An Object-Based Approach for Quantification of GCM Biases of The

15 DECEMBER 2014 Y O R G U N A N D R O O D 9139

An Object-Based Approach for Quantiﬁcation of GCM Biases of the Simulation of Orographic Precipitation. Part I: Idealized Simulations

M. SONER YORGUN AND RICHARD B. ROOD Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, Michigan

(Manuscript received 10 January 2014, in ﬁnal form 10 September 2014)

ABSTRACT

An object-based evaluation method to quantify biases of general circulation models (GCMs) is introduced using the National Center of Atmospheric Research (NCAR) Community Atmosphere Model (CAM). Idealized experiments with different topography are designed to reproduce the spatial characteristics of precipitation biases that were present in Atmospheric Model Intercomparison Project simulations using the CAM finite volume (FV) and CAM Eulerian spectral dynamical cores. Precipitation features are identified as ‘‘objects’’ to understand the causes of the differences between CAM FV and CAM Eulerian spectral dynamical cores. Three different mechanisms of precipitation were simulated in idealized experiments: stable upslope ascent, local surface fluxes, and resolved downstream waves. The results indicated stronger sensitivity of the CAM Eulerian spectral dynamical core to resolution. The application of spectral filtering to topography is shown to have a large effect on the CAM Eulerian spectral model simulation. The removal of filtering improved the results when the scales of the topography were resolvable. However, it reduced the simulation capability of the CAM Eulerian spectral dynamical core because of Gibbs oscillations, leading to unusable results. A clear perspective about models biases is provided from the quantitative evaluation of objects ex- tracted from these simulations and will be further discussed in part II of this study.

1. Introduction rather than the residue of global inadequacies of, for instance, model parameterizations. Deterministic weather All atmospheric general circulation models (GCMs) predictions are often validated with feature-by-feature have systematic errors in their simulation of the present comparison (Davis et al. 2006; Ebert and McBride 2000; climate. These systematic errors (i.e., biases like conti- Marzban and Sandgathe 2006; Micheas et al. 2007; Posselt nental precipitation, tropical mean state, etc.) are re- et al. 2012; Wernli et al. 2008; Xu et al. 2005). Probabilistic sistant to improvements in model formulation. It has weather forecasts and climate projects are evaluated proved difficult to isolate cause and effect: that is, link- with statistical methods (Airey and Hulme 1995). We ing model formulation or model components to the seek to develop model evaluation strategies that identify presence or absence of a particular bias. For example, similar ‘‘objects’’: coherent systems with an associated a common experimental approach is to change some set of measurable parameters (Douglass 2000). This model component (e.g., the convective parameteriza- makes it possible to evaluate processes in models with- tion or dynamical core) and evaluate the impact of the out needing to reproduce the time and location of, for change on the global climate. Improvements are some- example, a particular observed cloud system. Process- times realized and other times they are not; there is an and object-based evaluation preserves information in ambiguous mix of results. quantitative analyses by avoiding the need for extensive This study is motivated by the hypothesis that there is spatial and temporal averaging. Of particular interest in a subset of the biases in climate simulations that are at our research is the interaction of the dynamical core the mechanistic level; that is, the bias is the manifesta- (Williamson 2007) and the physical parameterizations tion of a poor representation of quasi-local mechanisms and how the interaction changes as resolution is increased. We investigate the representation of the oro- Corresponding author address: M. Soner Yorgun, Space Re- graphic precipitation (Roe 2005) by spectral and finite search Building, 2455 Hayward Street, Ann Arbor, MI 48109-2143. volume dynamical cores (McGuffie and Henderson- E-mail: [email protected] Sellers 2005, 170–174; Neale et al. 2010).

DOI: 10.1175/JCLI-D-14-00051.1

Ó 2014 American Meteorological Society 9140 JOURNAL OF CLIMATE VOLUME 27

FIG. 1. (left) The study domain (North American west coast: 208–658N, 1008–1608W) and (right) California showing the California Coast Ranges, Central Valley, and Sierra Nevada (Google Maps).

We focus on the wintertime western U.S. orographic the problematic representation of the cloud micro- precipitation. This phenomenon is easy to isolate and physics by GCMs due to the finescale of occurrence of has known physical mechanisms and sufficient obser- these processes, orography introduces complexity re- vational data. The map of our study domain is given in garding the dynamics of the flow like the stable upslope Fig. 1. ascent and the partial blocking of the air mass. Other The area in the red circle is the California Coast typical finescale mechanisms include lee-side conver- Ranges along the shore and the Sierra Nevada, with the gence, convection triggered by solar heating, and con- Central Valley in between. During winter, synoptic- vection due to the lifting above the level of free scale storms propagate from the Pacific Ocean and the convection. The stable upslope ascent is a straightfor- lift from the topography causes precipitation on the ward mechanism of orographic precipitation and has upslope of the mountain ranges, with far less pre- been utilized in many modeling studies of this variable cipitation in the Central Valley. (Roe and Baker 2006; Smith 2003; Smith and Barstad Section 2 gives theoretical information about oro- 2004). Figure 2 shows a typical precipitation response to graphic precipitation and the object-based approach we a stable upslope ascent (Roe and Baker 2006). aim to implement. Section 3 introduces the idealized test case setups, the models used and their simulation of orographic precipitation. The discussion of results is given in section 4, and section 5 contains the conclusions.

