Exploring the Parameters Space of the Regional Climate Model COSMO-CLM 5.0 for the CORDEX Central Asia Domain

The parameter uncertainty of a climate model represents the spectrum of the results obtained by perturbing its empirical and unconfined parameters used to represent sub-grid scale processes. In order to assess a model reliability and to better understand its limitations and sensitivity to different physical processes, the spread of model parameters needs to be carefully investigated. This is particularly true for Regional Climate Models (RCMs), whose performances are domaindependent. 5 In this study, the parameter space of the RCM COSMO-CLM is investigated for the CORDEX Central Asia domain, using a Perturbed Physics Ensemble (PPE) obtained by performing 1-year long simulations with different parameter values. The main goal is to characterize the parameter uncertainty of the model, and to determine the most sensitive parameters for the region. Moreover, the presented experiments are used to study the effect of several parameters on the simulation of selected variables for sub-regions characterized by different climate conditions, assessing by which degree it is possible to improve 10 model performances by properly selecting parameter inputs in each case. Finally, the paper explores the model parameter sensitivity over different domains, tackling the question of transferability of an RCM model setup to different regions of study. Results show that only a sub-set of model parameters present relevant changes in model performances for different parameter values. Importantly, for almost all parameter inputs, the model shows an opposite behavior among different clusters and regions. This indicates that conducting a calibration of the model against observations to determine optimal parameter values for the 15 Central Asia domain is particularly challenging: in this case, the use of objective calibration methods is highly necessary. Finally, the sensitivity of the model to parameters perturbation for Central Asia is different than the one observed for Europe, suggesting that an RCM should be re-tuned, and its parameter uncertainty properly investigated, when setting up modelexperiments to different domains of study. 1 https://doi.org/10.5194/gmd-2020-196 Preprint. Discussion started: 6 July 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
Climate models are representations of the climate system based on well-understood physics combined with simplified descriptions of sub-grid scale processes called parameterizations (Hourdin et al., 2017). These parameterizations usually depend on one or several empirical and unconfined parameters (Hourdin et al., 2017;Bellprat et al., 2012a;Tebaldi and Knutti, 2007) whose different values produce a wide spectrum of outcomes referred to as parameter uncertainty. Parameter uncertainty is 5 important because it allows to better understand model limitations and sensitivity to different physical processes. The common approach to sample model parameter uncertainty is to use ensembles of model simulations, called Perturbed Physics Ensembles (PPEs, Murphy et al., 2007;Bellprat, 2013;Tebaldi and Knutti, 2007;Paeth, 2015).
When producing climate projections for impact studies, as much uncertainty as possible should be accounted for in order to properly drive policy-makers in their decision-making process, providing a measure of model reliability (Knutti et al., 2002, of statistical surrogate models, also referred to as model emulators or meta models (O'Hagan, 2006;Bellprat et al., 2012b;Hourdin et al., 2017). These methods have the advantage to be a computationally cheap representation of the sensitivity of the climate model to the parameter space.
One of the first objective calibration methods using such a surrogate or meta model to tune an RCM is the one of Bellprat et al. (2012a, b). Their method is mainly composed of two parts: a first one in which the model parameter uncertainty is 5 investigated in order to determine a sub-sample of model most sensitive parameters; and a second one where a second order polynomial meta model, firstly proposed by Neelin et al. (2010), is applied to extrapolate the model behavior for all the possible values of the selected parameters and their mutual interactions. Bellprat et al. (2012b) firstly used their method for the calibration of the RCM COSMO-CLM (Rockel et al., 2008) for the Coordinated Regional Climate Downscaling Experiment (CORDEX, Giorgi et al., 2009) European domain. The same method has successively been employed in the study of Bellprat the latter case the data are interpolated on the CRU grid by means of a conservative remapping method prior to the analyses.
The considered observational data sets and the corresponding variables for which they are used are reported in Table 3. 25

