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PUBLICATIONS Journal of Geophysical Research: Atmospheres RESEARCH ARTICLE 10.1002/2014JD022195 Key Points: • The main challenges for extended-range mesoscale simulations are identified • Controlling large-scale atmospheric deviations improves surface layer outputs • Further improvements are possible by correcting the prognostic surface fields

Correspondence to: S. Z. Husain, [email protected]

Citation: Husain, S. Z., L. Separovic, W. Yu, and D. Fernig (2014), Extended-range high-resolution dynamical downscaling over a continental-scale spatial domain with atmospheric and surface nudging, J. Geophys. Res. Atmos., 119, 13,720–13,750, doi:10.1002/ 2014JD022195. Received 20 JUN 2014 Accepted 21 NOV 2014 Accepted article online 26 NOV 2014 Published online 19 DEC 2014

Extended-range high-resolution dynamical downscaling over a continental-scale spatial domain with atmospheric and surface nudging S. Z. Husain1, L. Separovic1, W. Yu1, and D. Fernig1 1

Atmospheric Numerical Prediction Research Section, Meteorological Research Division, Environment Canada, Dorval, Quebec, Canada

Abstract Extended-range high-resolution mesoscale simulations with limited-area atmospheric models when applied to downscale regional analysis fields over large spatial domains can provide valuable information for many applications including the weather-dependent renewable energy industry. Long-term simulations over a continental-scale spatial domain, however, require mechanisms to control the large-scale deviations in the high-resolution simulated fields from the coarse-resolution driving fields. As enforcement of the lateral boundary conditions is insufficient to restrict such deviations, large scales in the simulated high-resolution meteorological fields are therefore spectrally nudged toward the driving fields. Different spectral nudging approaches, including the appropriate nudging length scales as well as the vertical profiles and temporal relaxations for nudging, have been investigated to propose an optimal nudging strategy. Impacts of time-varying nudging and generation of hourly analysis estimates are explored to circumvent problems arising from the coarse temporal resolution of the regional analysis fields. Although controlling the evolution of the atmospheric large scales generally improves the outputs of high-resolution mesoscale simulations within the surface layer, the prognostically evolving surface fields can nevertheless deviate from their expected values leading to significant inaccuracies in the predicted surface layer meteorology. A forcing strategy based on grid nudging of the different surface fields, including surface temperature, soil moisture, and snow conditions, toward their expected values obtained from a high-resolution offline surface scheme is therefore proposed to limit any considerable deviation. Finally, wind speed and temperature at wind turbine hub height predicted by different spectrally nudged extended-range simulations are compared against observations to demonstrate possible improvements achievable using higher spatiotemporal resolution.

1. Introduction

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. Reproduced with the permission of the Minister of Environment.

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Meteorological fields with high spatial and temporal resolution available over extended time periods, ranging from months to years, are of tremendous interest to weather-dependent energy industries, particularly the wind and solar power sectors. Due to the large spatiotemporal variability in power available from these renewable resources, and with their ever increasing penetration into the energy mix around the world, it is necessary to evaluate the capabilities of the existing power grid infrastructures to cope with the fluctuating power generation. For example, the Canadian Wind Energy Association (CanWEA) has commissioned a Pan-Canadian Wind Integration Study [Tremblay et al., 2010] with a target to generate 20% of Canada’s electricity by 2025 from wind energy. In order to achieve the ambitious target, CanWEA needs access to multiyear surface layer wind and other meteorological data, with 2 km horizontal grid spacing and 10 min time resolution, over all of Canada. The data will be used to analyze time series of the relevant meteorological fields for devising a viable strategy for such a large-scale integration of wind energy within the Canadian power grids. Generating the required meteorological data for CanWEA has been the motivation for the present study. High-resolution meteorological fields can be generated by downscaling coarse-resolution global or regional model outputs by applying dynamical, statistical, or mixed statistical-dynamical methods. In the case of dynamic downscaling, outputs of a coarse-resolution simulation are used to drive higher-resolution atmospheric simulations over a limited area to add and improve small-scale information in the meteorological fields through better resolution of various dynamical and physical atmospheric processes ©2014. Environment Canada. American Geophysical Union.

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[Hong and Kanamitsu, 2014; Castro et al., 2005; Rockel et al., 2008]. Statistical downscaling, on the other hand, uses statistical equations, usually based on regression and neural network techniques, to convert coarse-resolution atmospheric fields from global climate or atmospheric models to higher-resolution fields over limited areas [Wilby et al., 2004; Busuioc et al., 2008; Cheng et al., 2014]. Statistical downscaling can improve model bias without significant computational effort although large error may appear in day-to-day or hour-to-hour outputs as the emphasis is generally more on long-term climate statistics. These methods can suffer from loss of spatiotemporal coherence within the downscaled fields [Kumar et al., 2012] and are also limited to regions with access to historical observations at meteorological stations. The mixed statistical-dynamical downscaling works by first dynamically downscaling some predefined large-scale weather patterns embedded within the coarse-resolution model outputs. The mean values of the downscaled variables are then obtained through a weighted average of mesoscale model-simulated values of each weather type and their corresponding occurrence frequencies. This approach, although computationally cheaper compared to the direct dynamical downscaling, usually provides only the mean value of the downscaled variables without additional information regarding their temporal evolution [Frey-Buness et al., 1995; Yu et al., 2006]. Martinez et al. [2013] proposed an empirical orthogonal function-based statistical-dynamical downscaling method which is capable of time series generation. The temporal sampling frequency of this method is nevertheless dictated by the temporal frequency of coarse-resolution forcing fields. Although dynamical downscaling, compared to the other options, is computationally more expensive, it, in general, provides the greatest improvement in the spatiotemporal distributions of the downscaled meteorological fields [Gutman et al., 2012; Yoon et al., 2012]. The majority of the applications of extended-range dynamical downscaling available in the literature is presented in the context of downscaling in regional climate models that typically involve coarse spatial resolution [von Storch et al., 2000; Castro et al., 2005; Rockel et al., 2008; Yoon et al., 2012]. Moreover, in the case of regional climate models (RCMs), rather than focusing on a skillful representation of instantaneous meteorological patterns, more emphasis is placed on the statistical similarity between the downscaled fields and the pertinent observations. In contrast, dynamical downscaling involving mesoscale simulations, as pursued in the present study, demands high temporal correlations between the model outputs and the observations for all scales. Nevertheless, the fundamental conclusions of the studies on RCMs are extendable and applicable to mesoscale simulations with limited-area versions/configurations of the forecast models. Large-scale atmospheric features in the meteorological fields simulated with limited-area models are susceptible to deviations from the generally coarse resolution driving fields over time, particularly for large continental-scale spatial domains [Leduc and Laprise, 2009]. As energy from the larger scales is transferred to the smaller scales through the energy cascade, any deviations in the large-scale structures of the simulated atmospheric fields can lead to inaccurate development of the small-scale structures [Denis et al., 2002b]. Discrepancies in the small scales may be particularly exacerbated within the surface layer, where surface-induced small-scale responses in the atmosphere are the most dominant. This poses scientific challenges that must be addressed when mesoscale simulations are applied for dynamical downscaling over an extended time period. In order to minimize the impact of large-scale deviations associated with a large spatial domain over extended-range simulations, the problem may be separated into multiple periods of sufficiently short time frames. Construction of a final continuous time series of any meteorological variable in this approach will need to address two challenges. First, the model outputs at the end of one time frame will have differences with the initial conditions for the following period obtained from regional (or global) analysis, primarily due to loss of model skills with temporal integrations. The final time series after merging different time periods is therefore likely to suffer from large fluctuations unless some sophisticated temporal blending scheme is implemented. Second, the analyzed initial conditions may often lack information regarding some atmospheric fields that require some temporal spin-up for proper development. For example, the regional analysis files from the Meteorological Service of Canada (MSC) do not include information regarding clouds. As a result, individual simulations covering the smaller time frames, when initialized with MSC’s regional analysis, would require spin-up times for development of clouds. This implies that the meteorological fields for the first few hours of such simulations must be discarded during temporal blending in order to avoid loss of accuracy, resulting in a substantial increase in computational cost as well as possible temporal discontinuities [Lucas-Picher et al., 2013].