2. Orographic precipitation and object-based analysis a. Orographic precipitation Orographic precipitation is a complex phenomenon because of the physical mechanisms involved, encom- passing ﬂuid dynamics, thermodynamics, microscale cloud processes, and topographical structure, as well as its dependence on the larger-scale patterns of the at- FIG. 2. Precipitation pattern for standard choice of parameters mospheric general circulation (Roe 2005). In addition to represented by the analytical model of Roe and Baker (2006). 15 DECEMBER 2014 Y O R G U N A N D R O O D 9141

21 FIG. 3. The 1979–2000 long-term-mean precipitation (mm day ) plots of (left) GPCC observations and (center) ﬁnite volume 0.58 model and (right) spectral T170 model run with CAM3 (Bala et al. 2008).

In Fig. 2, the moist air moves from left to right and is similar features in models and observations. This ap- lifted by the elevation on the windward side of the proach supplements the grid-level and grand-mean mountain. This causes the air column to be cooled, re- comparisons that are exemplified by many forecast sulting in condensation and precipitation. The peak evaluation techniques. These comparisons suffer from precipitation occurs at a distance before the mountain inadequacies such as loss of information on local biases peak. The air continues its movement over the mountain since the information is crunched to single numbers peak, leaving a significant portion of the moisture as (Gilleland et al. 2009). Here we identify features or ob- precipitation, and the descent on the leeward side of the jects that are representative of orographic precipitation mountain results in warming, which leads to suppression by two configurations of a GCM. We then pose an ide- of the precipitation. This forms the classic rain shadow, alized numerical experiment to investigate these features. which is observed in the study region (Fig. 1). The rain The identification of features consists of both shadow phenomenon is both observed and is consistent subjective (theory of orographic precipitation) and with underlying theory and understanding. This link objective input. The 21-yr (1979–2000) January-mean between observation and theory and how realistically it precipitation of two configurations of the Community is simulated drives our analysis. Atmosphere Model (CAM) (Bala et al. 2008) exhibits such features (Fig. 3). The configurations of the model in b. Object-based analysis Fig. 3 differ by the dynamical core, with one configuration Object-based analysis combines our theory-based using a finite volume (FV) core and the other using an mechanistic understanding of a meteorological feature, Eulerian spectral dynamical core. These dynamical cores with weather-scale observations describing the feature, are described in detail in the CAM model documentation and the morphology of how models represent the fea- (Neale et al. 2010). The two simulations are plotted along ture. These features are weather, and weather features with the Global Precipitation Climatology Centre are represented in climate models. The dynamics of the (GPCC) observations (limited to land) over our domain weather features organize the flow and hence pre- of interest (Rudolf et al. 2005; Schneider et al. 2013). cipitation. We define features such as fronts, rainbands, The CAM FV model and GPCC observations in Fig. 3 clouds in deep convection, etc., as objects (Posselt et al. have ;0.58 horizontal grid spacing, and the CAM Eu- 2012; Xu et al. 2005). These features can be composed of lerian spectral model has a T170 (;0.78) triangular clusters of small-scale processes in finer scales or they truncation. The color scale of the CAM Eulerian spectral can aggregate to form features that are observed in the model plot is reduced in order to show the structure of larger scale (Barros and Lettenmaier 1993). The pres- precipitation features better. The observed precipitation ence of small-scale structure in weather observations is concentrated on the coastline and closely linked to the provides powerful information on model performance mountain ranges on the western edge of the continent. that is both quantitative and qualitative. A focus on Closer examination of the observations shows similarities these as objects and how the objects relate to simulated with the simple description of orographic precipitation in and observed underlying structure allows us to look at Fig. 2. The rain is on the windward side of the mountains, 9142 JOURNAL OF CLIMATE VOLUME 27 associated with the moisture flux from the west. To the precipitation in the Atmospheric Model Intercomparison eastward (leeward) side of the mountains there is a rain Project (AMIP) runs to GCM structure. GCMs are shadow. In much of the western United States, the land to composed of multiple components that are connected the east of the mountains is semiarid or desert. together yielding a highly complex system. The two main The area in Fig. 3 (white circle) is the California Coast components of a GCM are the