Sensitivity study of planetary boundary layer scheme in numerical simulation of western disturbances over Northern India
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Abstract
A numerical weather forecasting model (WRF-ARW) is used to simulate the weather during western disturbances over India. The horizontal resolution of the model is 27 km, and the model covers a region extending from 40°E to 105°E and 10°N to 48°N. The Asymmetric Convective Model, version 2 (ACM2) scheme is used to parameterize planetary boundary layer in the simulations. This scheme uses several parameters which are hidden or implicit from the model users. Literature shows that a particular parameter ‘p’ used in this scheme to prescribe the vertical profile of eddy exchange coefficient has significant impact on mixing within the planetary boundary layer. Thus, the default value of ‘p’ may not be the most appropriate choice for all types of atmospheric conditions. In the present study, attempt has been made to study the effect of ‘p’ on the parameters like potential temperature and relative humidity within planetary boundary layer and also to prescribe an appropriate value of ‘p’ for the region under study. Our study reveals that the WRF-ARW model embedded with PBL parameterization (ACM2) is capable of more appropriately simulating the potential temperature and relative humidity by using ‘p’ value of 1.25 to prescribe the vertical profile of eddy exchange coefficient within the boundary layer especially during the daytime when the system is dominated by convective-scale eddies at least for the chosen domain and period of study.
Keywords
Numerical simulation Planetary boundary layer Parameterization scheme Western disturbance1 Introduction
Planetary boundary layer (PBL) is the lowermost portion of the atmosphere roughly constituting 1–3 km of the lower troposphere region and is characterized by friction and vertical mixing [1, 2]. Hydrometeorological process and dispersion of pollutants occurring within this PBL region are strongly dependent on the turbulent vertical mixing, and thus a good representation of vertical mixing in the planetary boundary layer (PBL) is important for modeling of meteorological and air quality phenomena. In numerical mesoscale modeling, it is vital to account for the subgrid-scale processes occurring within the confine of model grid for improving the model performance when the processes are not explicitly resolved in the model at coarser resolution. Since the scale of turbulent mixing is relatively smaller than the model resolution, the overall impact due to turbulent forcing on grid-scale variables of meteorology and air pollution is expressed through PBL parameterizations in numerical models. During the past few decades, various turbulent vertical mixing schemes for use in the PBL were developed and tested in 1D and 3D simulations in both meteorological and air quality modeling-related studies. These vertical mixing schemes can be local schemes or K-schemes [3, 4, 5, 6], non-local vertical mixing schemes [7, 8, 9, 10] or may be combination of local and non-local schemes [11]. Studies conducted by most of these schemes [12, 13] infer that modeling is sensitive to the vertical mixing scheme and appropriate apportion of flux between local and non-local component is crucial in representing mixing occurring within the PBL. The turbulence mixing can occur in a wide range of scale starting from subgrid scale to a scale as high as to the depth of the convective boundary layer. Performance of these PBL schemes in numerical weather prediction models varies with respect to the physics options, geography of the study region and time of the year [14, 15, 16, 17]. Therefore, careful examination of these schemes for a chosen domain is crucial to not only weather prediction and research, but also for air quality studies and other environmental investigations [18]. Atmospheric boundary layer representation during convective condition of atmosphere has long been a quest area in numerical simulation of meteorological processes and air quality prediction [10]. The subgrid-scale processes, viz. mixing of heat, momentum and moisture, occurring in the atmospheric boundary layer primarily take place through convective and mechanical forcing of the earth surface due to differential heating and cooling during the daytime and nighttime, respectively. Sensitivity experiments with different local (e.g., K-theory in Stull [1]) and non-local PBL schemes show that complex phenomenon occurring within the boundary layer is likely to affect the vertical mixing within the PBL and evolution of PBL parameters which ultimately influence the air quality dispersion of the region [19, 20, 21]. Performance of near-surface PBL structure variation is more influenced by the surface layer formulation, whereas the upper profile of PBL is more influenced by mixing algorithms of parameterization