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Dividing the problem into multiple mesoscale simulations over smaller domains each running for extended time periods (from weeks to months) followed by spatial blending of the end results can be considered as an alternate approach for dynamical downscaling [Potter et al., 2008]. Although sufficiently small spatial domains can help in addressing large-scale deviations [Diaconescu and Laprise, 2013], this approach is likely to result in spatial discontinuities in the meteorological fields, particularly along the lateral boundaries of the smaller domains that may require special treatments when spatial blending is performed to obtain spatially continuous meteorological fields [Potter et al., 2008]. Furthermore, in the context of regional climate modeling, Leduc and Laprise [2009] have demonstrated that the nested simulation domains need to be sufficiently large for proper development of small scales as large-scale information embedded in the driving fields needs to travel an adequate distance from the lateral boundaries to achieve full spin-up of small scales. In other words, flow from the lateral boundaries may pass through a small domain without permitting adequate time to achieve the complete development of small scales. The model outputs for small domains can also be deficient in small-scale variance, particularly at higher altitudes [Laprise et al., 2008]. Based on the aforementioned adverse implications associated with temporal and spatial blending, a continuous temporal integration over the entire spatial domain appears to be the most suitable approach, provided a mechanism is put in place to restrict large-scale deviations in the simulated fields. Large-scale atmospheric deviations may be controlled by nudging the model outputs to the driving fields. Nudging can be performed in the spectral space for a range of wave numbers or in the physical space over individual model grid cells, leading to approaches that are generally referred to as spectral and grid nudging, respectively [Waldron et al., 1996; von Storch et al., 2000; Liu et al., 2012]. Although grid nudging is computationally cheaper and relatively simpler to implement, spectral nudging allows far better control over the scales to be nudged [Liu et al., 2012]. Spectral nudging schemes can be tuned to reliably retain the large scale from the driving fields without suppressing the development of small-scale features [von Storch et al., 2000; Liu et al., 2012]. The relative advantages of spectral nudging thus make it a clear favorite for controlling the atmospheric fields in extended-range mesoscale simulations. Mesoscale downscaling for generating high-resolution meteorological fields requires minimization of model error within the surface layer, where most human activities take place and where the added spatial resolution is expected to have the greatest impact. Land surface parameterization schemes associated with mesoscale models usually resolve prognostic equations for various surface fields (e.g., soil moisture, surface temperature, and snow conditions) to produce the surface boundary conditions. In the case of extended-range simulations, these surface fields may deviate from their expected values due to the accumulation of error, primarily attributable to inherent model biases. Such error accumulation can be controlled by continuous readjustments of the surface fields using reference surface data from MSC’s regional analysis or generated by a high-resolution offline surface scheme. The present study explores the various strategies to control the large-scale atmospheric deviations and to limit any error accumulation in the prognostically evolving surface fields in order to propose an optimal approach for high-resolution dynamical downscaling with mesoscale models over an extended period. Section 2 presents the atmospheric model used for mesoscale simulations, the basic simulation strategy along with the general schemes applied for controlling deviations of the atmosphere and the surface. Section 3 presents the results of the investigations carried out in this study regarding the sensitivities of the upper atmosphere and surface layer meteorology to the different configurations of the nudging schemes to determine an optimal nudging strategy. Finally, outcomes of the present research are summarized in section 4.

2. Methodology 2.1. Atmospheric Model and Simulation Strategy The mesoscale simulations are carried out using the limited-area configuration of the Global Environmental Multiscale (GEM) atmospheric model (GEM-LAM hereafter) [Yeh et al., 2002; Zadra et al., 2008]. The current implementation of GEM uses a terrain following hybrid vertical coordinate and a staggered Charney-Phillips vertical grid structure [Girard et al., 2014] where wind speed is expressed at the momentum levels, while temperature and moisture are expressed at the thermal levels located midway between adjacent momentum levels.

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Figure 1. (a) Simulation domain for the 15 km (outer solid black rectangle) and 2 km (inner red dashed rectangle) GEM-LAM configurations. (b) The distribution of observation stations over different Canadian regions (BC: orange circles, Prairies: green circles, QC-ON: red circles, Maritimes: cyan circles, and the North: blue circles).

In general, the GEM model works by first solving a set of dynamical equations directly on the model grid. Physical processes including atmospheric radiation, fluxes from different land surface components, boundary layer turbulent mixing as well as clouds and precipitation are not directly resolved at the grid scale. These subgrid-scale processes are accounted for in the model by supplementing the solutions of the dynamical equations with parameterized tendencies associated with the pertinent physical processes. The basic simulation follows a two-stage strategy. First, the MSC’s regional analysis fields, available every 6 h (0000, 0600, 1200, and 1800 UTC, where UTC denotes the coordinated universal time), are used to initialize and drive a GEM-LAM simulation involving 15 km horizontal grid spacing. The purpose of the 15 km GEM-LAM (LAM-15 hereafter) simulation is to produce three-dimensional meteorological fields with large-scale features closely resembling those embedded in the driving analysis fields but available more frequently (every 20 min) to force the second-stage 2 km GEM-LAM (LAM-2 hereafter) simulation. The LAM-2 simulation thereby produces the final desired outputs. The domains for LAM-15 and LAM-2 simulations are illustrated in Figure 1a. It should be noted that the LAM-15 and LAM-2 simulation domains have 480 × 300 and 3000 × 1800 grid cells, respectively. Both the LAM-15 and LAM-2 simulation domains have the same grid rotation and employ 60 vertical levels with the upper and lowermost momentum levels at 10 hPa and 10 m agl (above ground level), respectively. Different physical parameterizations employed for the two simulations are presented in Table 1. Furthermore, sea surface temperature and sea ice fraction are continuously updated during the simulations using their values from regional analysis during both LAM-15 and LAM-2 simulations. It has been discussed earlier that mesoscale simulations conducted over an extended period may develop deviations in large scales, particularly in the case of large spatial domains. Such deviations are controlled in this study by nudging the large scales in the simulated fields to those in the driving fields in the spectral space. Erroneous fluxes of heat and moisture from the surface due to deviations in the prognostic surface fields over extended-range temporal integrations may lead to inaccurate surface layer predictions by the model. Deviations of surface fields from their expected values are controlled by readjusting the fields in accordance with more accurate reference values. Further details on the mechanism developed during the

Table 1. List of Various Physical Processes and Corresponding Parameterizations Physical Process Radiation Land surface Deep convection Shallow convection Mixing length Boundary layer turbulence Condensation

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Parameterization Scheme CCCMARAD [Li and Barker, 2005] ISBA [Noilhan and Planton, 1989; Bélair et al., 2003] Kain and Fritsch [1990] (Only for 15 km simulations) Kuo transient [Kuo, 1965; Bélair et al., 2005] Blackadar [1957] Benoit et al. [1989] Sundqvist et al. [1989]

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current study to control large-scale atmospheric deviations and accumulation of error in the surface fields are presented in sections 2.2 and 2.3, respectively. 2.2. Controlling Atmospheric Deviations Denis et al. [2002a] have shown that two-dimensional discrete cosine transform (2-D DCT) is more advantageous compared to the direct application of discrete Fourier transform to express any aperiodic two-dimensional meteorological field in the spectral space. When applied for spectral filtering, 2-D DCT permits reliable scale selection and largely avoids Gibbs phenomenon due to aperiodic lateral boundaries. Based on the conclusions drawn by Denis et al. [2002a], the 2-D DCT is selected in this study to compute the spectra of the meteorological fields of interest and to apply spectral filter on those fields. A meteorological field, Ψ(i,j), at a given model vertical level and over a grid size of (Ni × Nj) can be expressed using 2-D DCT as follows: Ψði; j Þ ¼

m¼N j 1 Xi 1 n¼N X m¼0

Ai ðmÞAj ðnÞ F ðm; nÞ cos½πmði þ 1=2Þ=Ni cos πnðj þ 1=2Þ=Nj ;

(1)

n¼0

where i = {0,1,…,Ni 1} and j = {0,1,…,Nj 1}. The coefficients F(m,n) in equation (1) denote the 2-D DCT of Ψ(i,j) which is defined as F ðm; nÞ ¼ Ai ðmÞAj ðnÞ

i¼N j 1 i 1 j¼N X X i¼0

Ψði; j Þ cos½πmði þ 1=2Þ=Ni cos πnðj þ 1=2Þ=Nj ;

(2)

j¼0

where the coefficients Ai(m) and Aj(n), to ensure orthonormal transform [Denis et al., 2002a], have the forms sffiffiffiffiffi rffiffiffiffiffiffi δm δn ; Aj ðnÞ ¼ ; (3) Ai ðmÞ ¼ Ni Nj with δ0 = 1 and δn = 2 for n > 0. The wavelengths that can be represented by a rectangular (Ni × Nj) domain with a horizontal grid spacing of Δ in the case of DCT are generally given by λ¼ where λ denotes the wavelength and α ¼

2Δ ; α

(4)

qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 m2 þ Nn 2 is the normalized two-dimensional wave number. The N2 i

j

factor 2 in equation (4) is attributable to the fact that the DCT domain includes a mirror reflection of the actual domain, and hence, the largest resolvable wavelength is twice the size of the domain [Denis et al., 2002a]. The objective of expressing Ψ(i,j) in the spectral space is to develop a spectral filter that will permit filtering out all scales smaller than a cutoff wavelength λC. It is, however, important to apply a soft cutoff of scales such that all scales corresponding to λ > λL are retained and the scales with λ < λS are eliminated while scales with λS < λ < λL are subjected to gradual cutoff. This helps to minimize Gibbs phenomena that may otherwise result from any abrupt cutoff of scales [Sardeshmukh and Hoskins, 1984]. Determination of suitable values of λS and λL (where λS < λC < λL) depends on spectral analyses of the fields of interest. Once the Fourier coefficients F(m,n) are known, a spectrally filtered field, ΨF(i,j), can be obtained by applying the inverse DCT defined by equation (1) on the filtered transform, FF(m,n), which is evaluated as F F ðm; nÞ ¼ F ðm; nÞ f F ðm; nÞ where fF(m,n) is the spectral filter. The general form of fF(m,n) as used in the present study is 8 0:0 if α^ ≥ Δ=λS > > > α^ ≥ Δ=λL ; > 2 λL =λS 1 > > : 1:0 if α^ < Δ=λL

(5)

(6)

where α^ ¼ Δ=λ is the 2-D wave number over the actual domain which is half the size of the domain over which DCT is applied.