physical parameterization Ranges and the Sierra Nevada, with the Central Valley suite and the dynamical core. In this study, we focus on in between. In this region, the rain shadow is observed in the dynamical core component of the National Center for both the Central Valley and to the east of the Sierra Atmospheric Research (NCAR) CAM versions 3.0 Nevada. The highest point in the area is Mount Whitney (Collins et al. 2006) and 5.0 (Neale et al. 2010). The dy- in the Sierra Nevada with an elevation of 4421 m, and namical core can be defined as the ‘‘resolved fluid flow’’ the average width of the mountains is 105 km (including component of the model (Williamson 2007). CAM serves the valley between the mountains). The California as the atmospheric component of the Community Earth Coast Ranges provide the orographic lift to the im- System Model, which supports several dynamical cores, pinging moist air leading to precipitation. As a result of including the two used here. The two dynamical cores the smaller-scale dynamical and physical mechanisms under analysis—namely, CAM FV and CAM Eulerian taking place in between two mountain ranges, the re- spectral—were run in two different resolutions for each maining moisture (if any) undergoes a second lift over dynamical core: that is, 18 and 0.58 for CAM FV and T85 the Sierra Nevada, which is on average higher than the and T170 for CAM Eulerian spectral. The two dynamical California Coast Ranges. The CAM Eulerian spectral cores were coupled with a reduced moist parameteriza- dynamical core in Fig. 3 created a big blob of pre- tion suite (‘‘Simple Physics’’) that was used to test the cipitation with the precipitation over the mountain simulation of tropical cyclones by GCMs and the effect of ranges combined into a single large precipitation fea- the dynamical core (Reed and Jablonowski 2012). CAM ture. On the other hand, the CAM FV model produced allows us to couple a simpler version of physics pa- a narrow band of precipitation over the mountain range rameterization with a dynamical core in order to assess 2 with a higher peak value (10 mm day 1)thanthatofthe the capabilities of each dynamical core and compare 2 CAM Eulerian spectral model (8.5 mm day 1). This them to each other in terms of simulation of orographic ‘‘spread out’’ effect in the CAM Eulerian spectral model precipitation. was also discussed by (Bala et al. 2008). The precipitation a. CAM Eulerian spectral feature produced by the CAM FV model visually represents the observations better than the CAM Eulerian In spectral models global basis functions are used to spectral model: it looks more realistic. The monthly- describe the spatial structure of the variables and hence mean plots (not shown) illustrate that this type of be- information from both upstream and downstream in- havior for the CAM FV and CAM Eulerian spectral fluences a particular point in space. Computational flow models is typical throughout the 21-yr period. As a result, of a spectral GCM proceeds as the data fields are the precipitation over the California Coast Ranges and transformed to grid space at every time step via fast Sierra Nevada is a good candidate for further analysis. Fourier transforms and Gaussian quadrature (a form of We use idealized GCM runs to provide analogs to the numerical integration) and back to spectral space via features to be investigated. For this purpose, a modification Legendre transforms and Fourier transforms (McGuffie tothemountainRossbywavetestcase(Jablonowski et al. and Henderson-Sellers 2005, 170–174). Vertical dis- 2008) was implemented to create suitable conditions of cretization is achieved via finite differences on a hybrid wind, moisture flux, and topography. The simpler—and coordinate system (Neale et al. 2010). Spectral har- controlled—experiments reveal relationships between the monics are susceptible to Gibbs oscillations, and spec- simulation of orographic precipitation and the components tral models are prone to produce unrealistic oscillatory of GCMs, including sensitivity to the dynamical core, the results especially when dealing with sharp gradients numerical representation of topography, and the complex- (e.g., orographic precipitation). Models employ differ- ity of the topography. We leave quantitative descriptions of ent forms of dissipation/diffusion to mitigate these ef- the simulation differences to part II of this study (Yorgun fects together with other numerical noise generated by and Rood 2014, manuscript submitted to J. Climate). dispersion errors or computational modes. Explicit diffusion with varying coefficients (such as second-, fourth-, or higher-order coefficients) is widely used to remove 3. Idealized test cases Gibbs oscillations in spectral models (Jablonowski and The idealized cases are the second step of our object- Williamson 2011). Relevant to our study, models also based approach and link the representation of orographic apply a terrain filter, which is an adoption of a monotonic 15 DECEMBER 2014 Y O R G U N A N D R O O D 9143

