1. Introduction

Orographic precipitation is the precipitation caused or enhanced by moist airflow past topography (Colle et al. 2013). It frequently occurs in mountainous regions, such as the east coast of East Asia (Kuo and Chen 1990; Lin et al. 2002), the west coast of North America (Galewsky and Sobel 2005; Ralph et al. 2006), and the Alpine region of Europe (Bougeault et al. 2001; Rotunno and Houze 2007). For these regions, orographic precipitation is not only an important source of freshwater (Dettinger et al. 2011), but sometimes the cause of floods and other devastating effects (Colle and Mass 2000; Ge et al. 2010; Ralph et al. 2013).

Saturated, nearly moist-neutral flow is also frequently observed in orographic precipitation events (Sawyer 1956; Doswell et al. 1998; Rotunno and Ferretti 2001; Ralph et al. 2005; Rotunno and Houze 2007). By definition, a moist-neutral profile is neutral with respect to saturated adiabatic process. It is worth mentioning that such a profile is stable with respect to the dry adiabatic process. Compared to the studies of conditionally unstable flow or stable flow, there are substantially fewer studies focusing on the dynamics and precipitation associated with saturated, nearly moist-neutral flow (Colle 2004; Miglietta and Rotunno 2005, 2006, hereafter MR05, MR06, respectively; Tushaus et al. 2015). In an idealized numerical study of saturated, nearly moist-neutral flow over a ridge (MR05), it was shown that when the mountain height was less than 250 m, the whole atmosphere could remain saturated, provided that the atmosphere initially contained a small amount of cloud water. In this situation, the flow is well described by linear theory. When the mountain height was between 250 and 1500 m, an upstream-propagating disturbance desaturated the atmosphere. When the mountain height was greater than 1500 m, the whole atmosphere upwind of the mountain remained saturated while the lower troposphere downwind of the mountain became desaturated. Furthermore, MR06 showed that the inclusion of the Coriolis force suppressed the upstream-propagating disturbance.

In previous studies that used nearly moist-neutral profiles to initialize simulations, three types of relative humidity profile have been considered: 1) as mentioned above, MR05 and MR06 considered the profile to be saturated from the surface to model top; 2) Colle (2004) considered the profile to have a constant relative humidity (98%) from the surface to model top; and 3) Morales et al. (2018) considered the profile to have a constant relative humidity (95%) below 4.5 km and have a decreasing relative humidity in the upper layer. As shown in those studies, these three types of profiles closely approximate some observed profiles.

Microphysics is also found to play an important role in orographic precipitation (Xue et al. 2010; Houze 2012; Stoelinga et al. 2013; Berg et al. 2017). MR06 compared liquid-only (without ice-phase microphysics) simulations to mixed-phase (with both liquid-phase and ice-phase microphysics) simulations. Their results showed that the inclusion of ice-phase microphysics substantially changed the distributions of updraft and cloud water mixing ratio. The inclusion of ice-phase microphysics generally shifted the surface precipitation farther upwind. The sensitivity study by Morales et al. (2018) showed that increasing the fall speed of snow particles also shifted the surface precipitation farther upwind.

This study investigates another type of relative humidity profile that is also observed to be associated with nearly moist-neutral flow. Unlike the three types of profiles mentioned above, this type of profile has a subsaturated, low-level layer below a saturated, upper-level layer. Figure 1a shows a sounding obtained from the west coast of North America. From 750 to 400 hPa, the profile is nearly moist neutral and saturated. Below 750 hPa, the profile is also nearly moist neutral but subsaturated. This low-level layer is stably stratified with respect to dry adiabatic process. Figure 1b shows another sounding obtained from the west coast of North America. From 800 to 400 hPa, the profile is also nearly moist neutral and saturated. Below 800 hPa, the temperature profile follows a dry adiabatic profile, and the air is subsaturated. Such a low-level layer is neutrally stratified with respect to dry adiabatic process.

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(a) Sounding at 0000 UTC 18 Mar 2017 at Medford, Oregon. (b) Sounding at 0000 UTC 27 Nov 2016 at Medford, Oregon. Blue lines show the temperatures and green lines show the dewpoint temperatures.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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In section 2 we describe the methods used herein. Section 3 describes the mechanisms through which the subsaturated low-level layers affect the dynamics and precipitation. In sections 4 and 5, the surface precipitation of the liquid-only simulations and the mixed-phase simulations are respectively described. In section 6, a prominent phenomenon taking place in the simulations is discussed in terms of linear theory. A summary of the major findings is given in section 7.