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Finally, large-scale deviations in any simulated meteorological field, Ψ, at a given model vertical level at the end of each model time step may be controlled as Ψ′M ¼ ΨM þ

β ðζ Þ ½Ψ D Ψ M L τ ðt Þ

(7)

where Ψ′M is the simulated field obtained after nudging correction. Furthermore, in equation (7) the subscripts M and D stand for model and driving fields, respectively, β(ζ ) is the vertical profile of nudging with ζ being the hybrid vertical coordinate in GEM [Girard et al., 2014], and τ(t) denotes the temporal relaxation factor which is a function of time t. The index L in equation (7) represents the spatial scale of interest, and the quantity [ΨD ΨM]L is determined following the steps described by equations (5) and (6) for a particular set of values of λL and λS. For the present study, the driving fields for the LAM-15 simulations are obtained from MSC’s regional analysis, whereas those for the LAM-2 simulations are provided by the outputs of LAM-15 simulations. The optimal shape of β(ζ ) as well as the appropriate values of τ(t), λL, and λS depends on various factors and is determined in section 3 to meet the objectives of the present study. 2.3. Controlling Deviations in the Evolving Surface Fields Any accumulation of error in a prognostically evolving surface field, Φ(i,j), over a domain of (Ni × Nj) grid cells, can be controlled by readjusting the field at a given time step for every model grid cell as follows Φ′M ði; j Þ ¼ ΦM ði; j Þ þ γF ½ΦR ði; jÞ ΦM ði; j Þ

(8)

where i = {0,1,…,Ni 1} and j = {0,1,…,Nj 1}. In equation (8), Φ′M is the model-simulated surface field obtained after readjustments, and the term γF represents a relaxation factor for adjusting the surface fields whose optimal value can be different for different surface variables. The subscript R denotes the reference surface fields that may be obtained from an external surface scheme or MSC’s regional analysis.

3. Results and Discussions This section presents simulations with various configurations for atmospheric and surface nudging with an objective to determine an optimal strategy for extended-range dynamic downscaling as pursued in this study. Extended-range simulations with the LAM-2 configuration are tremendously challenging from a computational cost perspective, primarily due to the enormous domain that involves 3000 × 1800 grid cells. As a result, most of the tests conducted in this study to formulate the conceptual basis of identifying an optimal nudging strategy are based on LAM-15 simulations. Once the proper approach is developed in the context of LAM-15 simulations, the concept is extended to LAM-2 simulations for further evaluations. 3.1. Large-Scale Deviations and the Impact on Near-Surface Meteorology Comparison of similarity between the model outputs and the driving fields with respect to the large and small scales, as proposed by von Storch et al. [2000], can help to illustrate the problem associated with large-scale deviations over extended-range temporal integrations. At a given pressure level p and for a given scale of interest L, similarities between the simulated and driving values of a meteorological variable Ψ(i,j) at an instant of time t can be evaluated using the following relation: D E ½ΨM ði; j; p; tÞ ΨD ði; j; p; t Þ2L E PΨ; L ðp; t Þ ¼ 1 D (9) ½ΨD ði; j; p; tÞ hΨD ði; j; p; tÞi 2L where i = {0,1,…,Ni 1}, j = {0,1,…,Nj 1}, and hi denotes spatial average over the entire model domain. As the MSC’s analysis fields are available every 6 h, all results pertinent to the temporal evolution of similarities for different simulations presented in this study only contain 6-hourly data. From its definition it is evident that increasing similarity between ΨM and ΨD for a given scale will result in a value of PΨ, L(p, t) closer to 1, and for decreasing similarities PΨ, L(p, t) < 1. According to the objectives of the present study, an optimal dynamical downscaling strategy should provide higher similarities for the large scales (i.e., λ > λL), while the smaller scales (i.e., λ < λL) should be allowed to evolve freely without suppression implying requirement of lower similarities. Figure 2 shows the evolution of large-scale similarities between the driving analysis fields and the corresponding LAM-15 simulation outputs over two seasonal periods, winter (1 February to 2 March) and

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Figure 2. Evolution of large-scale similarities in the simulated meteorological fields (UV: wind speed (m s ), 1 TT: temperature (°C), and HU: specific humidity (kg kg )) obtained using the control configuration for two seasonal conditions, winter (1 February to 2 March 2010) and summer (10 June to 9 July 2010), at three different pressure levels (300 hPa: grey lines; 500 hPa: red lines; and 850 hPa: blue lines).

summer (10 June to 9 July), for the year of 2010. Simulation results presented in Figure 2 are obtained using the control configuration of LAM-15 where no mechanism is employed to restrict the deviations of either the atmospheric or the surface fields. The large scales are computed by filtering the meteorological fields using equation (5) with λL = 450 km and λS = 150 km. As the effective spatial resolution of MSC’s regional analysis fields over North America is approximately 15 km, it is safe to assume that the analysis fields provide the best estimate of the atmosphere for scales larger than 450 km over this region. Further analysis on the spatial variance associated with the different meteorological fields for different length scales that corroborates this assumption is presented later in section 3.2. These values of λL and λS are kept the same in computing similarity for all model simulations hereafter. The figure clearly demonstrates substantial decrease in large-scale similarities at all pressure levels for all the meteorological fields. Although temperature initially exhibits somewhat higher large-scale similarity compared to wind speed and specific humidity, as the simulation moves forward it experiences similar reduction in large-scale similarity. Overall, large-scale similarities are found to be slightly better at 300 hPa except for specific humidity during summer where the large-scale similarity is considerably higher at 850 hPa. Higher value of similarity at 850 hPa during summer is not unusual as the lower part of the boundary layer is expected to have more large-scale homogeneity in the distribution of specific humidity, whereas the upper part of the troposphere only receives moisture through sporadic deep convections, and therefore, the corresponding values of large-scale similarities are lower. Although the results presented in Figure 2 do not allow any objective characterization of the seasonal behavior of similarity, at 850 hPa where surface forcing has a more pronounced impact, the simulated wind speed during summer is found to suffer from substantial loss of large-scale similarity. Evolution of small-scale similarities for the different meteorological fields (not shown) revealed even lower similarity values compared to those in the driving analysis. It should be noted that the small scales ( 1. For a given value of αk, the spectral variance σ 2(αk) is computed by combining all the variances for αk ≤ α < αk + 1 where αk ¼ k=N;

(13)

with k = {1,2,,…,N 1} and N = min(Ni,Nj). Finally, in order to account for the half wavelengths resulting from DCT, consecutive full and half wavelengths are gathered to produce the variance spectrum following Denis et al. [2002a] as Varðk Þ ¼ σ 2 ðα2k1 Þ þ σ 2 ðα2k Þ:

(14)

In addition to Var(k), the ratio of model to driving field spectral variance defined as VarRatio ðk Þ ¼ Var M ðk Þ= Var D ðk Þ;

(15)

is also used to compare the variance associated with the different length scales used in different model configurations. A comparison of spectral variance of temperature and wind speed fields at different vertical levels obtained from MSC’s regional analysis as well as from LAM-15 and LAM-2 simulations are presented in Figure 4. The analysis and LAM-15 domains cannot be cropped to exactly match the dimension of LAM-2 domain due to the differences in grid spacing and/or grid rotation. These differences can lead to changes in spectral variance that may be projected at any range of scales. In order to avoid such uncertainties, both analysis and LAM-15 fields are cubically interpolated to the LAM-2 grid before the spectra are computed. Although interpolation can introduce some noise in the spectra, it will only be projected at the smaller scales that are not reasonably represented in LAM-15 or analysis fields, and therefore, the interpolation error is expected to be smaller compared to possible error due to domain cropping. Both of the simulations (LAM-15 and LAM-2) are carried out using the control configuration, i.e., without any atmospheric or surface nudging, and the final spectra are constructed by averaging 6-hourly spectra of 48 h long simulations starting at 0000 UTC of 5 February 2010. Simulations are restricted to 48 h as large-scale deviations within this time period are not substantial (see Figure 2) and thus allows to limit any uncertainty associated with large-scale deviations due to extended temporal integrations. The figure shows that both close to the surface (850 hPa and 100 m agl) and in the upper atmosphere (500 hPa and 200 hPa) the analysis and LAM-15 fields have almost HUSAIN ET AL.


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Figure 4. Comparison of variance spectra of temperature (°C ) and wind speed (m s ) obtained using LAM-15 (red lines) and LAM-2 (green lines) simulations with control configurations and from MSC’s regional analysis (blue lines) at 200 hPa, 500 hPa, 800 hPa, and 100 m agl, computed by averaging over a period of 2 days (1–2 February 2010). Both simulations (LAM-15 and LAM-2) were initiated on 00 h00 UTC of 1 February 2010.