filter (Bala et al. 2008), to get a smoother topography, turbulence surface momentum fluxes, evaporation of thus damping the gradients to reduce Gibbs oscillations. water vapor at the surface, and kinematic eddy sensible These filters, useful in removing noise, create a trade-off heat fluxes are approximated by the bulk formulas. The between numerical artifacts, accuracy, and physical re- boundary layer is defined as all the levels with pressure alism, which will be discussed in section 4,wherethere- values greater than 850 hPa and the effect of boundary sults of our idealized test cases are presented. layer diffusion is tapered to zero above the 850-hPa level. There is no parameterized convection scheme. b. CAM FV The details of these parameterizations can be found in Lin (2004) developed a multidimensional flux-form Reed and Jablonowski (2012). The surface flux of semi-Lagrangian transport, finite volume method, which evaporation especially is an effective process in creating is a generalization of one-dimensional (1D) FV schemes precipitation over the mountains. Because our test cases to multiple dimensions combined with an efficient al- are on an aquaplanet setting (Neale and Hoskins 2000), gorithm to reduce the stringent time step stability re- the mountains are covered with water, and this leads to quirements. The algorithm aimed to conserve mass the reinforcement of the moisture in the lower atmo- without a posteriori restoration, compute fluxes based sphere via surface fluxes. This is analogous to a well- on the subgrid distribution in the upwind direction, known phenomenon called precipitation recycling, generate no new maxima or minima, preserve linear which is the contribution of evaporation within a region tracer correlations, and be computationally efficient in to precipitation in that same region (Bosilovich et al. spherical geometry (Lin and Rood 1996, 1997) The re- 2003; Eltahir and Bras 1996). This is observed in all cases sulting multidimensional scheme is free of the Gibbs in this study and gives valuable insight as to how it is oscillations (with the optional monotonicity constraint), simulated by different dynamical cores with varying mass conserving, and stable for a Courant number greater resolution. All experiments were conducted using 26 than one in the longitudinal direction, which made the hybrid vertical model levels. The physics and dynamics scheme competitive for the intended application on the time steps for CAM Eulerian spectral model are iden- sphere. The vertical discretization is Lagrangian with tical, and they are 1800 and 300 s for T85 and T170, re- a conservative remapping, which essentially makes it spectively. For the CAM FV model, the physics time quasi-Lagrangian (Neale et al. 2010). Rasch et al. (2006) steps are 1800 and 600 s and the dynamics time steps are compared the tracer transport properties of spectral, 180 and 60 s for 18 and 0.58, respectively. The total model semi-Lagrangian, and FV numerical methods in CAM3.0. run was for 30 days. They found that the FV core is, unlike spectral and semi- Lagrangian, conservative and less diffusive. It also accu- d. Test case setup rately maintains the nonlinear relationships (required by The initial conditions are similar to the mountain- thermodynamic and mass conservation constraint) among induced Rossby wave train test case (Jablonowski et al. conserved and nonconserved variables that are influenced 2008), which are similar to initial conditions by Tomita by adiabatic and nonadiabatic processes. and Satoh (2004). The main difference is the derivation c. Physics parameterization of the surface pressure for hydrostatic conditions. The simulation starts from smooth isothermal initial condi- As previously mentioned, the physical parameterizations that are a balanced analytic solution to the primi- tion is set to a simplified moist parameterization suite tive equations. called Simple-Physics suite (Reed and Jablonowski The horizontal wind components are prescribed as 2012) for both CAM FV and the CAM Eulerian spectral dynamical core. The suite allows physical processes that u(l, f, h) 5 u cosf and (1) are important for orographic precipitation (i.e., large- 0 scale condensation, boundary layer turbulence of hori- y l f h 5 21 zontal momentum, temperature, and specific humidity) ( , , ) 0ms , (2) and surface fluxes of horizontal momentum, evaporation (specific humidity), and sensible heat (temperature) where l, f, and h are longitude, latitude, and hybrid 21 from the surface to the lower atmosphere. model level, respectively, and u0 is a constant 20 m s Large-scale condensation is parameterized to occur for all experiments. The meridional wind is set to zero when the atmosphere becomes saturated. The atmo- initially. The experiments were run on an aquaplanet spheric profiles of moisture, temperature, and winds are setting where the temperature is isothermal given by not relaxed to specified states; therefore, they are T(l, f, h) 5 T0 5 288 K. This yields the constant Brunt– allowed to evolve throughout the model runs. The eddy Väisälä frequency (N) 9144 JOURNAL OF CLIMATE VOLUME 27

TABLE 1. The mountain speciﬁcations for three experimental setup cases.

Center point in Center point in latitude l f longitude ( c) ( c) Peak height (h0) (m) Half-width (km) Case No. 1st peak 2nd peak 1st peak 2nd peak 1st peak 2nd peak 1st peak 2nd peak 1978E—308N — 1500 — 1500 — 2908E978E308N308N 1500 1500 1500 1500 3908E938E308N308N 500 3000 500 500

sffiffiffiffiffiffiffiffiffiffi " 2 2 g 2 aN u u N 5 ’ 0:0182 s 1 , (3) p (l, f) 5 p exp 2 0 0 1 2V ( sin2f 2 1) c T s sp 2g2k a p 0 # N2 where g is the gravitational acceleration and cp is the 2 F (l, f) , (6) g2k s specific heat at constant pressure. The vertical temperature profile is also isothermal thus the atmosphere k has a zero lapse rate. The waves are triggered by ideal- where is the ideal gas constant for dry air (Rd) divided 2 V5 ized Gaussian bell–shaped mountains. The mountains by specific heat at constant pressure (cp) and is /7; 3 25 21 induce the disturbance to the initial conditions to create 7.292 12 10 s (Earth’s angular velocity); and psp baroclinic waves in the leeward side. The idealized denotes the surface pressure at the South Pole, which is Gaussian bell mountain is introduced via surface geo- set to 930 hPa. The moisture, which triggers the orographic precipitation, is initialized via specific humidity potential (Fs), calculated as F l f 5 5 2 2 s( , ) gzs gh0 exp[ (r/d) ], (4) q p q 5 0 , (7) ps,0 where zs is the surface height, h0 is the peak height of the mountain, and d is the half-width of the Gaussian where q is the specific humidity, p is a pressure level, ps,0 mountain profile. The term r is defined as the great circle is a reference surface pressure (1000 hPa), and q0 is the distance, specific humidity at the surface when the relative hu- 5 f f 1 f f l 2 l midity equals 80%. r a arccos[sin c sin cos s cos cos( c)], (5)