2. Methods

The simulations were conducted with version 3.9.1 of the Weather Research and Forecasting (WRF) Model (Skamarock et al. 2008). The model is configured to simulate a two-dimensional (2D) flow. In the present simulations, the length and depth of the domain are 2000 and 20 km, respectively. The horizontal and vertical grid lengths are 2 and 0.25 km, respectively. A damping layer is used in the uppermost 5 km to reduce the reflection of upward-propagating gravity waves. Following MR05, second-order diffusion is used with horizontal and vertical diffusion coefficients of 3000 and 3 m² s⁻¹, respectively. The lateral boundary conditions are radiative “open” conditions. The bottom boundary condition is free slip. The time step is 20 s for advection and 2 s for acoustic waves. It has been shown that this model configuration could well resolve saturated, nearly moist-neutral flow (MR05; MR06). In addition, each simulation was run for 40 h. Except for the simulations where the decelerated region on the upwind side of the mountain continuously moved upwind, the simulations reached steady state after 20 h. Thus, the results at 20 h are presented below.

Microphysics is represented with the Morrison two-moment scheme (Morrison et al. 2005, 2009), which predicts the mass mixing ratios and number concentrations of cloud droplets, rain droplets, ice crystals, snow particles, and graupel. The microphysics scheme can run in either a liquid-only scenario or a mixed-phase scenario. In the liquid-only scenario, the formation of precipitation relies on the autoconversion process, through which cloud droplets are automatically converted to rain droplets, provided that the cloud water mixing ratio is sufficiently large. The rain droplets can then grow through the accretion process (i.e., the rain droplets grow by collecting cloud droplets) and finally produce surface precipitation. In the mixed-phase scenario, ice crystals can heterogeneously form through immersion freezing, contact freezing, and deposition nucleation. When the temperature is lower than −40°C, ice crystals can also form through homogeneous freezing of cloud droplets. A complex chain of cold cloud processes can then lead to the formation of surface precipitation. In this study, we first ran the model in a liquid-only scenario. This was done in order to simplify the analysis of the dynamical processes. We then ran the model in a mixed-phase scenario to study the effect of ice-phase microphysics on the dynamics and precipitation.

The initial profiles with subsaturated low-level layers were obtained by modifying the saturated, nearly moist-neutral profiles. We first discuss the calculation of the saturated, nearly moist-neutral profiles. In the liquid-only simulations, the profile is saturated with respect to water from the surface to model top. It was calculated based on the method in MR05, except that the saturation vapor pressure was given by the empirical formula (Flatau et al. 1992) that was used in the Morrison microphysics scheme. In the mixed-phase simulations, as in MR06, the profile is saturated with respect to water below the freezing level, but is saturated with respect to ice above the freezing level. The saturation vapor pressure over ice was calculated with another empirical formula from Flatau et al. (1992). Following MR05 and MR06, the moist Brunt–Väisälä frequency used in the calculation of the saturated, nearly moist-neutral profile is $\sqrt{3}\hspace{0.17em}\mathrm{\times }{\mathrm{10}}^{\mathrm{-3}}\hspace{0.17em}{\mathrm{s}}^{\mathrm{-1}}$.

The layer below a transition height z_t was made subsaturated. This was done by setting the water vapor mixing ratio in this layer to the water vapor mixing ratio at z_t. The temperature profile was obtained using the dry Brunt–Väisälä frequency of the low-level layer N₂ and the hydrostatic approximation. As discussed in section 1, the subsaturated low-level layer can be either stable or nearly neutral with respect to dry adiabatic lifting. Based on this observation, we considered three values for N₂: 1.2 × 10⁻², 0.8 × 10⁻², and 0.4 × 10⁻² s⁻¹. The value of 1.2 × 10⁻² s⁻¹ is approximately the dry Brunt–Väisälä frequency of the nearly moist-neutral profile. In addition, no N₂ < 0.4 × 10⁻² s⁻¹ is considered because our results indicate that the simulations with N₂ < 0.4 × 10⁻² s⁻¹ are similar to those of the simulations with N₂ = 0.4 × 10⁻² s⁻¹. Six values of z_t were used: 0, 0.5, 1.0, 1.5, 2.0, 2.5 km. Note that the subsaturated layer is always below the freezing level (~3 km).