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indistinguishable variance spectra. This is not unexpected as the analysis and LAM-15 simulations have very similar horizontal grid spacing. Fields from LAM-2 simulations, however, reveal significantly increased spectral variance for scales less than 100 km compared to both analysis and LAM-15, while considerable difference is found for scales up to 300 km particularly in the upper atmosphere (i.e., at 500 hPa and 200 hPa levels). The significantly increased small-scale spectral variance in the LAM-2-simulated fields indicates the added information at these scales due to the increased horizontal grid resolution. Nudging of large scales therefore needs to be devised in a way that does not suppress free evolution of these scales (λ < 100 km) in the meteorological fields. Based on these comparisons, for both LAM-15 and LAM-2 simulations, the safe values of λL and λS, when computing [ΨD ΨM]L in equation (7) for nudging model-generated large scales toward the driving fields, are assumed to be 300 km and 100 km, respectively. 3.3. Impact of Different Spectral Nudging Configurations Depending on the objectives and requirements of dynamical downscaling, it is crucial to determine the optimal nudging vertical profile β(ζ ) and relaxation factor τ(t) presented in equation (7). A number of sensitivity tests are conducted to determine the impact of different forms of β(ζ ) and τ(t) on the variance spectra, similarity, and screen-level statistical scores. In addition, different spatial scales of nudging have also been studied to corroborate the optimal values of λL and λS established earlier using the results presented in Figure 4. The general shape of nudging vertical profile, commonly used for dynamical downscaling with regional climate models [von Storch et al., 2000; Liu et al., 2012], can be expressed in the context of GEM for this study as 8 > < 0 if ζ > ζ B βðζ Þ ¼ 1 if ζ < ζ T (16) > : f ðζ Þif ζ T < ζ < ζ B where the hybrid vertical coordinate ζ increases vertically in the downward direction with 0 < ζ < 1. The term f(ζ ) denotes a function that may be constant or allows smooth transition of β(ζ ) between two reference points ζ B and ζ T, which in the present study is defined as 2 π ζ ζT f ðζ Þ ¼ cos : (17) 2 ζB ζT A general form of temporal relaxation factor τ, on the other hand, may be expressed as tR τ¼ Δt ωðtÞ

(18)

where tR is the relaxation time scale, Δt refers to the size of model time step, and ω(t) is a time-dependent weighting function used for time-varying temporal relaxation. The time interval tD between two consecutive driving fields (e.g., 6 h for LAM-15 simulation) can be used as a suitable reference for tR. A large value of tR (e.g., tR ≥ tD) would result in weaker nudging of large scales, whereas smaller values (e.g., tR ≤ Δt) would lead to stronger control over the large scales to be nudged. The weighting function ω(t) in equation (18) has the form ωðt Þ ¼ ½cosfπ nΔt=t D gm

(19)

where n denotes the model time step number and the exponent m = {0, 2, 4, 6,…} determines the rate at which ω(t) changes between its maximum and minimum values within each tD interval. Setting the exponent m = 0 reduces τ to constant factor, while variable temporal relaxation approaches can be devised using m ≥ 2. The different representative shapes of β(ζ ) investigated during this study are shown in Figure 5a, while the shapes of different temporal relaxations used in this study are presented in Figure 5b, and the shapes of ω(t) corresponding to the different values of m are shown in Figure 5c. For convenience of reference and illustration, the different nudging configurations used in the various sensitivity analyses, to be presented hereafter, are referred to as N#T#S# where N#, T#, and S# represent the different nudging vertical profiles, temporal relaxations, and nudging length scales, respectively. A list of different nudging configurations along with their corresponding reference numbers is presented in Table 2. Unless otherwise noted, m = 2 is used as default for variable temporal relaxation. In general, variable temporal relaxation, i.e., m ≥ 2, allows better control over the nudging strength by putting more weight on the driving fields at the exact times when they HUSAIN ET AL.


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(c)

T

Figure 5. (a) Shape of different nudging vertical profiles. (b) Different shapes of the fixed and variable temporal relaxations. (c) Shapes of the weighting function ω(t) for different values of the exponent m in equation (19). The corresponding nudging configurations are presented in Table 2.

are available and gradually puts back weight on the model outputs during the intermediate times when the driving fields can only be obtained through temporal interpolation. This approach thus reduces the influence of any error that may be generated by temporal interpolation of the driving fields during spectral nudging. Comparison of variance ratio (see equation (15)) for LAM-15 simulations with different nudging vertical profiles for a fixed temporal relaxation and fixed nudging scales (λL = 300 km and λS = 100 km) averaged over the winter period is shown in Figure 6. At 500 hPa, compared to the analysis fields, spectra for both nudging configurations involving nonuniform nudging vertical profile (cases N1 and N2 in Table 2) are variance deficient for scales larger than 200 km. The significantly smaller nudging increments associated with these two configurations (N1 and N2), as compared to N3, lead to weaker nudging which are inadequate to ensure spectral similarity for the entire range of scales that are nudged. The issue of weaker nudging is apparently exacerbated by the fact that in between two valid analysis hours nudging is applied to the simulated fields using the temporally interpolated analysis fields as a reference. The combined effect of weak nudging increment and temporally interpolated analysis fields is presumably responsible for the variance deficiencies associated with the N1 and N2 configurations. Further discussion on variance deficiency in the simulated fields that is attributable to the interpolated analysis fields and possible strategies to overcome this issue are presented later in this section. As small scales are generally preconditioned by the large scales, the increased variance found for scales smaller than 200 km with the N1 and N2 configurations, particularly close to the surface (at 100 m agl), may therefore be unreliable and inaccurate. Use of a uniform vertical profile (N3) on the other hand leads to a close agreement in the variance spectra with analysis (i.e., VarRatio = 1.0) for scales larger than 300 km. Compared to analysis, for both temperature and wind speed, all nudging configurations, however, result in increased spectral variance at scales smaller than 200 km. The small-scale variance deficiency in the analysis fields is presumably caused by the lack of spin-up in the background fields used to generate the analysis compared, which is exacerbated by the lack of variance in the analysis increments at these scales and the smoothing of the fields as they are interpolated to the LAM-15 grid for comparison of spectral variance and similarities. The evolution of large-scale similarity for these nudging configurations is presented in Figure 7. All a

Table 2. List of Different Nudging Configurations Used for Sensitivity Studies f(ζ )

ζB

ζT

τ(t)

λS (km)

λL (km)

equation (17) equation (17) 1 (const) 1 (const) 1 (const) 1 (const) 1 (const) equation (17)

0.999 0.85 N/A N/A N/A N/A N/A 0.97

0.2 0.2 N/A N/A N/A N/A N/A 0.92

tR = tD, m = 0 tR = tD, m = 0 tR = tD, m = 0 tR = Δt, m = 2 tR = tD, m = 2 tR = Δt, m = 2 tR = Δt, m = 2 tR = Δt, m = 2

100 100 100 100 100 225 350 100

300 300 300 300 300 450 700 300

Configuration N1T1S1 N2T1S1 N3T1S1 N3T2S1 N3T3S1 N3T2S2 N3T2S3 N4T2S1 a

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Figure 6. Comparison of spectral variance ratio (see equation (15)) in temperature and wind speed fields obtained using LAM-15 simulations involving different nudging vertical profiles (N1T1S1: red circles, N2T1S1: grey circles, and N3T1S1: green circles) at different vertical levels (500 hPa and 100 m agl) averaged over the winter period (1 February to 2 March 2010). Variance ratio is computed using the MSC’s regional analysis fields as reference.

configurations lead to increased and sustained large-scale similarities for all meteorological variables compared to the control configuration (see Figure 2) throughout the duration of integration. Nonuniform nudging profiles (N1 and N2), however, result in slight reduction in large-scale similarity in wind speed compared to uniform nudging vertical profile. Although specific humidity is not explicitly nudged, all configurations also resulted in substantially improved large-scale similarities for specific humidity (P(t) > 0.8 with mean value of approximately 0.85) compared to the control configuration (see Figure 2). This justifies the selection of only horizontal wind and temperature for spectral nudging. Specific humidity could certainly be improved further by explicit nudging and may be necessary in certain scenarios. This would, however, increase the computational cost of downscaling and was not investigated further during this study. The impact of different β(ζ ) profiles on the screen-level statistical scores is presented in Figure 8. Compared to the LAM-15 CONTROL simulation, all the different nudging configurations are found to substantially improve both bias and standard error in temperature and wind speed. It is worth noting that although spectral nudging is not performed on specific humidity, the screen-level scores reveal similarly remarkable improvement in both bias and standard error of dew point temperature by all the nudging configurations. This again validates the selection of only temperature and horizontal wind speed for atmospheric nudging. Comparison of screen-level scores, particularly standard error in temperature and dew point temperature, shows that uniform nudging vertical profile (N3) delivers the most improvement. Standard error in the simulated screen-level wind speed is also slightly improved by N3 compared to the other configurations. Based on the comparisons of variance spectra, similarity, and near-surface statistics, uniform nudging vertical profile (N3) appears to be more appropriate for the purpose of the present study. Analyses of the different nudging configurations for the summer period also lead to similar findings and therefore are not shown. Sensitivity of LAM-15 simulations to different temporal relaxations for the case of uniform nudging vertical profile (N3) and for fixed nudging scales (S1, i.e., λL = 300 km and λS = 100 km) are presented in Figures 9 and 10. As can be seen in Figure 9, the configuration N3T3S1 results in variance deficiency in the large-scale

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Figure 7. Evolution of large-scale similarities in temperature, wind, and specific humidity at 500 hPa for LAM-15 simulations with different nudging vertical profiles (N1T1S1: red lines, N2T1S1: grey lines, and N3T1S1: green lines). Similarities are computed with respect to the driving analysis fields.