f l where a is Earth’s radius and c and c are center points 4. Discussion of idealized setup results in latitude and longitude, respectively. The mountain a. Case 1: Single mountain specifications for each setup are given in Table 1. The test cases are set up to progress from simple to- Figure 4 shows the surface geopotential overlaid by ward more complex to observe the evolution of com- 30-day-mean precipitation for CAM Eulerian spectral plexity in the simulation of orographic precipitation by T85 and T170 and CAM FV 18 and 0.58 resolutions. different models. The first case with a single mountain Surface geopotential contours (topography) are 5 3 102, 2 represents stable upslope ascent precipitation on the 2 3 103,53 103, and 11 3 103 m2 s 2 throughout all windward side of the mountain as well as the rain plots. Stable upslope ascent precipitation features are shadow on the leeward side. The baroclinic waves in- observed in all simulations on the northward and duced by the mountain also create precipitation after windward side of the mountains. The large-scale pre- some distance. The second case has a second mountain cipitation is initiated at the start of the simulation, peak of the same height in front of the first one to ob- moves northward, and loses intensity as the simulation serve the smaller-scale dynamics and the distribution continues. The intensity of the precipitation feature of precipitation between the two peaks. The third simulated by CAM Eulerian spectral T85 is significantly (‘‘realistic’’) case contains two mountains; however, the lower than that of other runs. This is mostly due to the altitudes resemble those of the California Coast Ranges spectral filtering applied to the topography: the effect of and the Sierra Nevada. which will be discussed in the next section (case 2). The The surface pressure field balances the initial condi- intensity for CAM Eulerian spectral T170 is lower than tions. For hydrostatic primitive equation models, it is that of both CAM FV models. The simulation is almost given by identical for CAM FV 18 and 0.58 resolutions in terms of 15 DECEMBER 2014 Y O R G U N A N D R O O D 9145

21 FIG. 4. The 30-day-mean total precipitation (mm day ) and surface geopotential for case 1 of experimental test cases, simulated by (a) CAM Eulerian spectral T85, (b) CAM Eulerian spectral T170, (c) CAM FV 18, and (d) CAM FV 0.58. both the shape and the intensity of the features. This features due to baroclinic waves (type 3) started to ap- difference in intensity between spectral and FV cores pear periodically as the simulation went on. These three was observed in AMIP runs (Fig. 3). This idealized feature types are all different in their origin and thus simulation also indicates the high sensitivity to resolu- present valuable insight in terms of their difference be- tion for spectral models. tween each dynamical core as they point toward a dif- Examining a daily precipitation plot (Fig. 5) reveals ferent aspect of models. Coarser-resolution models information about the types of simulated features: some (CAM Eulerian spectral T85 and CAM FV 18) do not of which are not apparent in the monthly-mean plot. simulate the small-scale features, although some very These feature types (as indicated by their corresponding low intensity precipitation can be observed for CAM FV numbers in Fig. 5d) are as follows: 18 model on the mountain peak. The ﬁner-resolution models simulate these features, but with the differ- 1) large-scale features due to stable upslope ascent; ence of CAM Eulerian spectral T170 simulating them 2) small-scale features due to local evaporation and lee- with larger spatial extent and higher intensity when side convergence; and compared to that of CAM FV 0.58. This sensitivity to 3) features due to leeward baroclinic waves. intensity is contrary to what is observed with the large- scale stable upslope ascent features. All models pro- The picture in Fig. 5 is different than Fig. 4, where the duced the features due to baroclinic waves (CAM FV 18 stable upslope ascent precipitation features (type 1) lost seems to have missed them in Fig. 5; however, they ap- intensity and moved northward, the small-scale features pear in other days because of the periodic nature of this (type 2) started to emerge (around day 18), and the phenomenon). 9146 JOURNAL OF CLIMATE VOLUME 27

21 FIG. 5. Day-23 total precipitation (mm day ) and surface geopotential for case 1 simulated by (a) CAM Eulerian spectral T85, (b) CAM Eulerian spectral T170, (c) CAM FV 18, and (d) CAM FV 0.58. Day 23 is selected because of the explicit appearance of the features of interest.