Figures 2a–c show the initial profiles of temperature and dewpoint temperature for the liquid-only simulations. Above z_t, the dewpoint temperature profile is the same as the temperature profile. Figures 2d–f show the initial profiles for the mixed-phase simulations. Above the freezing level (~700 hPa), the dewpoint temperature is lower than the temperature. This is because the saturation vapor pressure over ice is lower than that over water. The saturation ratio over water decreases from 100% at the freezing level to 53% at 11.5 km. In Figs. 2d–f, the dewpoint temperatures near 200 hPa are higher than expected because the formula used to calculate the saturation vapor pressure is cut off at −80°C. In all simulations, only cross-mountain wind was considered. Two wind speeds, 10 and 20 m s⁻¹, were used. These two wind speeds are commonly in studies investigating orographic precipitation (e.g., Jiang 2003; Colle 2004).

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Initial thermodynamic profiles (solid lines for temperature; dashed lines for dewpoint temperature) used in the liquid-only simulations with (a) N₂ = 1.2 × 10⁻², (b) N₂ = 0.8 × 10⁻², and (c) N₂ = 0.4 × 10⁻² s⁻¹. (d)–(f) As (a)–(c), respectively, but for those used in the mixed-phase simulations. Profiles with progressively higher transition heights are indicated with progressively warmer colors.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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Table 1 summarizes the tested parameters and their values. The property of the subsaturated low-level layer is represented with N₂ and z_t. The response of orographic precipitation to N₂ and z_t are investigated under different h_m and U. The effect of ice-phase microphysics is also investigated by running the simulations in different microphysical scenarios. The total number of simulations is 2 (h_m) × 2 (U) × 3 (N₂) × 6 (z_t) × 2 (microphysics scenario) = 144. It is worth mentioning that as long as h_m, U, and the microphysics scheme are the same, the simulation with z_t = 0 km does not change with N₂.

Table 1.

Summary of tested parameters and their values.

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3. Mechanisms

This section presents selected liquid-only simulations with h_m = 0.7 km and U = 10 m s⁻¹ to show the mechanisms through which the subsaturated low-level layer affects the dynamics and microphysics. Figure 3 shows the vertical velocities (first row), perturbation cross-mountain wind speeds (second row), cloud water mixing ratios (shadings in third row), rainwater mixing ratios (black contours in third row), autoconversion rates (fourth row), and accretion rates (fifth row) of three liquid-only simulations with h_m = 0.7 km, U = 10 m s⁻¹, and N₂ = 0.4 × 10⁻² s⁻¹. In the simulation with z_t = 0 km, the vertical velocity (Fig. 3a), perturbation cross-mountain wind speed (Fig. 3b), and cloud water mixing ratio (shading in Fig. 3c) are very similar to those in the simulation with the same h_m and U in MR05, although we use a different microphysics scheme and we do not add initial cloud water. The upwind propagating disturbance discussed in MR05 also appears in our simulation but has moved out of the display domain.

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Results at t = 20 h of three liquid-only simulations with h_m = 0.7 km, U = 10 m s⁻¹, and N₂ = 0.4 × 10⁻² s⁻¹; values of z_t (km) are shown above each column. Rows show (a),(f),(k) the vertical velocities (m s⁻¹); (b),(g),(l) the perturbation cross-mountain wind speeds (m s⁻¹); (c),(h),(m) the cloud water mixing ratios (g kg⁻¹; shaded) and rainwater mixing ratios (g kg⁻¹; black contours starting from 0.01 g kg⁻¹ with a contour interval of 0.05 g kg⁻¹); (d),(i),(n) the autoconversion rates (g kg⁻¹ h⁻¹); and (e),(j),(o) the accretion rates (g kg⁻¹ h⁻¹). We note that the ordinate ranges of the bottom two rows are different from those of the first three rows.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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We now compare the simulation with z_t = 1 km (Figs. 3f–j) to the simulation with z_t = 0 km (Figs. 3a–e). In the simulation with z_t = 1 km, Fig. 3g shows that the deceleration on the upwind side of the mountain is negligible, suggesting a negligible flow blocking. Figure 3f therefore shows that the vertical velocity in the simulation with z_t = 1 km is similar to that in the simulation with z_t = 0 km (cf. Fig. 3a), indicating that the dynamical response to z_t is very weak as z_t increases from 0 to 1 km. In the simulation with z_t = 1 km, Fig. 3h reveals that the cloud water mixing ratio below z = 1 km is much smaller than that in the simulation with z_t = 0 km (cf. Fig. 3c). As z_t increases from 0 to 1 km, the humidity of the low-level layer decreases. This reduces the amount of vapor transported to the mountain. Thus, less cloud water is formed as the low-level air ascends along the upwind slope. The smaller cloud water mixing ratio below z = 1 km has two straightforward consequences. First, Fig. 3i suggests that autoconversion does not take place below z = 1 km. This is because the cloud water mixing ratio is too small to trigger autoconversion. Second, Fig. 3j suggests that no accretion occurs below z = 1 km. This is due to the fact that, on the one hand, the suppression of autoconversion reduces the number of rain droplets; on the other hand, there is less cloud water available to be collected when the rain droplets fall below z = 1 km. Because both autoconversion and accretion are suppressed, Fig. 3h shows that the rainwater mixing ratio is much smaller in the simulation with z_t = 1 km than in the simulation with z_t = 0 km (cf. Fig. 3c).