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spectra which is more pronounced at 500 hPa. Temporal relaxation T3 leads to the smallest nudging increments and similar to the N1T1S1 and N2T1S1 configurations (see Figure 6) does not allow strong control over the scales to be nudged, resulting in the large-scale variance deficiency seen in Figure 9. The configurations involving T1 and T2, on the other hand, provide similar variance spectra particularly close to the surface (at 100 m agl). Both T1 and T2 produce equivalent strong large-scale similarities throughout the simulation period, and as expected, T3 (in N3T3S1) is found to suffer from somewhat reduced large-scale similarity (not shown). Furthermore, results presented in Figure 10 show that compared to N3T3S1, both N3T1S1 and N3T2S1 lead to similarly improved standard error in screen-level temperature and dew point temperature. As far as wind speed is concerned, both T1 and T2 lead to similar improvement in bias compared to T3; however, T1 suffers from slightly higher standard error compared to the other two configurations. Overall, comparisons of variance spectra,

Figure 8. Diurnal variations of bias and standard error of screen-level temperature (°C), dew point (°C), and wind speed 1 (m s ) for the winter period associated with the fields obtained using LAM-15 simulations involving different nudging vertical profiles (N1T1S1: red lines, N2T1S1: grey lines, and N3T1S1: green lines). Results associated with LAM-15 control simulation (CONTROL: turquoise lines) and MSC’s operational regional forecasts (REG FORECAST: blue lines) are also included for reference.

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Figure 9. Same as Figure 6 but for different temporal relaxations (N3T1S1: red circles, N3T2S1: grey circles, and N3T3S1: green circles).

scale-specific similarities, and screen-level statistical scores demonstrate that with uniform nudging vertical profile configuration (N3), temporal relaxation approaches T1 and T2 lead to equivalent results. The two approaches, T1 and T2, are, however, conceptually different. Nudging based on the T2 relaxation approach varies with the frequency of the availability of the driving fields and puts the maximum weight on the driving fields when the model time step coincides with times when driving fields are available, and the weight is shifted back to the simulations at the intermediate time steps. This allows the simulated fields to evolve more freely during these intermediate time steps and can potentially result in better resolution of the small scales compared to the T1 approach which puts equal but smaller weight on the driving fields at all time steps. Temporal relaxation

Figure 10. Same as Figure 8 but for different temporal relaxations (N3T1S1: red lines, N3T2S1: grey lines, and N3T3S1: green lines).

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associated with the N3T2S1 configuration, i.e., T2, can therefore be assumed to be optimal for downscaling with LAM-15 simulations. Different values of the exponent m in the expression for variable weight ω(t) for the N3T2S1 configuration have been tested (not shown) and are found to result in equivalent screen-level scores. Unless otherwise stated, all results with the T2 approach presented in this paper are based on m = 2. A further look into the variance spectra ratio presented in Figure 9 reveals that both temperature and wind speed fields, particularly at 500 hPa level, suffer from variance deficiency around 200 km length scale when the N3T2S1 nudging strategy is employed. It should be noted that the reference driving fields for spectral nudging during the intermediate time steps—in between two consecutive analysis hours—are generally obtained through temporal interpolation. As the regional analysis fields are only available every 6 h, these temporally interpolated reference driving fields therefore can lead to variance deficiency resulting from smoothing of the fields around the cutoff wavelengths as can be seen in Figure 9. For the present study, where the focus of downscaling is the surface layer, the lack of variance around 200 km length scale for the upper air is not a major concern. Nevertheless, depending on the objective of downscaling, this issue may be addressed in multiple ways. Nudging only at the analysis hours can be a simple solution in this regard although it may lead to significant jumps in the temperature and wind time series. Increasing the value of the exponent m in the expression for variable weight ω(t) in equation (19) can also help in reducing the variance deficiency. Too high a value of m on the other hand can also lead to abrupt changes around the analysis hours in the time series. An alternate approach to reducing the lack in spectral variance without causing abrupt changes in time series can be devised by producing hourly estimates of the analysis fields for nudging. This can be achieved by running 6 h long LAM-15 CONTROL simulations initialized with the MSC’s regional analysis at 0000, 0600, 1200, and 1800 UTC. Differences between the model outputs of a given variable on the sixth hour and the available analysis field valid at the same time provide measure for model error. The hourly forecasts can then be corrected by assuming that model error grows linearly during the first 6 h and thereby producing the hourly analysis estimates. This needs to be followed by a separate LAM-15 N3T2S1 simulation where the hourly analysis estimates are used as reference for spectral nudging of temperature and wind. This approach, however, doubles the computational cost associated with the LAM-15 simulations. Figure 11 demonstrates the impact of the aforementioned approaches on the variance ratio for temperature and wind speed fields obtained with LAM-15 simulations using N3T2S1 configuration. The figure shows that the method involving hourly estimation of analysis fields, as expected, leads to the most significant improvements in variance ratio for both temperature and wind at 500 hPa. Further improvement can be obtained by computing the analysis estimates more frequently, e.g., every half an hour, without increasing the computational costs any further. Increasing the exponent in ω(t) from m = 2 to m = 6 also results in some improvement although not as significant and therefore not recommendable as a remedy to tackle upper air variance deficiency resulting from interpolation of driving fields. The issue of lack of variance around 200 km length scale may also be addressed by increasing the magnitude of length scales for nudging that needs to be retained in the LAM-15 simulations. The effects of changing nudging length scales on variance ratio are presented in Figure 12. As the sensitivity of extended-range simulations to nudging length scales may vary differently with seasonal conditions, results obtained for both winter and summer periods are shown. It is evident from the figure that any increment in the values of λL and λS is almost inconsequential for the small-scale variance spectra, particularly at 100 m agl for scales smaller than 200 km. Although increasing the values of λL and λS (cases N3T2S2 and N3T2S3) shows increased variance for scales larger than 200 km, it does not necessarily indicate any improvement of accuracy, especially within the surface layer. To the contrary, it has been shown earlier that the analysis fields are more reliable at these scales (see Figure 4), and therefore, an optimal nudging strategy is expected to yield spectral variance closer to analysis for scales larger than 300 km. All three configurations of nudging scales, as expected, provide high degree of similarities for the large scales while allowing small scales to evolve largely freely (not shown). Increasing the nudging length scales (N3T2S2 and N3T2S3), however, leads to small but consistent reduction in large-scale similarities that can have adverse effects on the generated small scales. Statistical scores for screen-level wind, dew point temperature, and temperature presented in Figure 13 show that all three configurations provide similar accuracy although the S1 configuration delivers considerably smaller standard error for temperature during both winter and summer, particularly during daytime (1500–0000 UTC). Wind speed obtained with S1 nudging length scales also reveals relatively smaller bias and standard error compared to the other configurations.

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Figure 11. Impact of different nudging configurations on spectral variance ratio in temperature and wind speed fields obtained using LAM-15 simulations with N3T2S1 configuration (N3T2S1: with m = 2 and 6-hourly analysis, blue circles; N3T2S1_M6: with m = 6 and 6-hourly analysis, green circles; and N3T2S1_HA: m = 2 and hourly analysis estimates, red circles) averaged over 3 days (1–3 February 2010). All other conditions are as in Figure 9.

Based on the different sensitivity tests presented in this section, the N3T2S1 configuration, i.e., uniform nudging at all model vertical levels with variable temporal relaxation based on the frequency driving fields availability and nudging cutoff scales corresponding to the smallest-scale reliably embedded in the driving fields from MSC’s analysis, is found to be the most effective strategy for the dynamical downscaling, particularly with LAM-15 simulations. 3.4. Impact of Surface Nudging Configurations Results presented in section 3.2 demonstrated that large-scale atmospheric nudging improves the resolved small scales which are evident from the substantially improved screen-level statistical scores by the different nudging schemes compared to the control configuration. However, error can accumulate in the prognostically evolving surface fields, and at times these fields can substantially deviate from their expected values. This may lead to erroneous fluxes of heat and moisture from the surface, leading to reduced accuracy in the simulated meteorological fields within the surface layer. To illustrate the issue further, the evolution of the spatially averaged near-surface and root-zone soil moisture level as present in MSC’s analysis and as obtained using the LAM15-N3T2S1 simulation over a period of approximately 6 months (1 February to 20 July 2010) is presented in Figure 14. It should be noted that the near-surface soil moisture shown in the figure represents the total volumetric water content (liquid and frozen), whereas the root-zone layer values only include the liquid phase and do not account for the frozen fraction of soil water content. The figure shows that in the absence of any control mechanism both near-surface and root-zone soil moisture level can develop considerable differences compared to their analysis counterparts, particularly during spring when snow melts as well as until early summer while the surface receives significant amount of precipitation. Although the differences are found to diminish later in the summer, these differences during spring can adversely influence the heat and moisture fluxes from surface and as a result reduce accuracy of the simulated humidity and temperature fields. At times it may also affect the surface layer thermal stability and through enhanced or reduced buoyancy driven turbulence can adversely impact the prediction of surface layer wind.