To understand these differences, it is essential to un- equation for water vapor using the material derivative derstand the genesis and evolution of these features. and the continuity equation on generalized vertical co- Vertical pressure velocity (v), moisture flux conver- ordinates (Collins et al. 2006), gence (MFC), and zonal winds were plotted for the lowest model level and are given in Fig. 6. › ›p 1 › ›p › ›p 8 q 52 uq 1 yq cosf Diagnostics for CAM FV 0.5 are chosen to explain ›t ›h a cosf ›l ›h ›f ›h the evolution of features because it has all the features › › : › simulated. There is negative pressure velocity, upward 2 p h 1 2 p ›h q ›h (E P) ›h, motion (Fig. 7b), on the windward side of the mountain, where the large-scale precipitation feature is observed. (8) This is consistent with the stable upslope ascent process and the subsequent condensation/precipitation ex- where q is the specific humidity, E is evaporation, and P: plained in section 2a (Fig. 2). is precipitation. The term h represents the model level, h MFC is a prognostic quantity for forecasting convec- is dh/dt, Vh is the horizontal velocity vector, $ is the two- tive initiation, with an emphasis on determining the fa- dimensional gradient on constant h surfaces, and ›p /›h vorable spatial location(s) for such development is the hybrid vertical coordinate pseudo density. This (Banacos and Schultz 2005). In our study, we use this equation is an expression of the moisture budget of an quantity as a diagnostic to understand the behavior of air parcel. All terms in this equation are divided by g the small-scale features appearing on the peak of our (gravitational acceleration); thus, the MFC unit is 2 2 mountains. MFC can be derived from the conservation kg m 2 s 1. The first, bracketed term in the right-hand 15 DECEMBER 2014 Y O R G U N A N D R O O D 9147

FIG. 6. Day-23 (a) total precipitation, (b) vertical pressure velocity (v), (c) MFC, and (d) zonal velocity (U) overlaid by surface geopotential for case 1 simulated by CAM FV 0.58. side of the above equation is the MFC and is plotted in evaporation over the mountain peak where pre- Fig. 6c. We calculated the surface MFC on the lowest cipitation is observed. These small-scale features, unlike hybrid model level. The second term is the vertical the large-scale stable upslope ascent features, remain MFC. MFC has traditionally been calculated as a verti- stationary after their inception. However, there is cally integrated quantity (Frankhauser 1965; Hudson a convergence of zonal wind (Fig. 6d) around the 1970); however, Newman (1971) calculated the surface mountain toward the leeward side. This convergence of MFC to be able to make use of high-resolution temporal the zonal winds transport moisture to this area repre- and spatial observations of the lower-level atmosphere. senting another mechanism of orographic precipitation: The majority of the studies computed surface, not ver- that is, lee-side convergence (Roe 2005). Also, addi- tically integrated, MFC since then. Given the variable of tional model runs were made with varying the surface interest being total precipitation on the surface in our temperature of the aquaplanet setting, which showed study, we also calculated surface MFC to be able to have increased intensity of these small-scale precipitation a sensible diagnosis. features with increasing temperature. Reducing the The small-scale precipitation features (type 2) in surface temperature led to the disappearance of these Fig. 5 have complex and multiple underlying causes. The features. This sensitivity of the surface ﬂux parameteri- location of peak convergence of moisture ﬂux in Fig. 6c zation in the simple physics suite to temperature dem- (on the mountain peak) is where the small-scale pre- onstrates the role of local evaporation. Therefore, these cipitation is observed. Previous studies also showed small-scale features are labeled as features due to local a strong relationship between surface MFC and the evaporation and lee-side convergence. precipitation (Becker et al. 2011; Bhushan and Barros As summary for this initial case, we were able to ob- 2007; Holman and Vavrus 2012). This convergence can serve and identify causes and evolution of orographic have multiple reasons, such as moisture transport from precipitation features observed in AMIP runs in Fig. 3. the moist air impinging on the mountain and local The small-scale precipitation features (type 2) were lost 9148 JOURNAL OF CLIMATE VOLUME 27

21 FIG. 7. The 30-day-mean total precipitation (mm day ) and surface geopotential for case 2 simulated by (a) CAM Eulerian spectral T85, (b) CAM Eulerian spectral T170, (c) CAM FV 18, and (d) CAM FV 0.58. via averaging in Fig. 3; however, the large-scale upslope simulated by CAM Eulerian spectral T170. There is al- features (type 1) were apparent. The features due to the most a total merge in CAM Eulerian spectral T85 with 2 baroclinic waves (type 3) were inherent to the setup we relatively low peak intensity (1 mm day 1), whereas created and do not have easy analogs in the AMIP runs features of the other three simulations have peak in- 2 we examined. tensities at around 1.7 mm day 1. The main reason for the difference at the spectral b. Case 2: Double mountain resolutions is the spectral filtering applied to the to- Figure 7 shows the surface geopotential and 30-day- pography for the spectral model. To understand the ef- mean total precipitation (as in Fig. 5) for case 2, two fect of topographic filtering, additional model runs were mountains of the same size. The large-scale stable up- made with CAM Eulerian spectral T85 and T170 with- slope ascent precipitation features appear in this case as out the topographic filtering (Fig. 8). separate features on the windward side of each moun- The filtering reduces the peak height of CAM Euler- tain. The features in front of the eastward, downstream ian spectral T85 by 243 m, which is 16% of the total peak are lower in intensity and smaller in extent as the height of the mountain (the reduction is 42 m for CAM moist air precipitates at the first peak. Daily pre- Eulerian spectral T170). The spectral filtering for cipitation plots (not shown) exhibit these features ap- smoothing the topography in CAM5.0 is a two- pearing in front of the peaks on day 1 with high intensity. dimensional filter applied to the Fourier and Legendre They then move northward and lose intensity every day. coefficients equally and is only a function of the total The large-scale features simulated by CAM Eulerian wavenumber. Such filters are effective, but they are spectral T170 are similar to CAM FV; however, there is shown to result in strong smoothing and do not guar- a higher amount of merging between the two features antee shape preservation of the horizontal features 15 DECEMBER 2014 Y O R G U N A N D R O O D 9149

