted as illustrating examples. In the first example, the convective instability relaxation time scale (TAU) in the deep convection parameterization was strongly perturbed from its default value of 1 to 8 h. Qualitatively, the decreases in convective precipitation and the compensating increases in large-scale rainfall were captured by nudged simulations that used a 6 h relaxation time scale for temperature and/or horizontal winds, but the global mean responses were not reproduced accurately, and certain regional features were underestimated or not captured at all. Ensembles of short free-running simulations suggested that the response in the resolved-scale dynamics were rather strong in this case; it is therefore understandable that suppressing the circulation responses can cause damaging side effects in the assessment of model sensitivity. In this example, we had a strong perturbation in a model parameter that directly affected precipitation, and the interannual variabilities in precipitation and cloud forcing were weak compared to the responses caused by parameter perturbation. Thus, the model sensitivities in precipitation and cloud forcing were well captured by 1 year free-running simulations with a 1 month spin-up. There was therefore no reduction in computational cost in the nudged simulations as long as the focus of analysis was on the annual averages. In the second set of simulations, the same parameter TAU was changed from 1 to 0.5 h. While nudging still introduced side effects, the 1 year free-running simulations were no longer as

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Figure 7. The same as Figure 3, but for the case with the weak perturbation in TAU (1 h to half-an-hour).

effective because of the more evident impact of noise caused by internal variability. In the third set of simulations, the threshold relative humidity for low-cloud formation was perturbed from 0.8875 to 0.99, which had a direct impact on the simulated clouds but indirect impact on precipitation. In this case, the 1 year averages of precipitation rates from the free-running simulations were severely affected by internal variability, while 1 year nudged simulations produced results that were comparable to 5 year unconstrained simulations, with much less noise and at substantially lower computational costs. These results indicate that there is not a simple answer to the question whether nudging can be used to quantify precipitation sensitivities in a general circulation model. The fidelity of the constrained simulations depends on the detailed implementation of nudging (e.g., UVT-nudging versus UV nudging), and the mechanism through which the perturbed parameter affects precipitation (e.g., whether the impact is direct or whether there is substantial interaction with the resolved-scale circulation). The relative computational costs of nudged and freerunning simulations, as measured by the simulation length required for sufficiently distinguish signal and noise, are affected by the magnitude of internal variability in the physical quantities of interest, as well as the magnitude of the parameter perturbation.

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Journal of Advances in Modeling Earth Systems (a) Free (30 yrs)

(b) Free (1 yr)

(c) Nudged UVT (1 yr)

(d) Nudged UV (1 yr)

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Figure 8. Spatial distribution of annual mean convective precipitation change (mm/d) in response to a perturbation of TAU from 1 to 0.5 h. (a) 30 year average of the reference (freerunning) simulations; other plots: the first year of (b) the free-running, (c) nudged UVT, and (d) nudged UV simulations. Stippling in plot (a) indicates where the signal is significant at the 95% confidence interval according to the Student’s t-test.

Our results from the perturbed large-scale condensation case (i.e., our third example) are qualitatively similar to those of Kooperman et al. [2012] who showed that nudging was helpful for quantifying the aerosol indirect forcing. In both cases, the perturbation of rhminl and aerosol emissions changed the horizontal winds very little. Nudging wind thus added an artificial but negligible forcing to the ‘‘physical’’ forcing caused by parameter/emission perturbation. Moreover, in both cases, the signal-to-noise ratio was low, making it difficult to detect signal from a short period of time in the unconstrained simulations. Our conclusion that nudging produced adverse results in simulations with perturbed convection in CAM5, on the other hand, is in line with the earlier findings of Lohmann and Hoose [2009] and Zhang et al. [2014]. In the present paper, we did not attempt to increase the nudging time scale and investigate whether there exists an optimal strength of nudging that could sufficiently reduce noise in the results and meanwhile avoid overly strong suppression of the physics-dynamics interaction. A future investigation might provide useful information. An important implication of our results is that in the routine practice of model evaluation and tuning, without a quantitative understanding of the extent to which a certain parameter perturbation would interact with the resolved winds and/or be affected by internal variability, it will be difficult to determine a priori whether nudging would be useful or harmful for the sensitivity experiments. Our method used in this study, namely comparing results from long free-running simulations and shorter nudged simulations can only be used to show proofs of concept. Using such a method extensively would contradict the original motivation of reducing computational cost of the parametric sensitivity quantification exercises. One possible way to