The analysis above reveals the first mechanism through which the subsaturated low-level layer affects the dynamics and microphysics. Briefly, when the dynamical effect is negligible, such as the simulations discussed above, increasing z_t decreases the amount of vapor transported to the mountain, suppressing both autoconversion and accretion, and finally leads to a smaller rainwater mixing ratio. This effect is termed the “vapor-transport effect.” When z_t is further increased to 2 km (Figs. 3k–o), Fig. 3k suggests that the dynamical effect is still negligible. In this situation, the vapor-transport effect further reduces the rainwater mixing ratio (cf. Figs. 3m,h).

Figure 4 shows the results of three liquid-only simulations with h_m = 0.7 km, U = 10 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹. In the simulation with z_t = 1 km, the low-level layer is initially very stable. Although Fig. 4h indicates that condensation occurs as the low-level air ascends along the upwind slope, the condensation rate is very small. The release of latent heat does not substantially reduce the stability of the low-level layer. Figure 4g reveals a prominent deceleration on the upwind side of the mountain, indicating a strong flow blocking. The blocking effectively extends the mountain upwind. The updraft over the upwind slope therefore becomes much wider than that in the simulation with z_t = 0 km (cf. Figs. 4f,a). In the simulation with z_t = 1 km, Fig. 4g shows that the full cross-mountain wind (which is the sum of the perturbation cross-mountain wind and U) between z = 1 and 4 km is only slightly faster than that in the simulation with z_t = 0 km (cf. Fig. 4b). In this situation, the wider updraft in the simulation with z_t = 1 km means that the parcels between z = 1 and 4 km experience ascent for a longer time, and hence rise to higher elevations. Thus, condensation occurs higher up and farther upwind in the simulation with z_t = 1 km than in the simulation with z_t = 0 km (cf. Figs. 4h,c). As a result, Fig. 4i shows that autoconversion takes place higher up and farther upwind in the simulation with z_t = 1 km (cf. Fig. 4d). Figure 4j further suggests that accretion occurs over a wider region and has a larger maximum value in the simulation with z_t = 1 km (cf. Fig. 4e), indicating that more cloud water is collected by the falling rain droplets, and is consequently converted to rainwater. As a result, Fig. 4h shows that the rainwater mixing ratio in the simulation with z_t = 1 km is larger than that in the simulation with z_t = 0 km (cf. Fig. 4c).

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As in Fig. 3, but for three liquid-only simulations with h_m = 0.7 km, U = 10 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹. The arrows in (l)–(m) show the direction of movement.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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The analysis above reveals the second mechanism through which the subsaturated low-level layer affects the dynamics and microphysics. Increasing z_t widens the updraft, enhancing the conversion from cloud water to rainwater, and consequently producing a larger rainwater mixing ratio. This effect is termed the “updraft-width effect.” We note that the vapor-transport effect is also active in the examples discussed above (h_m = 0.7 km, U = 10 m s⁻¹, N₂ = 1.2 × 10⁻² s⁻¹, and z_t increases from 0 to 1 km); however, it is much weaker than the updraft-width effect.