21 FIG. 8. The 30-day-mean total precipitation (mm day ) and surface geopotential for case 2 simulated by (a) CAM Eulerian spectral T85 and (b) CAM Eulerian spectral T170 without the spectral ﬁltering applied to topography.

(Navarra et al. 1994). The effect of removing the spectral start to form at the peak points of the mountains as filtering is especially apparent in CAM Eulerian spectral apparent in Figs. 7b,d. The second mountain leads to T85 precipitation plot (Fig. 8a; cf. Fig. 7a), where the small-scale dynamics, especially in between the two mountains are more structured and two the large-scale mountains (Fig. 10d). features in front of each mountain are more distinct in Figure 10 shows diagnostic measures as in Fig. 6. The the case of unfiltered topography. However, these fea- more structured manifestation of smaller-scale features tures still have relatively low intensity when compared compared to case 1 (Fig. 5), over both mountain peaks is to other three simulations. The peak precipitation apparent in Fig. 10a. A similar manifestation can also be values of the two large-scale features for CAM Eulerian observed in MFC in Fig. 10c, because of the smaller- spectral T170 (Fig. 8b) increased with the steeper to- scale local dynamics. In addition to the surface flux pa- pography. The change in the topography of CAM Eu- rameterization of the simple physics suite feeding lerian spectral T85 as a result of filtering can also be moisture back to the atmosphere, turbulence can also observed via the surface geopotential plot (Fig. 9). play a role in making the smaller-scale features more The orographic precipitation simulated by CAM structured. Houze and Medina (2005) showed that, even Eulerian spectral T170 strongly resembles CAM FV if a stable flow impinges on the mountains, it can models due to the setup of the case 2, which is not observed in the AMIP runs given in Fig. 3. The mountains in case 2 are larger than the real topography and the related precipitation due to impinging airflow is easily resolvable for a fine-resolution spectral model. The separation distance between the two mountains is another parameter affecting the distribution of precipitation. The first mountain is located at 908E and the second is located at 978E, which allows a 10 gridpoint distance between them for CAM Eulerian spectral T170 and a 5 gridpoint distance for CAM Eulerian spectral T85. Having 10 grid points for CAM Eulerian spectral T170 allows for better resolution, so it was able to simulate the dryer region. As the simulation proceeds, smaller precipitation features start to form after day 10 for all models except CAM Eulerian spectral T85 (they are not as apparent FIG. 9. The surface geopotential vs longitude plot of CAM Eu- for CAM FV 18 because of their relatively lower values lerian spectral T85 for filtered (blue) and unfiltered (red) topog- thus being lost in the 30-day-mean plots). These features raphy. The latitude is 308N, where the mountains have peak height. 9150 JOURNAL OF CLIMATE VOLUME 27

FIG. 10. Day-23 (a) total precipitation, (b) vertical pressure velocity (v), (c) MFC, and (d) zonal velocity (U) overlaid by surface geopotential for case 2 simulated by CAM FV 0.58. organize itself to produce a layer of smaller-scale cel- CAM FV resolutions were able to create distinct moun- lular overturning because of either shear-induced tur- tains separated from each other. The CAM Eulerian bulence or buoyancy oscillations in the shear layer that spectral T170 has connected the two mountains, leaving are forced by the lower terrain. 5 grid points between peaks and CAM Eulerian spectral Case 2 revealed that the size and the grid spacing T85 merged the mountains into one (geopotential con- between the two mountains significantly affect the sim- tours in Figs. 11a,b). This shows that, as the topography ulation of orographic precipitation as well as the treat- gets smaller and structured, the ability of all models to ment of topography (i.e., the spectral filtering). We have simulate orographic precipitation is reduced. The CAM yet to see the merging of the large features due to stable FV dynamical core represents the spatial structure and upslope ascent in front of each mountain peak for CAM relationship with underlying topography more realistically Eulerian spectral T170. However, as we move toward than the CAM Eulerian spectral dynamical core (Fig. 3). less resolvable scales (case 3) that are more resembling In case 2, there was the suggestion that topographical of California Coast Ranges and the Sierra Nevada re- filtering adversely affects the simulation of orographic gion, the differences between CAM FV and CAM precipitation. In case 3, the CAM Eulerian spectral core Eulerian spectral models become more apparent. run without the filter, introduced significant amounts of noise due to Gibbs oscillations, thus producing smaller- c. Case 3: Realistic scale precipitation features that dominate the entire field In this case the differences between CAM FV and in a short period of simulation time. Therefore, without CAM Eulerian spectral models are much more apparent the topography filter, the simulation is not realistic. (Fig. 11). Both CAM FV model resolutions were able to In case 3, there are significant differences between two simulate the dry region between the mountains, whereas resolutions of the CAM FV model. In both CAM FV there is a merge between two precipitation features in simulations, a precipitation feature occurs at the peak of the cases of CAM Eulerian spectral T85 and T170. Both the first, westward, mountain, which is lower than the 15 DECEMBER 2014 Y O R G U N A N D R O O D 9151

