Assessment of WRF model parameter sensitivity for high-intensity precipitation events during the Indian summer monsoon

Default values for many model parameters in Numerical Weather Prediction models are typically adopted based on theoretical or experimental investigations by scheme designers. Short-range forecasts are substantially affected by the specification of parameters in the Weather Research and Forecasting (WRF) model. The presence of a multitude of parameters and several output variables in the WRF model renders appropriate parameter value identification quite challenging. The objective of the current study is to reduce the uncertainty in the model outcomes through the recognition of parameters that strongly influence the model performance using a Global Sensitivity Analysis (GSA) method. Morris one-step-at-a-time (MOAT), GSA method, is used to identify the sensitivities of 23 chosen tunable parameters corresponding to seven physical parameterization schemes of the WRF model. The sensitivity measures (MOAT mean and standard deviation) are evaluated for eleven output variables, out of which some are surface meteorological variables and the remaining are atmospheric variables, which are simulated by the WRF model with different parameters. Twelve high-intensity four day precipitation events during the Indian summer monsoon (ISM) for the years 2015, 2016, and 2017 over the monsoon core region in India are considered for the study. Six out of 23 parameters have high MOAT mean in the case of almost all the model output variables indicating that these parameters have a considerable effect on the outcome of the simulations. MOAT mean values of a few parameters are noticeably small for all the model output variables, and thus the uncertainty associated with them has a negligible effect on the WRF model performance. The study also presents the physical insights into the trends of the parameter sensitivity.


Introduction
Indian summer monsoon (ISM) or the southwest monsoon is one of the oldest global monsoon phenomena. ISM is irregular and erratic, whose vagaries remarkably affect India both agriculturally and economically Krishna Kumar et al. [1]. Bursting refers to the quirk increase in mean daily rainfall and is a characteristic of ISM. Quintessentially, ISM bursts at the beginning of June and slowly withdraws towards the start of October. Therefore, the ISM rainfall (ISMR) is more often than not referred to as June-September rainfall. ISMR contributes to more than 80 % of the annual rainfall in India [2]. The monsoon core region (MCR; 69 • E to 88 • E and 18 • N to 28 • N) is a critical zone where ISMR plays a crucial role [3] corresponding to mean monsoon and intraseasonal variability. Besides being a conspicuous contributor to the food security and water resources of South Asian region, the ISM rainfall, representing an abundant heat source, has a significant impact on the global climate and general circulation [4,5]. Consequently, accurate predictions of the ISMR over the monsoon core region are critical not only for the water resource management in India but also for a superior seasonal forecast across the globe.
Mesoscale Numerical Weather Prediction (NWP) models are imperative in providing accurate seasonal and long-range predictions of the summer monsoon. Over the years, NWP models are significantly improved with refined temporal and spatial resolution, more precise dynamical methods to represent climate models, ability to simulate largescale systems, and longer lead times in forecasting [6,7,8,9,10,11]. The Advent of Advanced Weather Research and Forecasting (WRF) model, because of its ability to assimilate modules developed separately [12], is a breakthrough in mesoscale modelling.
The uncertainties exhibited by NWP systems such as a WRF model can be due to four primary sources of errors: (i) the determination of initial and lateral boundary conditions, (ii) the representation of physical processes, (iii) the specification of model input variables, and (iv) the computational precision used in the model. All the causes of uncertainties are required to be quantified and reduced for better model performance.
Generally, the initial and lateral boundary conditions for a WRF model are provided by large scale global analyses but with the constraints of low resolution and insufficient depiction of regional mesoscale characteristics. Different data assimilation techniques, which ingest the localized observational data, such as variational and ensemble data assimilation methods are integral to WRF and have been shown to have a considerable effect on the rainfall forecast in India [13,14].
Accurate depiction of all the physical process occurring in the atmosphere is impractical to incorporate in a numerical model even with the state-of-the-art super-computing technology. Therefore, NWP developers use parameterization schemes. WRF provides a plethora of advanced physics parameterization schemes [15] to represent the physical processes (related to the surface layer, cumulus, microphysics, short-wave and long-wave radiation, ocean model, land surface and planetary boundary layer). Any reasonable combination of physics schemes compounds to a different version of the WRF model.
In literature, many studies have explored a different set of schemes for various physical processes like cyclones, severe storms, and semi-arid precipitation [16,17,18,19] over different Indian regions. A few studies have also investigated the best possible physics schemes, with significant improvement in the forecast performance, for the Indian summer monsoon [20,21].
Nonetheless, to obtain reliable seasonal predictions that are close to the truth, refined initial and boundary conditions and the employment of appropriate parameterization schemes alone are not adequate. The appropriate specification of model input variables within the model physics considered plays a pivotal role in the reliability of WRF model simulations. Each parameterization scheme has a vast number of parameters whose default values are fixed based on experimental or abstract investigations by the scheme designers. Some researchers have investigated the different possible parameter sets for various regions using trial and error based techniques [22,23] but the effectiveness of this approach is contingent on the skill of the model observer. Many examined the utility of inverse techniques, a more objective strategy, through parameter adjustment by pruning the objective function to match the simulation results with those of observations. The presence of a vast number of tunable parameters, numerous atmospheric output variables from the simulations and computationally expensive NWP models make suitable parameter specification using conventional inverse routines extremely demanding.
A systematic and mathematically robust approach for parameter uncertainty quantification is required, which identifies the model input variables that have a considerable impact on the model outcome and later enables the adjustment of parameters to obtain the ideal solution. Sensitivity analysis (SA) is the most frequently utilized statistical tool to recognize the most important parameters when there is uncertainty involved. There are various SA studies on uncertainty quantification of parameters which concentrates on parameters of a particular scheme [24,25,26,27]. A few studies comprehensively considered many parameters across various physics schemes [28,29]. But these studies are conducted over small regions. The objective of the present study is to apply the SA methods to parameters corresponding to seven different physics schemes on a larger region (Monsoon core region) when the output variables are evaluated for sensitivities concerning high-intensity precipitation events during the Indian summer monsoon. This paper is organized as follows. Section 2 gives an introduction to the Morris one at a time SA technique. Section 3 gives a detailed description of the parameters, physics schemes, and events considered for the SA. Section 4 lists out the critical results and inferences related to the sensitivity measures.