In the simulation with z_t = 1.5 km (Figs. 4k–o), initially there is no condensation occurring below the maximum mountain height (not shown). The low-level layer is therefore stable. Figure 4l reveals a remarkable deceleration on the upwind side of the mountain, indicating a strong flow blocking. Unlike the simulations with z_t < 1.5 km, where the decelerated region is stationary (cf. Fig. 4g); in the simulation with z_t = 1.5 km, the decelerated region moves upwind. This upwind movement forces the deep updraft to move away from the mountain peak. At t = 20 h, Fig. 4k shows that the updraft near the mountain peak is much shallower and weaker than that in the simulations with z_t < 1.5 km. On the upwind side of the mountain, Fig. 4m suggests that the cloud water mixing ratio is very small. Figure 4n thus suggests that the autoconversion rate is much smaller than that in the simulations with z_t < 1.5 km. Figure 4o reveals that the accretion rate is almost negligible. Thus, very little rainwater forms on the upwind side of the mountain (Fig. 4m).

The analysis above reveals the third mechanism through which the subsaturated low-level layer affects the dynamics and microphysics. When z_t is greater than a certain value, the decelerated region on the upwind side of the mountain moves upwind, resulting in a very shallow and weak updraft near the mountain peak. As a consequence, the rainwater mixing ratio near the mountain peak becomes very small. The upwind movement of the decelerated region will be further discussed in section 6.

4. Surface precipitation of liquid-only simulations

In this section, we present the response of surface precipitation to the subsaturated low-level layers in the liquid-only simulations. For most simulations, we simply use the three mechanisms identified in section 3 to explain the variation of surface precipitation with z_t. For the other simulations, the details are presented because they are more complicated.

a. h_m = 0.7 km and U = 10 m s⁻¹

Figure 5a shows the rain-rate distributions in the simulations with h_m = 0.7 km, U = 10 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹. Note that rain rate in this study specifically refers to the rain rate on the surface. When z_t increases from 0 to 1 km, the updraft-width effect dominates the vapor-transport effect. Thus, the rain rate increases with z_t (Fig. 5a). Figure 5a also reveals that the precipitation in the simulation with z_t = 1 km is located farther upwind compared to that in the simulation with z_t = 0 km, consistent with the fact that autoconversion occurs farther upwind in the simulation with z_t = 1 km (cf. Figs. 4i,d). In the simulations with z_t ≥ 1.5 km, the rain rate near the mountain peak is negligible, consistent with the negligible rainwater mixing ratio near the mountain (Fig. 4m). However, Fig. 5a indicates that surface precipitation forms on the downwind side of the mountain in the simulations with z_t ≥ 1.5 km. On the downwind side of the mountain, Fig. 4k shows that the updraft aloft is quite strong. This produces a sufficiently large cloud water mixing ratio aloft (Fig. 4m), leading to the formation of rainwater (Fig. 4m). In addition, due to the vapor-transport effect, Fig. 5a shows that the rain rate on the downwind side of the mountain decreases with z_t.

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The surface rain rate as a function of distance from the mountain peak (at x = 0) at t = 20 h of the liquid-only simulations with h_m = 0.7 km and U = 10 m s⁻¹. (a) N₂ = 1.2 × 10⁻², (b) N₂ = 0.8 × 10⁻², and (c) N₂ = 0.4 × 10⁻² s⁻¹. Simulations with different z_t (km) are shown with different colors.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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Figure 5b shows the rain-rate distributions in the simulations with a smaller N₂ = 0.8 × 10⁻² s⁻¹. Due to the smaller N₂, the flow blocking in the simulations with N₂ = 0.8 × 10⁻² s⁻¹ is generally weaker than that in the simulations with N₂ = 1.2 × 10⁻² s⁻¹. In the simulations with z_t ≤ 1.5 km, the updraft-width effect is weaker than the vapor-transport effect, Fig. 5b therefore reveals a decrease of rain rate with z_t. In the simulations with z_t ≥ 2 km, the decelerated region moves upwind (not shown). However, in the simulation with z_t = 2 km, the upwind movement occurs very slowly; at t = 20 h, the updraft is still near the mountain peak and becomes much wider than that in the simulation with z_t = 1.5 km (not shown). The updraft-width effect counteracts the vapor-transport effect. Therefore, Fig. 5b shows that the surface precipitation in the simulation with z_t = 2 km is almost the same as that in the simulation with z_t = 1.5 km, except that the surface precipitation is shifted upwind. In the simulation with z_t = 2 km, surface precipitation also forms on the downwind side of the mountain (Fig. 5b). In the simulation with z_t = 2.5 km, the decelerated region rapidly moves upwind. Thus, Fig. 5b suggests that very little surface precipitation forms near the mountain peak.