schemes [22]. Results also indicate that there is a large variation in the mixing layer height estimated by the model using different combinations of surface and PBL schemes [23]. All the above studies show that appropriate representation of vertical mixing occurring within the confine of planetary boundary layer is thus one of the important components which needs our keen attention for meteorological and air quality modeling under different conditions of atmosphere and geography. Moreover, uncertainty associated with the PBL schemes remains one of the key sources of inaccuracy in model simulations [12, 24]. Inadequate parameterizations of physical processes or faulty parameter estimation cannot be justified by merely optimizing the initial and boundary condition [25]. Data assimilation techniques enable us to improve the accuracy of parameterizations in PBL schemes by estimating the most appropriate value of the model parameter. Parameter estimation using variational data assimilation method and ensemble Kalman filter are robust approaches to deal with model error associated with incorrect parameter value in PBL scheme [26, 27, 28]. It is also appropriate to say that parameterization of subgrid-scale meteorological process often ends up with range of a model parameter values which need to be optimized for the chosen domain of study. Therefore, parameters optimized for specific purpose within a PBL scheme are not essentially confined to the constant values assigned in the parameterization formulation under different spatial and temporal domains. Hence, it is also important to optimize the parameter values intended for parameter estimation over specific temporal and spatial domains. A numerical weather forecasting model like WRF-ARW offers several options of parameterization schemes for different physical processes. Routinely Planetary Boundary Layer (PBL) schemes are appropriately used to parameterize the vertical turbulent fluxes of heat, momentum and moisture within the planetary boundary layer as well as in free atmosphere. Within these PBL schemes, there are many less known hidden or implicit parameters which govern the mixing within the boundary layer. Each parameterization scheme contains several parameters which can vary over a range of values, and the choice of a value of parameter may depend on the geographical and meteorological conditions. One of such parameter in ACM2 [11, 24] scheme is ‘p’ which appears in the model equation to express the eddy exchange coefficient K_{z} in non-local closure scheme. This parameter is believed to govern the local mixing profile within the unstable portion of the boundary layer. It determines the maximum value of K_{z} and the height at which K_{z} will be maximum. Study carried out by Nielsen-Gammon et al. [25] also states that among all the parameters, ‘p’ has maximum impact on the vertical mixing in the boundary layer during the daytime. Thus, sensitivity study with a suitable choice of implicit or less known parameters in the boundary layer parameterization schemes is crucial for accurate simulation of extreme weather conditions, especially when the system is dominated by convective-scale eddies. However, it is also appropriate to admit that performance of different meteorological variables in numerical model also depends on combination of different physical processes like cumulus convection, cloud microphysics and definition of model initial state in the simulation of low temperature, strong wind and heavy precipitation [29]. In order to evaluate the dependency, sensitivity experiments need to be carried out to determine the most appropriate value of ‘p’ for the region of study. Thus, the objective of the present study is to accurately simulate the meteorological variables such as potential temperature and relative humidity by modifying these parameters in the boundary layer parameterization scheme suitable for the chosen region of study.
Subgrid-scale turbulent fluxes of heat, momentum and moisture within the planetary boundary layer are expressed in terms of mean quantities and their gradients with the help of turbulent closure method in the PBL scheme. A local closure scheme is more appropriate in a stable atmosphere than in an atmospheric condition where the turbulent fluxes are dominated by large eddies. Since an extreme weather event like western disturbance is characterized by large-scale advective and convective types of phenomena, the local closure schemes will produce insufficient mixing. Thus, in contrast, a non-local scheme will be more appropriate to use the profile of eddy diffusivity and incorporates the non-local effect of transport by the large eddies in the model. Besides, the counter-gradient fluxes are also taken into consideration by the non-local approach. It is also considered to be more robust numerically as stability oscillations do not affect it considerably [30].