Sensitivity analysis method
Sensitivity Analysis (SA) is defined as the recalculation of outcomes of the model (numerical or otherwise) under alternative assumptions, owing to the uncertainties in the model inputs, to ascertain the influence of different input variables (i.e., parameters). SA finds its application, among the other things, in robustness evaluation, uncertainty reduction, error search, and model simplification. However, the prime focus of the present study is to identify the model input variables that cause substantial uncertainty in the model outcome, which then can be further researched for improved robustness of the model. nonlinear or involves interactions with other model input variables [31].
Before applying the MOAT method, all the ranges of k number of parameters have to be mapped to the parent domain [0,1]. One way of doing this is by obtaining the cumulative distribution function (CDF) for the given parameter distribution, as CDF is bounded by 0 and 1 and is also uniformly distributed over [0,1]. When the parameter distribution itself is uniform, CDF will be a linear mapping from the parameter domain to the parent domain. Then the parent domain corresponding to each parameter is divided into p equally spaced intervals. This process creates an input space Ω with a k dimensional unit cube discretized into p selected levels along each dimension. An initial parameter set or a base value The elementary effect or the gradient corresponding to the i th parameter, when x l and x l+1 of j th trajectory differ by ∆ l in their i th component is where y(x) is the objective function, an output variable in the context of a WRF model.
The elementary effect represents the effect on the model objective function y(x) due to the ∆ l change in the i th parameter. When all the r elementary effects corresponding to the i th parameter are computed, the sensitivity measures µ i and σ i can be calculated.   Short-wave radiation Dudhia scheme [39] Long-wave radiation RRTM scheme [40] Land surface Noah land surface model scheme [41] Planetary boundary layer Yonsei University (YSU) scheme [42] [35], where a sensitivity of physical parameterization schemes concerning the Indian summer monsoon was performed and the best set of schemes was proposed. The microphysics scheme alone was chosen differently from that set as WSM6 scheme represents more categories of hydrometeors compared to the WSM3 scheme. The schemes used in this study are shown in Table 1.
A set of 23 tunable parameters from the physics parameterization schemes in Table   1 are used for analysis in this study, similar to [29]. By no means is this set exhaustive; nonetheless, the present parametric study can be considered as a precursor for further investigation of the sensitivity of other potential parameters for ISM. The overall list of parameters and their allowable ranges of variations are presented in Table 2.
where MOAT sensitivity plots for the output variable precipitation are shown in Figure 3. MOAT standard deviation, respectively. It is observed that P4 has the highest MOAT mean value for all the days, which implies that this parameter influences precipitation the most, and P13 has the least MOAT mean and thus has no influence on the precipitation. Out of all the remaining parameters P8, P5, P3, and P16 have higher MOAT mean values compared to others which indicate that the precipitation is more sensitive to these parameters.  Similar sensitivity plots are generated for other surface meteorological variables represented in Figure 4. Figures 4(a) Sensitivity plots are also obtained for atmospheric variables represented in Figure 5.   The spatial patterns of the daily average of output variables PR, SAP, SAT and WS10 over 48 days (12 four-day events) for the optimum parameter (minimum RMSE out of 240) set and the default parameter set are compared against the observed data and is shown in Figures 8-11. It can be seen that the output variables from the optimum parameter

Conclusions
The current study evaluated the sensitivity of eleven WRF model output variables and identified those parameters which have a higher influence on these outputs. Those parameters which have a very minimal effect on the model outcome are also vetted out in this process. The parametric study considered a total of 23 parameters corresponding to seven different physics schemes for the sensitivity analysis. Morris one at a time method, which is a global sensitivity analysis method, is utilized for the present parametric study. to which the output variables may be more sensitive compared to the selected parameters.
Additionally, the sensitivity to the parameters in this study is obtained over the monsoon core region. The sensitivity of the output variables to the parameters may not remain the same for other areas of interest. The present parametric study can be considered as a precursor for further investigation of the sensitivities of other potential parameters for the Indian summer monsoon. Further, optimization of the sensitive parameters to accurately simulate the output variables can be done using advanced optimization techniques.