In the simulations with an even smaller N₂ = 0.4 × 10⁻² s⁻¹, the flow blocking is even weaker (e.g., Figs. 3b,g,l). As discussed in section 3, the updraft-width effect is negligible, while the vapor-transport effect is active. Figure 5c thus indicates a decreases of rain rate with z_t. In all the simulations with N₂ = 0.4 × 10⁻² s⁻¹, the decelerated regions do not move upwind.

b. h_m = 1.5 km and U = 10 m s⁻¹

Figure 6 shows the results of three liquid-only simulations with h_m = 1.5 km, U = 10 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹. In the simulation with z_t = 0 km, the vertical velocity (Fig. 6a) and perturbation cross-mountain wind speed (Fig. 6b) are very similar to those in the simulation with h_m = 0.7 km (Figs. 3a,b), except that the magnitudes are nearly doubled. This doubling is consistent with linear theory, where the patterns of vertical velocity and perturbation cross-mountain wind speed do not change with h_m but their magnitudes proportionally increase with h_m (Lin 2007, 109–112). However, the microphysical responses are more complicated. In the simulation with h_m = 0.7 km, autoconversion mainly occurs below z = 4 km (Fig. 3d), and the accretion rate is very small (Fig. 3e), so only a small portion of cloud water is converted to rainwater. In the simulation with h_m = 1.5 km, Fig. 6c shows that the higher mountain produces a larger cloud water mixing ratio (cf. Fig. 3c). Autoconversion is initiated higher up (not shown). The converted rain droplets hence collect much more cloud water (not shown), leading to a much larger rainwater mixing ratio (cf. Figs. 6c and 3c). For the simulations with z_t = 0 km, Fig. 7a shows that the rain rate in the simulation with h_m = 1.5 km is much larger than that in the simulation with h_m = 0.7 km (cf. Fig. 5a). On the downwind side of the mountain, Fig. 6a shows that the updraft aloft is very strong, leading to the formation of cloud water (Fig. 6c) and consequently surface precipitation (Fig. 7a).

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Results at t = 20 h of three liquid-only simulations with h_m = 1.5 km, U = 10 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹; values of z_t (km) are shown above each column. Rows show (a),(d),(g) the vertical velocity (m s⁻¹); (b),(e),(h) the perturbation cross-mountain wind (m s⁻¹); and (c),(f),(i) the cloud water mixing ratio (g kg⁻¹; shaded) and rainwater mixing ratio (g kg⁻¹; black contours starting from 0.1 g kg⁻¹ with a contour interval of 0.2 g kg⁻¹). The arrows in (h) and (i) show the direction of propagation.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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As in Fig. 5, but for the liquid-only simulations with h_m = 1.5 km and U = 10 m s⁻¹.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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Figure 7a shows the effect of varying z_t on the rain-rate distribution in the simulations with h_m = 1.5 km, U = 10 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹. As z_t increases from 0 to 0.5 km, the updraft-width effect nearly counteracts the vapor-transport effect. Figure 7a thus shows similar rain rates in these two simulations. As z_t further increases to 1 km, the situation becomes slightly more complicated. Figure 6e shows that flow blocking is strong in the simulation with z_t = 1 km. Compared with the simulation with z_t = 0 km, the simulation with z_t = 1 km has a wider but weaker updraft over the upwind slope (cf. Figs. 6d,a). Consequently, rainwater forms over a wider region but has a smaller maximum value (cf. Figs. 6f,c). Figure 7a hence indicates that the rain rate is spread over a wider region but has a smaller maximum value. In the simulations with z_t ≥ 1.5 km, the decelerated region moves upwind (e.g., Figs. 6h,i). At t = 20 h, the updraft over the upwind slope becomes very weak (e.g., Fig. 6g). Nevertheless, Fig. 6i suggests that cloud water still forms near the mountain peak, and is finally converted to rainwater. Figure 7a therefore shows that surface precipitation forms near the mountain peak. In the simulations with z_t ≥ 1.5 km, the updraft-width effect does not take effect while the vapor-transport effect is still active. Figure 7a thus reveals a decrease of rain rate with z_t. On the downwind side of the mountain, increasing z_t generally increases the width of the updraft aloft (cf. Figs. 6a,d,g). Rain rate therefore increases with z_t (Fig. 7a).