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Large-scale

(a) Free (30 yrs)

(b) Free (30 yrs)

(c) Free (1 yr)

(d) Free (1 yr)

(e) Nudged UV (1 yr)

(f) Nudged UV (1 yr)

Figure 9. (left column) The spatial distribution of convective and (right column) large-scale precipitation change (mm/d) in response to the perturbation of rhminl from 0.8875 to 0.99. The top row shows 30 year averages from the reference (free-running) simulations. The middle row shows annual averages from the first year of the free-running simulations. The third row shows annual averages from the first year of nudged simulations in which the horizontal winds were nudged toward those of the reference simulations. Stippling in the top plots indicates regions where the signal is significant at the 95% confidence interval according to the Student’s t-test.

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Figure 10. The same as Figure 3, but for the case with the perturbation in rhminl (0.8875–0.99). UVT-nudging simulations were not performed in this case and thus not shown in this figure.

address this difficulty could be to look for methods to evaluate the fidelity of the nudged simulations after the fact, for example, by monitoring the wind tendencies induced by nudging, and trusting the suggested model sensitivities only when and where the nudging tendencies are weak compared to the tendencies caused by the physical processes. Meanwhile, the nudging tendencies need to be strong enough to sufficiently constrain the large-scale circulation thus reduce the impact of internal variability. Future research is needed to find out whether this could be a feasible strategy, and whether a ‘‘sweet spot’’ can be found for the nudging strength. In the example of strongly perturbed convection, we mentioned that the short ensemble simulations, like the nudged runs, did not provide a substantial reduction in computational cost for the quantification of precipitation sensitivities. Nevertheless, the short ensembles provided important information on the magnitude and evolution of circulation responses to the parameter perturbation, thus helped to understand the limitation of wind nudging, and provided an estimate of the spin-up needed in free-running simulations. This demonstrates that short ensemble simulations can be very useful for obtaining detailed understanding of model sensitivities.

Appendix A In this appendix, we present the global mean, pattern correlation, and root-mean-square error (RMSE) for the case with a strong perturbation in convection (Table A1), for the case with a weak

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perturbation in convection (Table A2), and for the case with perturbation in large-scale condensation (Table A3). We also show the response of cloud radiative forcing to parameter perturbations in Figures A1–A3. Table A1. Global Mean, Pattern Correlation, and Root-Mean-Square Error (RMSE) of Difference Between the Simulation With TAU 5 8 h and the Simulation With TAU 5 1 ha

Convective precipitation (mm/d) Large-scale precipitation (mm/d) Shortwave cloud forcing (W/m2) Longwave cloud forcing (W/m2)

Global mean Pattern correlation RMSE Global mean Pattern correlation RMSE Global mean Pattern correlation RMSE Global mean Pattern correlation RMSE

Free (30 year Averages)

Nudged UVT (5 year Averages)

Nudged UVT (1 year Averages)

Nudged UV (5 year Averages)

Nudged UV (1 year Averages)

Free (5 year Averages)

Free (3 year Averages)

Free (1 year Averages)

20.62

20.46 0.83 0.62 0.46 0.82 0.80 0.55 0.45 7.87 22.04 0.80 3.20

20.46 0.81 0.65 0.46 0.80 0.81 0.54 0.40 8.04 22.01 0.79 3.29

20.63 0.88 0.52 0.68 0.82 0.78 2.89 0.84 4.70 21.90 0.81 3.02

20.63 0.87 0.54 0.68 0.80 0.83 2.85 0.83 4.82 21.89 0.80 3.17

20.62 (3.14e-3) 0.99 (4.53e-4) 0.16 (3.40e-3) 0.72 (3.84e-3) 0.98 (1.17e-3) 0.22 (8.73e-3) 3.48 (7.31e-2) 0.98 (1.29e-3) 1.75 (3.41e-2) 22.91 (7.65e-2) 0.98 (9.63e-4) 0.88 (2.43e-2)