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(a) Winter (Feb 1 – Mar 2, 2010)

(b) Summer (June 10 – July 9, 2010)

Figure 12. Same as Figure 6 but for different nudging length scales (N3T2S1: red circles, N3T2S2: grey circles, and N3T2S3: green circles). Results are presented for both (a) winter and (b) summer.

The impact of unrestricted evolution of prognostic surface fields is illustrated in terms of screen-level statistical score in Figure 15. For screen-level temperature, both N3T2S1_EXT (initialized on 1 February 2010) and N3T2S1 (initialized on 10 June 2010) lead to similar level of bias and standard error during the summer period. It is, however, evident that the extended-range simulation N3T3S1_EXT, which was initialized almost 4 months earlier than N3T2S1, suffers from larger standard error in dew point temperature. This increase in standard error is primarily caused by deviations in soil moisture fields attributable to the extended length of temporal integrations of the prognostic soil moisture equations. This clearly demonstrates the possibility of potential improvements in surface layer meteorology that can be achieved by controlling the evolution of some of the prognostic surface fields. HUSAIN ET AL.


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Figure 13. Same as Figure 8 but for different nudging length scales (N3T2S1: red lines, N3T2S2: grey lines, and N3T2S3: blue lines) for both (a) winter and (b) summer.

3

3

Figure 14. Comparison of evolution of near-surface and root-zone soil moisture (m m ) averaged over the entire domain as obtained from LAM-15 N3T2S1 simulation (red lines) and MSC’s regional analysis (blue lines) over a period of 169 days (1 February to 20 July 2010).

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Figure 15. Comparison of screen-level statistical scores (averaged over the summer period: 10 June to 9 July 2010) between LAM-15 simulations involving N3T2S1 nudging configuration initialized at two different times. Simulation N3T2S1 (red lines) was initialized on 10 June 2010 while simulation N3T2S1_EXT (grey lines) was initialized on 1 February 2010. Scores for the MSC’s regional forecasts (REG FORECAST: blue lines) are included as a reference.

Surface fields that are considered to be the most important to minimize erroneous surface fluxes are surface (aggregate of soil, vegetation, and snow) temperature (ST), soil moisture (SM), snow depth (SD), and snow density (DN). In addition to MSC’s regional analysis, surface fields obtained from high-resolution offline Surface Prediction System (SPS), which is based on the same ISBA (Interactions between Soil, Biosphere, and Atmosphere) model [Bélair et al., 2003] used in GEM to parameterize the effects of soil, snow, and vegetation, have been tested as reference for nudging in this study. Further investigations were carried out at Environment Canada [Separovic et al., 2014] to improve the atmospheric forcing mechanism in SPS for producing highresolution reference surface fields with improved spatiotemporal variability. The resulting fields were used in this study to readjust the prognostic surface fields for extended-range mesoscale simulations. Figure 16 shows the impact of grid nudging of prognostic surface fields ST, SM, SD, and DN with reference fields obtained from MSC’s analysis and SPS on screen-level temperature, dew point temperature, and wind speed over winter and summer periods. Although the influence of surface nudging is found to be neutral for screen-level wind, the figure illustrates clear improvement in screen-level temperature and dew point temperature during both seasons. Improvement gained through surface nudging is more pronounced for dew point temperature and particularly during winter. From the results presented in Figure 16, it is also evident that using SPS-generated surface fields as reference generally leads to better improvement compared to the analysis fields, and the benefits of SPS are found to be more pronounced during winter when spatial variability are, in general, significantly larger compared to summer. The results shown in Figure 16 were obtained using weak surface nudging with a nudging relaxation factor γF = 0.01 (see equation (8)) used for all the surface fields. The impact of increasing the value of γF from 0.01 to 0.25 is demonstrated in Figure 17. As can be seen in Figure 17, remarkable improvements of up to 0.5°C were obtained in screen-level temperature and dew point temperature in winter with strong surface nudging (N3T2S1_SPSV3). During summer, although screen-level temperature is substantially improved with strong nudging, the results are less remarkable for dew point temperature particularly during daytime (1800–0000 UTC). As expected, the impact of strong surface nudging is found to be neutral for screen-level wind. Sensitivity tests were also conducted to determine the surface fields that are the most critical for nudging in order to obtain improved surface layer simulations during both winter and summer conditions. The corresponding results are illustrated in terms of screen-level statistical scores in Figure 18. The figure reveals that during winter strong nudging of only snow density and snow depth (N3T2S1_SD-DN) produces neutral effects on both screen-level temperature and dew point temperature. Strong nudging of surface temperature alone (N3T2S1_ST), on the other hand, results in similar remarkable improvements in both temperature and dew point temperature during winter. Most of the spatial domain of interest for this study is covered with snow during

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Figure 16. Impact of surface nudging with MSC’s analysis (N3T2S1_ANA: grey lines) and SPS-generated (N3T2S1_SPS: green lines) surface fields used as reference as compared to no surface nudging (N3T2S1: red lines) and regional forecast (REG FORECAST: blue lines) on screen-level temperature, dew point temperature, and wind speed. All surface fields are readjusted in accordance with equation (8) with γF = 0.01.

winter making the influence of soil moisture negligible, and therefore, sensitivity of soil moisture nudging is not investigated for winter. During summer, strong nudging of surface temperature alone (N3T2S1_ST) leads to significant improvements in screen-level temperature, whereas the accuracy in screen-level dew point temperature cannot be improved significantly without nudging being applied on soil moisture as well. The results thus demonstrate the strong influence of both soil moisture and surface temperature during summer in order to reliably predict specific humidity and temperature fields within the surface layer. Based on screen-level statistical scores presented in Figure 18, it is imperative to nudge both soil moisture and surface temperature for improved surface layer simulation throughout the year. No clear impact of

Figure 17. Influence of surface nudging relaxation factor with SPS-generated surface fields (N3T2S1_SPS: grey lines with γF = 0.01 and N3T2S1_SPSV3: green lines with γF = 0.25) used as reference compared to no surface nudging (N3T2S1: red lines) and the regional forecast (REG FORECAST: blue lines) on standard error of screen-level temperature, dew point temperature, and wind speed.

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Figure 18. Sensitivity in screen-level standard error of temperature, dew point temperature, and wind speed with respect to different surface fields selected for surface nudging during winter (N3T2S1_ST: grey lines, only surface temperature is nudged and N3T2S1_SD-DN: green lines, only snow density and snow depth are nudged) and summer conditions (N3T2S1_ST: grey lines, only surface temperature is nudged and N3T2S1_SM: green lines, only soil moisture is nudged). All surface fields are readjusted in accordance with equation (8) with γF = 0.25.

nudging of snow density and snow depth was revealed during the winter period. It should, however, be noted that the parameterization of heat transfer coefficient for the prognostic surface temperature equation in ISBA is by design more sensitive to changes to snow conditions for moderate values of snow depth through changes in the snow water equivalent and by extension the snow cover fraction [Noilhan and Planton, 1989; Bélair et al., 2003]. As a result snow conditions are expected to have more influence on screen-level temperature and dew point temperature during the thawing season when snow depth values are relatively moderate. It may therefore be prudent to include snow conditions within the surface nudging scheme for proper estimation of heat and moisture fluxes during spring, and the associated increase in computational cost is also insignificant. 3.5. Extension of the Downscaling Strategy to 2 km GEM-LAM Simulations Results presented in sections 3.2 and 3.3 demonstrated the impact of atmospheric and surface nudging in the context of extended-range LAM-15 simulations. It has been mentioned earlier that the primary motivation of this study is to produce Canada-wide multiyear surface layer meteorological data with a horizontal grid spacing of 2 km. The majority of the conclusions derived by analyzing the results associated with LAM-15 simulations, including the underlying concept of dynamical downscaling, can nevertheless be extended to simulations with higher spatial resolutions. Although uniform nudging vertical profile (N3) for all prognostic model levels has been found to be optimal for LAM-15 simulations, an additional nudging vertical profile N4, which incorporates a steep gradient within the surface layer (see Figure 5) where the impact of surface-induced forcing is dominant, is also investigated for the LAM-2 simulations. As for temporal relaxation, a constant factor of τ = 1.0 denoted by T4, where TR = Δt and m = 0 in equation (18), is also studied for LAM-2 simulations. The rationale behind τ = 1.0 is based on the assumption that the driving fields for LAM-2 simulations, which are derived from LAM-15 simulations, are available every 20 min, and large-scale deviations are expected to be insignificant over such a short period. The detailed configurations associated with the different nudging configurations for LAM-2 simulations are presented in Table 2 with the corresponding shapes of nudging vertical profile and temporal relaxations shown in Figure 5. Spectral variance ratios for LAM-2 simulations (involving N4T2S1 configuration with and without surface nudging and N3T4S1 with surface nudging) compared to the driving LAM-15 fields (N3T2S1 configuration) are presented in Figure 19. As expected, a noticeable increase in spectral variance for scales smaller than

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Figure 19. Spectral variance ratio LAM-2 simulations with N4T2S1 (grey circles), N4T2S1_SPSV3 (green circles), and N3T4S1_SPSV3 (turquoise circles) configurations compared to the corresponding LAM-15 driving fields averaged over a 14 day winter period (5–18 February 2010) at 500 hPa and 100 m agl.