This paper is organized as follows. Section 2 provides a description of the model, and Sect. 3 provides the configuration of the simulations. In Sect. 4, the results are presented, mainly focusing on the comparison of the simulation results with observations or analyses. Section 5 formulates the conclusions.
2 Model description
Overview of the ARW model configuration used for the present study
Number of domains | 2 |
Horizontal grid distances | 27 km, 9 km |
Integration time step | Adaptive |
Number of grid points | X-direction—231 points (40°E to 105°E) |
Y-direction—160 points (10°N to 48°N) | |
Vertical coordinate | Terrain-following hydrostatic-pressure coordinate (38 level) |
η values at the model levels are: 1, 0.99734, 0.99165, 0.98522, 0.97793, 0.96973, 0.96049, 0.95012, 0.93849, 0.92552, 0.91106, 0.89506, 0.87739, 0.85797, 0.83674, 0.81366, 0.78872, 0.76194, 0.73339, 0.70319, 0.67148, 0.63846, 0.60438, 0.56950, 0.53415, 0.49863, 0.39437, 0.29953, 0.21939, 0.15579, 0.10778, 0.07289, 0.04823, 0.03115, 0.01948, 0.01157, 0.00625, 0 | |
Model top | 10 mb |
Microphysics | Lin et al. [39] scheme |
Cumulus parameterization schemes | Kain–Fritsch scheme |
Radiation scheme (long wave) | RRTM scheme |
Radiation scheme (short wave) | Dudhia’s short-wave radiation |
Surface layer physics | Monin–Obukhov scheme |
PBL parameterization | ACM2 scheme |
Time integration | Runge–Kutta second- and third-order time integration scheme |
Spatial differencing scheme | Second- and sixth-order differencing scheme |
Map projection | Mercator |
Initial and boundary conditions | Three-dimensional real-data (FNL: 1° × 1°) |
3 Methodology
Dates of the WD cases simulated in the present study
Case | Date of event |
---|---|
1 | January 11, 2007 |
2 | December 12, 2007 |
3 | January 15, 2007 |
4 | January 02, 2006 |
5 | February 04, 2005 |
6 | January 01, 2005 |
7 | December 8, 2008 |
8 | December 17, 2008 |
9 | December 9, 2009 |
A coarse horizontal grid of size 27 km cannot resolve subgrid-level phenomena; thus, parameterization schemes are required to represent the subgrid-scale processes. In the present case, cumulus parameterization is necessary to take care of latent heat release on a realistic timescale in the convective column. The modified version of the Kain–Fritsch scheme [37] has been chosen as the cumulus parameterization scheme in the WRF-ARW model system. It uses a simple cloud model with moist updrafts and downdrafts, which include the effects of detrainment, entrainment and relatively simple microphysics. This modified version of the Kain–Fritsch scheme is different from the original KF scheme [38] in many ways which is briefly described in the technical note of ARW version 3.
Lin et al. [39] scheme has been chosen as cloud microphysics scheme for this study. It has been taken from Purdue cloud model. The Lin et al. scheme includes six classes of hydrometeors. These hydrometeors are water vapor, cloud water, rain, cloud ice, snow and graupel. It uses the bulk water microphysical parameterization technique to represent the precipitation fields which follow exponential size distribution functions. The detailed description of this scheme is available in Chen and Sun [40].
For the present investigation, the asymmetric convective model, version 2 (ACM2) scheme has been used as planetary boundary layer parameterization scheme to simulate various cases of western disturbances in WRF-ARW model. ACM2 can better represent the shape of the vertical profiles of model variables, especially the gradually decreasing gradient near the surface. ACM2 has been chosen for our experiments as comparatively lower bias was reported in the sensitivity experiments than other non-local PBL schemes [12]. This PBL parameterization scheme has been included in WRF-ARW model very recently. ACM2 is a non-local model and it considers the non-local fluxes explicitly through a transilient term [9]. This scheme contains several parameters which can vary over a range of values, and the choice of a value of a parameter may depend on the geographical and meteorological circumstances.