Analysis Methods and Evaluation Metrics
The analyses are conducted on the regional means of monthly values of the considered variables for different regions characterized by differing climate conditions. After averaging, the model residuals with respect to observations become quasi-Gaussian, allowing the use of normal estimators of model disagreement (Von Storch and Zwiers, 2001;Bellprat et al., 2012a).
A k-means clustering technique (Steinhaus, 1956;Ball and Hall Dj, 1965;MacQueen et al., 1967;Lloyd, 1982;Jain, 2010; to decompose the domain into a set of sub-regions with different climate conditions. K-means allows the separation of similar data into groups, using the concept of Euclidean distance from the centroids of a pre-determined group of clusters. Following several tests and the results of other studies (Mannig et al., 2013;Russo et al., 2019) a total number of eleven clusters have been selected for the Central Asia domain. As input for the clustering procedure, q-normalized values of monthly climatologies of T2M and CLCT derived from the CRU data set and PRE values derived from the GPCC are used. The results of the k-means 5 clustering are shown in Fig. 2.
The metrics used for investigating the COSMO-CLM parameters uncertainty is the Performance Index (PI) presented in Bellprat et al. (2012a) and derived from the Climate Performance Index (CPI) of Murphy et al. (2004). PI represents a normalized multivariate root-mean-square error (RMSE), weighted over different sources of uncertainties and averaged over the model variables, the considered regions and the months of a selected year: where V = 3 represents the number of variables considered, R = 11 is the number of the domain sub-regions and T = 12 is the number of months of the given year. The terms m and o represent the model and the observational monthly means calculated for each variable, month and region. σ o is the monthly standard deviation of the interannual variations calculated from the observations over the period 1996-2005; σ iv is the monthly standard deviation of the internal variability of the regional model 15 for the same period; σ is the monthly standard deviation of the observational error derived from different reference datasets, for the selected year.
PI represents an objective measure of model reliability, where higher (lower) values indicate bad (good) performances. In order to make inferences about the sensitivity of model parameters, Bellprat et al. (2012a, b) used the PI to define a positive Performance Score (PS), that can be interpreted as an approximation of the likelihood that the residuals come from a distribution 20 with zero mean and variance given by σ o , σ iv and σ : Basically, PI allows to quantify model parameter uncertainty, while PS is used as an estimate of the model sensitivity to each single tested parameter.
In this study, first PI and PS are calculated for the three considered variables together. Then, given the assumption that 25 changes in PS are expected to be smooth (Bellprat et al., 2012a;Neelin et al., 2010), a quadratic regression is fitted to the obtained values of PS for each parameter, representing an estimate of model sensitivity for that specific parameter. Successively, the same analyses are repeated for each variable separately, taking into account the fact that the obtained PS values might be due to a compensation effect of the results for single variables. This will contribute to discriminate the model most sensitive parameters for the region.

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In a successive step, model parameter uncertainties for different areas of the domain are investigated. For this purpose PI is calculated separately for each variable and sub-region. Then, the variable and region dependent PI is expressed with respect to the one of the reference simulation using a Skill Score (SS) defined as: Positive (negative) SS values indicate an improvement (worsening) of the considered experiment over the reference simula-5 tion, in terms of the proposed metrics PI.
The range of different errors and their effects on the considered metrics will be additionally investigated to support the presented analyses.
Finally, for the comparison of the model results obtained for Central Asia with the ones for Europe, the same PS metrics, calculated for a sub-set of selected parameters over the entire domain, will be considered. to get the effective surface area used in the land-surface scheme, and qi0, being the parameter for the cloud ice treshold for autoconversion used in the microphysics parametrization scheme. Other parameters, which have some considerable impact on PS, are d_mom, the factor for turbulent momentum dissipation, v0snow, controlling the fall velocity of snow, radfac, which represents the fraction of clouds water/ice used in the radiation scheme, tkhmin, the minimum value for the turbulence heat diffusion coefficient, and rlam_heat, the scaling factor of the laminar boundary layer for heat. Thus, for each parametrization 20 scheme, excluding convection, there is at-least one or two parameters that shows the potential to sensibly improve model performances when an optimal value is set. For some of the parameters such as c_diff, the factor for turbulent diffusion in the turbulent kinetic Energy (TKE) scheme, and z0m_ dia, representing the roughness length of a typical synoptic station used for the interpolation of values of the 10-m wind, strong changes in PS are evident in Fig. 3. However, in these cases the model performs similarly for all tested inputs, suggesting that the evinced sensitivity is an artificial result of the quadratic interpolation.