100 km, both close to the surface (100 m agl) and at 500 hPa, is produced by all the different LAM-2 configurations. Strong spectral nudging is found to result in close to one variance ratio for both large-scale temperature and wind in the upper air (at 500 hPa), and no variance deficiency originating from interpolation of driving LAM-15 fields is visible even with the T4 temporal relaxation. This validates the assumption that the impact of temporal relaxation applied to the spectral nudging term becomes insignificant when the driving fields are available with a higher frequency. In the lower part of the atmospheric boundary layer all nudging configurations are, however, found to produce considerable differences in large-scale variance in the LAM-2-simulated fields compared to the LAM-15 counterparts. Differences in variance for scales over 200 km are more pronounced for temperature and are apparently attributable to the differences in the resolved vertical profiles of stable boundary layer, particularly during nighttime, as predicted by LAM-2 simulations compared to observations, and by extension, the MSC’s regional analysis, over a large patch of the Canadian prairies and over the Hudson’s bay (not shown). Numerical weather prediction models generally suffer from excessive mixing within stable boundary layer that occasionally leads to overestimation of boundary layer height [Holtslag et al., 2013] and is apparently responsible for the large-scale differences tens of meters above the ground. Results presented in the figure show that gradually increasing nudging vertical profile (N4), which implies weak to no nudging tens of meter above the surface, actually exacerbates the problem and considerably alters variance for scales larger than 1500 km, for which a variance ratio as close to 1 as possible is desirable. Nudging of surface fields toward SPS outputs (N4T2S1_SPSV3) is found to bring the large-scale spectra of 100 m temperature somewhat closer to those in the driving LAM-15 field. Strong nudging within the surface layer (N3), on the other hand, is found to exert significantly stronger influence on the large-scale variance and results in a variance ratio of approximately 1 for scales larger than 200 km in horizontal wind speed. Uniform vertical nudging (N3) also leads to substantially improved variance ratio (closer to 1) for temperature scales larger than 700 km. Further reduction in large-scale variance differences may be attained by reducing mixing in strongly stable conditions within the vertical diffusion scheme that parameterizes boundary layer turbulence in GEM. Work to improve the turbulent diffusion through detailed investigation of the

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Figure 20. Evolution of large- and small-scale similarities in wind and temperature fields obtained using LAM-2 simulations with N4T2S1 (grey lines), N4T2S1_SPSV3 (green lines), and N3T4S1_SPSV3 (turquoise lines) configurations compared to the corresponding LAM-15-simulated scales over a 14 day winter period (5–18 February 2010).

underlying physical mechanism is currently in progress at Meteorological Service of Canada and is beyond the scope of the present work. Figure 20 illustrates the temporal evolution of large- and small-scale similarities associated with LAM-2 simulations involving the different nudging configurations. All LAM-2 simulations produce high large-scale similarities when compared to the driving LAM-15 temperature and wind speed fields. Small-scale similarities at 850 hPa, as expected, are found to be lower for both wind and temperature for all configurations, implying the ability of the nudging mechanism to allow unsuppressed development of the small scales. A comparison of screen-level standard error in the temperature and wind fields obtained using the different configurations of LAM-2 and LAM-15 simulations along with the operational regional forecast is presented in Figure 21. Results are presented for the entire simulation domain as well as for different regions of Canada (see Figure 1b). Similar to what has been seen earlier for LAM-15 simulations, strong adjustments made to the surface fields toward their SPS-generated reference values substantially improve screen-level temperature for LAM-2 simulations (N4T2S1_SPSV3 and N3T4S1_SPSV3) over the entire domain as well as over the individual regions. In the BC (British Columbia) region, where orography is more challenging compared to the rest of the domain, LAM-2 simulations with strong surface nudging (N4T2S1_SPSV3 and N3T4S1_SPSV3) show clear improvements in temperature standard error over LAM-15 simulation with similar surface nudging. With optimal spectral nudging configurations, both LAM-15 and LAM-2 simulations are found to result in significant improvements in screen-level temperature, with up to 1°C reduction in standard error, when compared against SE of operational regional forecast. Improvements in screen-level wind from the LAM-2 simulations are found to be less remarkable over the full domain as well as for most of the regions except in BC and the North. The terrain in both BC and the North has larger orographic variance, and the improvements due to higher spatial resolution with the LAM-2 simulations are evident in these regions from Figure 21b. As the majority of the observation stations is located within the Prairies and the QC-ON regions, any statistical score over the entire domain is predominantly influenced by the outcome in these regions and does not adequately reflect specific improvements associated with other regions. Overall, the results presented in Figure 21 demonstrate that LAM-2 simulations, involving strong surface readjustments toward the SPS-generated fields, for both atmospheric nudging configurations (N4T2S1_SPSV3 and N3T4S1_SPSV3) are equivalent as far as the screen-level scores are concerned. However, in order to properly assess the impact of these nudging configurations, it will be prudent to evaluate their performance tens of meters above model surface. Temperature and wind speed data recorded at the existing

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(a) Temperature

(b) Wind speed

1

Figure 21. Comparison of standard error in screen-level (a) temperature (°C) and (b) wind speed (m s ) obtained using LAM-15 N3T2S1_SPSV3 (red lines), LAM-2 N4T2S1 (grey lines), LAM-2 N4T2S1_SPSV3 (green lines), and LAM2-N3T4S1_SPSV3 (turquoise lines) simulations averaged over a 14 day winter period (5–18 February 2010).

wind farm locations across Canada could be tremendously useful for such validations. Observational records from wind farms are, however, not as widely available or accessible as the ground-based observation stations used in this study. In fact, the authors had access to only three wind farm locations, situated in Quebec, Canada, for further evaluation of LAM-15 and LAM-2 simulations. The exact locations of these parks cannot be revealed due to restrictive nondisclosure agreements. Temporal evolution of horizontal wind speed at 80 m agl as predicted by the LAM-15 and LAM-2 simulations with atmospheric and surface nudging along with its observed values (67 m agl) at the three wind farm locations is presented in Figure 22. The 80 m height is selected for comparison as it coincides with a prognostic model vertical level used in this study and also because the average hub height for commercial wind turbines is typically 80 m or higher. Although wind speed observation data at the locations presented in Figure 22 are available for 80 m agl, the corresponding anemometers are nonheated leading to inaccurate readings during winter conditions and therefore not suitable for evaluating model performance. Heated anemometers are only available at 67 m agl. The figure shows that both LAM-15 and LAM-2 simulations are, in general, capable of capturing the observed temporal variations at all three stations. For more objective

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1

Figure 22. Time series of wind speed (m s ) at three wind farm locations in Quebec, Canada, obtained from observations (at 67 m agl, grey lines) and model simulations (at 80 m agl) using LAM15-N3T2S1_SPSV3 (red lines), LAM2-N4T2S1_SPSV3 (green lines), and LAM2-N3T4S1_SPSV3 (turquoise lines) configurations over a 14 day winter period (5–18 February 2010).

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1

Table 3. Statistical Comparisons Between Wind Speeds (m s , at 80 m agl) Obtained Through LAM-15 Simulation With N3T2S1_SPSV3 Configuration and LAM-2 Simulations With N3T4S1_SPSV3 and N4T2S1_SPSV3 (Within Parentheses in the Table) Configurations at Three Wind Farm Locations in Quebec, Canada, Over a 14 a Day Winter Period (5–18 February 2010) 2 2

Variance (m s

)

Bias (m s

1

)

RMSE (m s

1

1

)

SE (m s

)

Correlation

Station

OBS

LAM-15

LAM-2

LAM-15

LAM-2

LAM-15

LAM-2

LAM-15

LAM-2

LAM-15

LAM-2

1 2 3

11.8 8.5 6.4

15.4 7.6 5.4

11.0 (11.0) 7.4 (8.0) 6.8 (6.5)

0.7 1.2 2.0

0.5 (0.1) 0.1 (0.3) 0.4 (0.9)

2.2 2.3 3.0

1.8 (1.7) 1.8 (2.0) 2.1 (2.6)

2.1 2.0 2.3

1.7 (1.7) 1.8 (1.9) 2.1 (2.5)

0.85 0.76 0.56

0.87 (0.88) 0.88 (0.78) 0.66 (0.53)

a

Observations from heated anemometers at approximately 67 m agl were used to compute bias, RMSE, and SE for the two model configurations. Results presented in the table have been rounded off.

comparison, statistical scores associated with the simulated wind time series at these stations over the 14 day period are computed, and the corresponding results are presented in Table 3. Results presented in the table demonstrate that both LAM-2 simulations are in very good agreement with the observed temporal variance of wind speed for all the stations, whereas the LAM-15 simulation, when compared against observations, somewhat overpredicts temporal variance for station 1 and slightly underpredicts the variance for stations 2 and 3. The magnitude of bias in 80 m wind speed is found to be significantly lower for all

Figure 23. Time series of air temperature (°C) at 40 m and 80 m agl at a wind farm location in Quebec, Canada, obtained from observations (grey lines) and model simulations using LAM15-N3T2S1_SPSV3 (red lines), LAM2-N4T2S1_SPSV3 (green lines), and LAM2-N3T4S1_SPSV3 (turquoise lines) configurations over a 14 day winter period (5–18 February 2010).