In ACM2 scheme, a weighting factor f_{conv} controls the mixing due to local diffusion and non-local transport. f_{conv} = 0 corresponds to fully local mixing and f_{conv} = 1 corresponds to fully non-local mixing. For stable and neutral conditions, the portion of mixing due to non-local transport becomes zero and this scheme handles vertical mixing by pure local eddy diffusion component.
From Eq. 2, it can be seen that there are many parameters that affect the vertical mixing in this scheme. Values of these parameters used in this scheme are kept hidden from WRF-ARW model users. Different roles played by these parameters and their plausible values are tabulated in Nielsen-Gammon et al. [25]. The detailed investigation of Nielsen-Gammon et al. [25] reveals that among the ten parameters, ‘p’ plays the most important role in governing the vertical mixing in the daytime. This parameter (p) determines the value of the local eddy vertical mixing coefficient within the convective PBL, with larger p leading to smaller vertical mixing.
Selection of most appropriate value of hidden parameter ‘p’ through sensitivity experiments is important as ‘p’ influences the vertical mixing mostly within the PBL. The present study aims at finding out the impact of the variation of p values on boundary layer during WDs and the most appropriate value of ‘p’ for simulation of western disturbance over the region of study. Two variables that are mostly affected by the variation of vertical mixing are potential temperature (θ) and relative humidity (RH). The resultant effect due to change of ‘p’ values will be studied on them. Since the vertical profile form of K_{z} is applicable in the daytime boundary layer, the behavior of potential temperature (θ) and relative humidity (RH) profile within daytime boundary layer will be discussed. Thus, model outputs are taken at 00, 06, 12 and 18 UTC and the θ and RH profiles at 06 UTC are expected to be influenced most by the variation of p values. In the present study, six values of ‘p’ between 1 and 3 were chosen. These values are 1.25, 1.50, 1.75, 2.0, 2.50 and 2.75.
4 Results and discussion
4.1 Impact of ‘p’ values on potential temperature profile
In majority of the cases, the potential temperature profile for p = 1.25 shows closer proximity to the analysis profile within the lowest kilometer of the atmosphere. This reveals that modified formulation of ACM2 with p = 1.25 is capable of producing adequate mixing of heat flux in the morning neutral condition of lower boundary of the PBL during severe weather phenomenon of WD.
4.2 Impact of ‘p’ values on relative humidity profile
4.3 Root-mean-square errors of potential temperature and relative humidity
5 Conclusion
In the above study, we have presented the results of numerical meteorological simulation for greater area of Northern India at a spatial resolution of 27 km. Sensitivity experiments have been carried out to assess whether WRF-ARW model embedded with ACM2 PBL scheme is capable of correctly reproducing observed meteorological quantities at different values of model hidden parameter ‘p’. To demonstrate this, model-simulated potential temperature and relative humidity profiles over Delhi at 06:00 UTC were compared with analysis data and RMSEs were computed. The comparison shows that p = 1.25 scores better than other values of ‘p’ for both potential temperature and relative humidity. As a result, we believe that our approach with ‘p’ value of 1.25 in the model code is more promising in defining the vertical profile of the PBL especially when one is interested to simulate extreme weather events like WD dominated by convective phenomenon at least for the period and domain under study.
Notes
Acknowledgements
This project was supported by Department of Science and Technology (DST), Ministry of Science and Technology, Government of India (SR/S4/AS:99/2012). We sincerely thank DST for kindly supporting this project. We are thankful to the principal and the director, Jaipur Engineering College of Research Centre, for providing logistics as well as infrastructural facilities. We are also thankful to the director, National Centre for Medium Range Weather Forecasting, for allowing this project to complete and providing necessary support. We would like to thank India Meteorological Department, New Delhi. We thank National Center for Atmospheric Research (NCAR) for making WRF model and the input data freely available. These have been used to study various western disturbance cases.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
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