21 FIG. 11. The 30-day-mean total precipitation (mm day ) and surface geopotential for case 3 simulated by (a) CAM Eulerian spectral T85, (b) CAM Eulerian spectral T170, (c) CAM FV 18, and (d) CAM FV 0.58. second mountain. On the second mountain, two sepa- CAM Eulerian spectral T170 (Fig. 12d): there is no rate precipitation features are observed over both the precipitation over the first mountain but it is apparent north and south ends of the Gaussian bell shape. The over the second mountain, creating the single large features simulated by CAM FV 18 are significantly lower precipitation peak observed in Fig. 12b. The reason we in intensity when compared to CAM FV 0.58. This sep- do not observe such single precipitation feature for CAM aration of large-scale stable upslope ascent features into FV simulation (Fig. 12a) is the structured manifestation two is not observed in either CAM Eulerian spectral of both vertical velocity and the MFC (Fig. 12e)overthe simulation; there is one large-scale feature related to second mountain. Both stable upslope ascent and surface each mountain peak as in the previous cases. These fluxes contribute to the organization of the precipitation large-scale features are connected to the ones simulated for the CAM FV model, and both convergence/divergence over the first mountain peaks, creating a wet region boundaries and the negative vertical velocities occur between the mountains in both CAM Eulerian spectral at both tails of the second mountain, producing pre- simulations as opposed to the dry region in the CAM FV cipitation features over that area. models. To understand these differences, total precipitation, vertical velocity, and MFC are plotted for 5. Conclusions both CAM FV 0.58 and CAM Eulerian spectral T170, for day 3. In this study, we aim to identify the local biases in- The negative vertical pressure velocity (upward mo- herent to GCMs, with a focus on dynamical cores, by tion) at the windward side of the first mountain of CAM qualitatively assessing and comparing their performance in FV 0.58 simulation leads to the large-scale stable upslope simulating orographic precipitation. We used observations ascent precipitation (Fig. 12c). This is not the case for and results of AMIP runs over a specific local area that 9152 JOURNAL OF CLIMATE VOLUME 27

FIG. 12. Day-3 total precipitation, vertical pressure velocity (v), and MFC overlaid by surface geopotential, for case 3 simulated by (a),(c),(e) CAM FV 0.58 and (b),(d),(f) CAM Eulerian spectral T170. introduces challenging conditions for GCMs (California understanding about the sources of biases related to Coast Ranges and Sierra Nevada) as reference simulations GCM structure and how the biases evolve with varying of orographic precipitation to be tested via idealized setups resolution. CAM FV model simulations resembled with CAM Eulerian spectral and CAM FV dynamical observations, producing precipitation consistent with cores in varying resolutions using a simple physics pa- underlying topography as well as the dry regions. The rameterization. Our conclusions can be summarized as fine-resolution CAM Eulerian spectral model ex- follows: hibited similar behavior, when the mountains were well separated and the same height (cases 1 and 2). The d We were able to reproduce the large-scale stable CAM Eulerian spectral simulation developed biases upslope ascent precipitation features present in ob- similar to the AMIP simulations when the mountains servations and simulated in AMIP runs (Fig. 3). The were of different height and closer together (case 3). It simulation of small-scale features was also observed in was also noted that the effect of resolution is much the idealized experiments. We were able to identify more pronounced for CAM Eulerian spectral models the origins of these features via orographic precipita- compared to CAM FV models, because the improve- tion theory and diagnostic measures and classify them ment of results from T85 to T170 was significant while as 1) large-scale features due to stable upslope ascent, CAM FV 18 and 0.58 consistently produced similar 2) smaller-scale features due to local surface fluxes, results. and 3) leeward side features due to baroclinic waves. d The merger of two large-scale stable upslope ascent d Examination of the differences in simulation of these features observed in AMIP runs for CAM Eulerian features by CAM FV and CAM Eulerian spectral spectral T170 were not observed in case 2, where dynamical cores with varying resolutions led to deeper mountains were well separated. Furthermore in case 2, 15 DECEMBER 2014 Y O R G U N A N D R O O D 9153

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