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Table 4. Statistical Comparisons Between Temperature (°C, at 80 m and 40 m agl) Obtained Through LAM-15 Simulation With N3T2S1_SPSV3 Configuration and LAM-2 Simulations With N3T4S1_SPSV3 and N4T2S1_SPSV3 (Within Parentheses in the Table) Configurations at Station 1 Location Over an 11 Day Winter Period a (8–18 February 2010) 2

Variance (°C )

Bias (°C)

RMSE (°C)

SE (°C)

Correlation

Height (m)

OBS

LAM-15

LAM-2

LAM-15

LAM-2

LAM-15

LAM-2

LAM-15

LAM-2

LAM-15

LAM-2

40 80

3.8 4.0

3.3 3.6

4.4 (5.1) 3.7 (5.2)

0.4 1.0

0.3 (0.2) 0.4 (0.7)

1.2 1.5

0.9 (0.9) 1.0 (1.1)

1.1 1.1

0.9 (0.8) 0.9 (0.9)

0.84 0.85

0.91 (0.93) 0.90 (0.92)

a

Results presented in the table have been rounded off.

thestations with both LAM-2 simulations while RMSE is also smaller compared to LAM-15. Wind speed computed by LAM-2 with variable vertical nudging within the surface layer (N4) is, however, found to have a larger SE for station 3 compared to simulations, both LAM-15 and LAM-2, with uniform vertical nudging (N3). It is worth noting that the observed wind speed time series at station 3 location exhibits a behavior which is quite different from the other two stations and is marked by a generally lower magnitude of wind speed as well as more chaotic temporal variations (see Figure 22). This makes station 3 a difficult case for numerical prediction, as evidenced by the significantly lower correlation for both LAM-15 and LAM-2 simulations compared to the other two stations (see Table 3). Standard error, by definition, is a function of variance and correlation. Results presented in Table 3, however, show that LAM-2 simulation using N3T4S1 configuration leads to substantial improvement in temporal correlation for station 3–10% improvement compared to LAM-15 and 13% compared to the other LAM-2 configuration (N4T2S1_SPSV3). Figure 23 shows the time series of temperature at 40 m and 80 m agl for the same time period presented in Figure 22, but only for station 3. Temperature data are not available for the two other stations during the stipulated period. Similar to wind speed, Figure 23 demonstrates that all simulations, LAM-15 and both configurations of LAM-2, are capable of predicting the evolution of temperature at both vertical levels with very good temporal correlation. The corresponding statistical scores are presented in Table 4. It should be noted that during the first 3 days (5–7 February 2010) all simulations as well as the observational records reveal a significant warming trend. In order to reduce the impact of this trend, the first 3 days are not considered while computing the statistical scores for the different LAM-15 and LAM-2 simulations (see Table 4). Results presented in Table 4 show that both LAM-2 simulations lead to slightly better accuracy in terms of lower magnitude of bias and SE at the two vertical levels. Although wind speed at station 3 suffers from low temporal correlation, all simulations (LAM-15 and LAM-2) predict temperature at both vertical levels with very high temporal correlation (greater than 0.8). Overall, in addition to predicting surface layer meteorology with a higher spatial resolution, the LAM-2 simulation with the N3T4S1 configuration, which involves uniform nudging vertical profile and fixed temporal relaxation along with strong surface nudging, predicts the surface layer wind speed and temperature time series with better statistical accuracy compared to LAM-15 simulation for the three wind farm locations investigated in this study. As a result, N3T4S1 can be recommended as the optimal approach for downscaling with LAM-2 simulation as pursued in this study.

4. Conclusions A dynamical downscaling strategy based on high-resolution mesoscale simulations over a large continental-scale spatial domain and an extended time period is presented in this paper. Continuous temporal integration over the entire domain, as opposed to extended integrations over smaller spatial domains or multiple simulations with shorter time periods over larger domains followed by spatiotemporal blending, is found to be the most suitable approach for accomplishing the high-resolution downscaling objectives. Large-scale deviations in the different meteorological fields pose the biggest challenge for extended-range simulations over large domains. Spectral nudging of the atmospheric large scales, as implemented in this study, is shown to effectively control any undesirable deviation without considerable suppression of the small scales. The paper shows that simple temporal interpolation to derive the reference fields, in between two analysis hours, can lead to mesoscale variance deficiency in the spectrally nudged simulated fields. Two different strategies have been proposed and examined in this paper to deal with such variance deficiencies. One option is to use a time-varying nudging coefficient with a larger value of the exponent m (see equation (19)) that puts the maximum weight on the analyses fields only when the HUSAIN ET AL.


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simulation time is very close to the time for which valid analyses fields are available. The other approach, which has been demonstrated in the paper to be more effective, is to produce hourly estimates of analyses by running 6 h forecasts initialized with the analyses and assuming a linear growth of forecast error within the first 6 h of model simulation. The later approach is found to effectively eliminate any variance deficiency associated with the temporally interpolated analysis fields. Extensive sensitivity studies have been carried out to identify the optimal nudging configuration in terms of the shape of nudging vertical profile, nudging length scales, and the type of temporal relaxation. Overall, uniform vertical profile for nudging is found to be optimal for extended-range simulations for both the coarse-resolution LAM-15 and high-resolution LAM-2 configurations. Although time-varying strong temporal relaxation is more appropriate for LAM-15 simulations, where the driving fields obtained from MSC’s regional analysis are only available every 6 h, strong time-constant relaxation is shown to be the better option for LAM-2 simulations. Large-scale spectral nudging of horizontal wind speed and temperature is found to adequately control large-scale deviations in specific humidity. Ensuring large-scale atmospheric similarities also helps to restrict substantial deviations in the prognostically evolving surface fields and delivers screen-level statistical scores for temperature, dew point temperature, and horizontal wind speed that are comparable to the operational regional forecasts. Nevertheless, extended-range temporal integrations over multiple months can lead to considerable deviations in the evolving surface fields, particularly soil moisture during spring, and may lead to erroneous surface-induced fluxes of heat and moisture. As a consequence, inaccuracies can increase in the simulation of the near-surface meteorology during this period. In order to overcome this issue, surface fields including surface temperature, soil moisture, snow density, and snow cover fraction are nudged toward some reliable reference data set obtained from either the MSC’s regional analysis or the SPS external surface model. Results show that using the SPS fields as reference for nudging leads to more improved screen-level scores for both temperature and dew point. Nudging of the surface fields is, however, found to be neutral for the screen-level wind speed. Increasing the strength of surface nudging is shown to improve screen-level scores further.

Acknowledgments The source code for the version of GEM model used for the simulations along with the additional codes associated with the implementations of the spectral and surface nudging schemes can be made available upon request. The enormous volume of model-generated data used in this study (approximately 20 TB) makes it unfeasible to share using any public data center. Any data used to produce the figures and tables in this paper will, however, be archived for at least 5 years, and all attempts will be made to make any part of it available for review, reproduction, or any other purpose. The authors wish to sincerely thank Stéphane Bélair, Marcel Vallée, Minwei Qian, Yosvany Martinez, Michel Desgane, Laurent Chardon, Marco Carrera, and the Shared Services of Canada for their valuable cooperation during the different stages of this research. Funding for this project was provided by the ecoENERGY Innovation Initiative of Canada (project: RENI 546).

HUSAIN ET AL.

Meteorological fields obtained through high-resolution LAM-2 simulations following the nudging strategy adopted in this study are able to maintain large-scale similarity with the driving LAM-15 fields, while adding substantially increased spatial variance for the smaller scales (less than 200 km). In terms of screen-level score, LAM-2 simulations are, in general, found to be equivalent compared to the LAM-15 simulations over the entire domain, although over BC and the North, where orography-induced spatial variance is more influential, LAM-2 simulations are found to improve both screen-level temperature and wind speed. Performance of different atmospheric nudging configurations for both LAM-15 and LAM-2 simulations is also evaluated against 80 m wind and temperature data obtained from three wind farm locations. For all three stations, LAM-2 simulation with its optimal nudging configuration is found to deliver better statistical accuracy for both wind speed and temperature over its LAM-15 counterpart. More data from the existing wind farms across Canada could be of tremendous use for further evaluation of the different nudging configurations. Such extensive evaluation was, however, not possible in the course of the present work due to restrictive nondisclosure requirements. In future, a systematic study should be carried out to assess the impact of domain size and grid resolution on the large-scale deviations with short-term forecasts obtained through high-resolution deterministic prediction systems as well as the scope of spectral nudging in improving such forecasts.

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