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Changes in PS are also evident for soilhyd, a multiplying factor for soil hydraulic conductivity and diffusivity, fac_rootdp2, an uniform factor for the root depth field, tur_len, defining the maximal turbulent length scale, uc1, used for computing the amount of cloud cover in saturated conditions, and q_crit, representing the critical value for normalized over-saturation. For all other parameters, variations of PS are considerably small or zero.
When investigating how PS depends on each variable (Fig. 4), similar results are obtained for all the parameters. Largest 30 variations in PS are evident, for each of the variables, for e_surf and qi0. Remarkable changes in PS for T2M are also identified for tkhmin. In this case, also c_diff shows significant changes but, as already stated above, the PS seems to be at its maximum for the parameter values lower and higher limits, suggesting that any parameter input in this range will not produce an improvement in temperatures. For PRE, more pronounced variations of PS are also found for d_mom, v0snow and rlam_heat. Finally, for CLCT, considerable changes in PS are also evident for tkhmin, showing an opposite behavior with respect to the one of temperatures. Other parameters are characterized by particularly small variations in the PS calculated for single variables, but 5 these changes are coherent among all the different variables and translate into slightly larger changes in the PS calculated over the three variables together. This is the case of radfac, soilhyd, tur_len, rat_lam, uc1 (Fig. 3). In all other cases, variations of the PS calculated for different variables compensate each other, leading to really small or zero changes in the total PS. In general, it is important to notice that the values of PS are lower for PRE than for the other two variables.
Based on these results, the nine most sensitive model parameters for the region, highlighted in blue in Tab. 3, are identified.  remarkable, making any assumption on parameters selection almost equivalent. Only the parameter d_mom seems to be able to produce small, but positive, improvements with respect to the reference simulation, for all the clusters.
For CLCT, changes in the SS are significant only for a specific sub-set of parameters (Fig. 7). In particular, for qi0, mainly

Considerations on Different Uncertainty Sources
To better understand the role of different uncertainty sources on the calculation of PI, here a more detailed analysis of the 25 considered errors is presented. Fig. 8 shows the values of the different uncertainty terms considered in the calculation of PI.
For T2M and PRE the highest uncertainties are obtained from the observational interannual variability (σ o ), for almost all months and clusters. In the first case the highest uncertainties characterize winter months, especially over Western Siberia (SAR, CSA and DSS, Fig.2) and the Steppe region East of the Caspian Sea (STE, Fig.2). In the second, highest uncertainties are evident for summer months over the monsoon areas (MTT and IMO, Fig.2). Conversely, for CLCT, the largest contribution 30 to the sum of the uncertainties is given by the mean differences in the considered observational data sets (σ ) for all months and regions. it is possible to see that for the calculation of PI, uncertainties have a greater weight for T2M and CLCT than for PRE. This suggests that the lower PS values obtained for PRE are mainly due to particularly large model biases in this case, rather than to uncertainties in the observational datasets. The PS calculated for the considered parameter values for Europe and Central Asia is presented in Fig. 11

Conclusions
In this paper the parameter space of the Regional Climate Model ( The model is particularly sensitive to a sub-set of all the tested parameters. The parameters with the largest effect on model 5 performances are qi0, the cloud ice threshold for autoconversion, and e_surf, the exponent to get the effective surface area.
Another particularly important parameter for the area and all considered variables is rlam_heat, the scaling factor of the laminar boundary layer for heat. In addition to these three, six other most-sensitive parameters are individuated: d_mom, the factor for turbulent momentum dissipation, v0snow, controlling the fall velocity of snow, radfac, which represents the fraction of clouds water/ice used in the radiation scheme, tkhmin, the minimum value for the turbulence heat diffusion coefficient, The same is particularly true also for the parameter e_surf.

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Parameters related to soil and land-surface atmosphere interactions representation, such as rlam_heat and soilhyd, are notably relevant for the simulation of near surface temperature over a large part of the domain sub-regions, in particular over Western Siberia and the area North of the Black Sea. Nevertheless, the same parameters do not have the same influence on the simulation of precipitation and total cloud cover for the majority of the sub-domains. Parameters used in the turbulence parameterization scheme, such as tkhmin, have an important impact on many regions, in particular for near surface temperature 25 and cloud cover, for areas characterized by complex topography and the ones with stable vertical stratification. In the latter case, tkhmin produces opposite results for the considered variables, confirming an already known model structural problem related to the production of excessive mixing over these regions. Among the parameters employed in the radiation processes representation, uc1 shows a strong sensitivity, in particular for total cloud cover, over all the domain sub-regions. Over some sub-regions ( e.g. Turkey and the northern part of Iran ) parameters related to ocean-surface processes, such as rat_sea and 30 c_sea, have a relevant effect on the simulation of precipitation. For some regions, such as Western Siberia, even though changes in model results are possible by perturbing parameter values, they do not seem to be large enough in order to sensibly improve model biases. In this case, the reason for the biases is most likely related to some structural error in the model formulation.
For the calculation of the considered metrics, a larger role is played by the uncertainties in near surface temperature and cloud cover, than the ones in precipitation. For cloud cover, the contribution of the observational uncertainties is larger than the The experiments for each parameter are enumerated in an increasing order, according to its tested values, from the lowest to the highest.  30 https://doi.org/10.5194/gmd-2020-196 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License.  -2020-196 Preprint. Discussion started: 6 July 2020 c Author(s) 2020. CC BY 4.0 License. fac_rootdp2 Uniform factor for the root depth field (0.5,1,1.5)