In the simulations with a smaller N₂ = 0.8 × 10⁻² s⁻¹ (not shown), the flow blocking is generally weaker than that in the simulations with N₂ = 1.2 × 10⁻² s⁻¹. With reduced blocking, the updraft-width effect is generally weaker than the vapor-transport effect. Figure 7b therefore shows that the rain rate decreases as z_t increases from 0 to 2 km. In the simulation with z_t = 2.5 km, the decelerated region moves upwind, resulting in negligible precipitation near the mountain peak (Fig. 7b). In all the simulations with N₂ = 0.8 × 10⁻² s⁻¹, Fig. 7b shows that surface precipitation occurs on the downwind side of the mountain. In addition, when z_t ≥ 0.5 km, surface precipitation spreads over a wide region. For an even smaller N₂ = 0.4 × 10⁻² s⁻¹ (not shown), the flow blocking is even weaker, and the updraft-width effect becomes even weaker than the vapor-transport effect. Consequently, rain rate monotonically decreases with z_t (Fig. 7c). In addition, surface precipitation also occurs on the downwind side of the mountain (Fig. 7c). In all simulations with N₂ = 0.4 × 10⁻² s⁻¹, the decelerated regions do not move upwind (not shown).

c. h_m = 1.5 km and U = 20 m s⁻¹

Figure 8 shows the results of three liquid-only simulations with h_m = 1.5 km, U = 20 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹. Figure 8a shows that in the simulation with z_t = 0 km, the updraft over the upwind slope is approximately twice as deep as that in the simulation with U = 10 m s⁻¹ (cf. Fig. 6a). This doubling is also consistent with linear theory, where the vertical wavelength is proportional to U (Lin 2007, 109–112). The much deeper updraft produces a much deeper cloud (cf. Figs. 8c and 6c), which subsequently produces a larger rainwater mixing ratio. For the simulations with z_t = 0 km, Fig. 9a shows that the rain rate in the simulation with U = 20 m s⁻¹ is much larger than that in the simulation with U = 10 m s⁻¹ (cf. Fig. 7a).

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Results at t = 20 h of three liquid-only simulations with h_m = 1.5 km, U = 20 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹; values of z_t (km) are shown above each column. Rows show (a),(d),(g) the vertical velocity (m s⁻¹); (b),(e),(h) the perturbation cross-mountain wind (m s⁻¹); and (c),(f),(i) the cloud water mixing ratio (g kg⁻¹; shaded) and rainwater mixing ratio (g kg⁻¹; black contours starting from 0.5 g kg⁻¹ with a contour interval of 0.5 g kg⁻¹). The arrows in (h) and (i) show the direction of propagation.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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As in Fig. 5, but for the liquid-only simulations with h_m = 1.5 km and U = 20 m s⁻¹.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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Figure 9a shows the rain-rate distributions for the simulations with h_m = 1.5 km, U = 20 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹. Increasing z_t from 0 to 1.5 km does not significantly change the rain rate, because the updraft-width effect nearly counteracts the vapor-transport effect in these simulations. However, Fig. 9a indicates that the rain rate in the simulation with z_t = 2 km is larger than that in the simulations with z_t = 1.5 km. In the simulation with z_t = 2 km, Fig. 8e suggests a strong flow blocking. Figure 8d therefore indicates that the updraft over the upwind slope becomes very wide. As z_t increases from 1.5 to 2 km, the updraft-width effect surpasses the vapor-transport effect, leading to an increase of rain rate. Figure 9a also shows that the rain rate near the mountain peak is very small in the simulation with z_t = 2.5 km. This is because the decelerated region moves upwind in this simulation (Figs. 8g–i).

In the simulations with a smaller N₂ = 0.8 × 10⁻² s⁻¹ (not shown), the flow blocking is generally weaker than those in the simulations with N₂ = 1.2 × 10⁻² s⁻¹. In these simulations, the updraft-width effect is generally weaker than the vapor-transport effect. Consequently, Fig. 9b shows that the rain rate decreases monotonically with z_t. The simulations with N₂ = 0.4 × 10⁻² s⁻¹ are similar to the simulations with N₂ = 0.8 × 10⁻² s⁻¹, except that the rain rate decreases with z_t even faster (Fig. 9c). In all simulations with N₂ = 0.8 × 10⁻² and 0.4 × 10⁻² s⁻¹, the decelerated regions do not move upwind (not shown).

d. h_m = 0.7 km and U = 20 m s⁻¹

Figure 10 shows the results of three liquid-only simulations with h_m = 0.7 km, U = 20 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹. The vertical velocity suggests that lee waves form in these simulations (Figs. 10a,d,g). In a two-layer atmosphere, the condition for lee waves is (Scorer 1949; Lehner et al. 2016)