20.62 (5.60e-3) 0.98 (1.63e-3) 0.22 (1.11e-2) 0.72 (4.80e-3) 0.97 (2.05e-3) 0.30 (1.02e-2) 3.48 (9.06e-2) 0.96 (2.17e-3) 2.34 (7.38e-2) 22.91 (8.12e-2) 0.97 (2.03e-3) 1.18 (4.21e-2)

20.62 (9.14e-3) 0.94 (6.79e-3) 0.40 (2.04e-2) 0.72 (1.07e-2) 0.91 (5.32e-3) 0.55 (1.85e-2) 3.48 (1.63e-1) 0.88 (1.18e-2) 4.24 (2.02e-1) 22.91(1.0e-1) 0.91 (8.58e-3) 2.17 (1.03e-1)

0.72

3.48

22.91

a The pattern correlation and RMSE are computed against the difference obtained from 30 year free-running simulations. The numbers in parentheses show the stand deviations of 5 year averages, 3 year averages, and 1 year average. Free stands for free-running simulations; nudged UVT stands for the nudged UVT simulations; nudged UV stands for the nudged UV simulations.

(a) Free (30 yrs)

(c) Nudged UVT (1 yr)

(b) Free (1 yr)

(d) Nudged UV (1yr)

Figure A1. Spatial distribution of annual mean shortwave cloud forcing change (W/m2) in response to a perturbation of TAU from 1 to 8 h. (a) 30 year average of the reference (freerunning) simulations; other plots: the first year of (b) the free-running, (c) nudged UVT, and (d) nudged UV simulations. Stippling in plot (a) indicates where the signal is significant at the 95% confidence interval according to the Student’s t-test.

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Table A2. The Same as Table A1, Except for the Difference Between the Simulation With TAU 5 1 h and the Simulation With TAU 5 0.5 h Free (30 year Averages) Convective precipitation (mm/d) Large-scale precipitation (mm/d) Shortwave cloud forcing (W/m2) Longwave cloud forcing (W/m2)

Global mean Pattern correlation RMSE Global mean Pattern correlation RMSE Global mean Pattern correlation RMSE Global mean Pattern correlation RMSE

0.17

20.14

1.11

20.72

Nudged UVT (5 year Averages)

Nudged UVT (1 year Averages)

Nudged UV (5 year Averages)

Nudged UV (1 year Averages)

Free (5 year Averages)

Free (3 year Averages)

Free (1 year Averages)

0.21 0.72 0.29 20.16 0.92 0.14 1.48 0.66 2.14 20.42 0.55 1.48

0.21 0.66 0.32 20.16 0.90 0.16 1.49 0.64 2.24 20.43 0.53 1.50

0.17 0.80 0.23 20.14 0.95 0.11 0.93 0.71 1.99 20.68 0.79 1.08

0.17 0.73 0.27 20.14 0.91 0.16 0.93 0.65 2.18 20.65 0.71 1.24

0.17 (3.62e-3) 0.92 (8.67e-3) 0.17 (6.40e-3) 20.14 (4.43e-3) 0.93 (1.65e-3) 0.13 (2.15e-3) 1.11 (9.85e-2) 0.82 (1.13e-2) 1.81 (6.01e-2) 20.72 (5.64e-2) 0.87 (1.44e-2) 0.92 (2.62e-2)

0.17 (5.60e-3) 0.86 (1.83e-2) 0.22 (1.46e-2) 20.14 (3.91e-3) 0.89 (6.89e-3) 0.17 (3.89e-3) 1.11 (9.94e-2) 0.73 (2.33e-2) 2.39 (9.7e-2) 20.72 (5.91e-2) 0.80 (2.03e-2) 1.21 (6.59e-2)

0.17 (9.47e-3) 0.69 (4.39e-2) 0.40 (2.87e-2) 20.14 (8.48e-3) 0.73 (2.43e-2) 0.32 (1.52e-2) (1.73e-1) 0.51 (3.87e-2) 4.32 (2.16e-1) 20.72 (9.73e-2) 0.59 (3.52e-2) 2.25 (1.23e-1)

(a) Free (30 yrs)

(b) Free (1 yr)

(c) Nudged UVT (1 yr)

(d) Nudged UV (1 yr)

Figure A2. Spatial distribution of annual mean longwave cloud forcing change (W/m2) in response to a perturbation of TAU from 1 to 8 h. (a) 30 year average of the reference (freerunning) simulations; other plots: the first year of (b) the free-running, (c) nudged UVT, and (d) nudged UV simulations. Stippling in plot (a) indicates where the signal is significant at the 95% confidence interval according to the Student’s t-test.

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Journal of Advances in Modeling Earth Systems SWCF (a) Free (30 yrs)

(b) Free (30 yrs)

(c) Free (1 yr)

(d) Free (1 yr)

(e) Nudged UV(1 yr)

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LWCF

(f ) Nudged UV (1 yr)

Figure A3. (left column) The spatial distribution of shortwave cloud forcing and (right column) longwave cloud forcing change (W/m2) in response to the perturbation of rhminl from 0.8875 to 0.99. The top row shows 30 year averages from the reference (free-running) simulations. The middle row shows annual averages from the first year of the free-running simulations. The third row shows annual averages from the first year of nudged simulations in which the horizontal winds were nudged toward those of the reference simulations. Stippling in the top plots indicates regions where the signal is significant at the 95% confidence interval according to the Student’s t-test.

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Table A3. The Same as Table A1, Except for the Difference Between the Simulation With rhminl 5 0.8875 and the Simulation With rhminl 5 0.99

Convective precipitation (mm/d)

Large-scale precipitation (mm/d)

Shortwave cloud forcing (W/m2) Longwave cloud forcing (W/m2)

Global mean Pattern correlation RMSE Global mean Pattern correlation RMSE Global mean Pattern correlation RMSE Global mean Pattern correlation RMSE

Acknowledgments The study described in this paper was supported by the U.S. Department of Energy (DOE) Office of Science as part of the Scientific Discovery through Advanced Computing (SciDAC) Program. The research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under contract DE-AC02-05CH11231. Pacific Northwest National Laboratory is operated by Battelle Memorial Institute for DOE under contract DE-AC0576RL01830. Model results can be accessed from https://portal.nersc.gov/ project/m1704/gxlin.

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Free (30 year Averages)

Nudged UV (5 year Averages)

Nudged UV (1 year Averages)

Free (5 year Averages)

Free (3 year Averages)

Free (1 year Averages)

24.73 3 1022

24.91 3 1022

5.18e-2

0.76 0.13 21.85 3 1022

0.65 0.16 21.64e-2

0.59 9.93 3 1022 9.79 0.99 1.30 20.75 0.87 0.77

0.44 0.13 9.76 0.99 1.70 20.74 0.82 0.92

24.73 3 1022 (3.8e-3) 0.79 (1.0e-2) 0.15 (3.5e-3) 21.27 3 1022 (4.44e-3) 0.63 (2.78e-2) 0.15 (4.45e-3) 9.81 (8.17e-2) 0.99 (6.20e-4) 1.75 (2.52e-2) 20.83 (5.0e-2) 0.86 (1.74e-2) 0.92 (5.09e-2)

24.73 3 1022 (4.82e-3) 0.68 (2.96e-2) 0.21 (8.32e-3) 1.27 3 1022 (4.44e-3) 0.52 (4.06e-2) 0.20 (6.14e-3) 9.81 (1.07e-1) 0.98 (1.34e-3) 2.35 (5.95e-2) 20.83 (4.33e-2) 0.77 (2.47e-2) 1.26 (5.64e-2)

24.73 3 1022 (9.24e-3) 0.46 (4.93e-2) 0.37 (2.26e-2) 21.27 3 1022 (1.00e-2) 0.32 (5.63e-2) 0.36 (1.60e-2) 9.81 (2.03e-1) 0.94 (5.25e-3) 4.19 (1.69e-1) 20.83 (8.33e-2) 0.57(3.61e-2) 2.24 (1.15e-1)

21.27 3 10

9.81

20.83

22

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