$l_l^2-l_u^2>{\displaystyle \frac{{\pi }^2}{4z_l^2}},$(3)

where z_l is the thickness of the lower layer, and l_l and l_u are, respectively, the Scorer parameters of the lower and the upper layers, and

$l_i^2={\displaystyle \frac{N_i^2}{U_i^2}}-{\displaystyle \frac{1}{U_i}}{\displaystyle \frac{d^2{U}_i}{d{z}^2}},$(4)

where i refers to l or u, and N_i and U_i are, respectively, the Brunt–Väisälä frequency and ambient wind of the ith layer.

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Results at t = 20 h of three liquid-only simulations with h_m = 0.7 km, U = 20 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹; values of z_t (km) are shown above each column. Rows show (a),(d),(g) the vertical velocity (m s⁻¹); (b),(e),(h) the perturbation cross-mountain wind (m s⁻¹); and (c),(f),(i) the cloud water mixing ratio (g kg⁻¹; shaded) and rainwater mixing ratio (g kg⁻¹; black contours starting from 0.001 g kg⁻¹ with a contour interval of 0.001 g kg⁻¹).

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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In our simulations, the nonlinear interaction between the dynamics and microphysics produces a two-layer structure on the downwind of the mountain. The lower desaturated layer goes from the surface to z ≈ 4 km (Figs. 10c,f,i); the dry Brunt–Väisälä frequency in this layer N_l ≈ 1.2 × 10⁻² s⁻¹. The upper layer goes from z ≈ 4 km to the top of the troposphere, and its Brunt–Väisälä frequency is the moist Brunt–Väisälä frequency $N_u\mathrm{=}\sqrt{3}\mathrm{\times }{10}^{\mathrm{-}3}\hspace{0.17em}{\mathrm{s}}^{\mathrm{-1}}$. In addition, the ambient wind is 20 m s⁻¹ throughout the whole atmosphere. Calculation shows that (3) is satisfied, indicating that lee waves can occur in these simulations.

In these simulations, the vertical velocity is almost independent of z_t (Figs. 10a,d,g), similar to that found in Durran and Klemp (1982). In this situation, the updraft-width effect is negligible. However, the vapor-transport effect is still active, as revealed by the decreasing cloud water mixing ratio with z_t (cf. Figs. 10c,f,i). Thus, Fig. 11a shows that increasing z_t decreases the rain rate. For smaller values of N₂, that is, 0.8 × 10⁻² and 0.4 × 10⁻² s⁻¹, (3) is still satisfied and these simulations also produce lee waves. Increasing z_t therefore decreases the rain rate (Figs. 11b,c). In all the simulations with h_m = 0.7 km, U = 20 m s⁻¹, the flow is not blocked (e.g., Figs. 10b,e,h).

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As in Fig. 5, but for the liquid-only simulations with h_m = 0.7 km and U = 20 m s⁻¹.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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5. Surface precipitation of mixed-phase simulations

In this section, we present the mixed-phase simulations to show the effect of ice-phase microphysics on the dynamics and precipitation. For each combination of h_m and U, only the simulation with z_t = 0 km is shown in detail. Note that the simulation with z_t = 0 km is independent of N₂. For the simulations with z_t > 0 km, only the rain-rate distributions are presented; the details of the simulations are not presented because they are similar to those in the liquid-only simulations.

a. h_m = 0.7 km and U = 10 m s⁻¹

Figure 12a shows the vertical velocity of the mixed-phase simulation with h_m = 0.7 km, U = 10 m s⁻¹, and z_t = 0 km. It can be seen that the updraft over the upwind slope is shallower in the mixed-phase simulation than in the liquid-only simulation (cf. Figs. 12a and 3a). In the mixed-phase simulations, as mentioned in section 2, the initial profile above the freezing level is subsaturated with respect to water. In this situation, N above the freezing level becomes larger. According to linear theory, the vertical wavelength is inversely proportional to N (Lin 2007, 109–112). Therefore, the vertical wavelength is shorter in the mixed-phase simulation than in the liquid-only simulation. Figure 12a also shows that the updraft over the upwind slope is mostly below the freezing level (~3 km). Figure 12b thus suggests that ice formation is negligible on the upwind side of the mountain. In addition, a shallower updraft leads to less condensation (cf. Figs. 12b and 3c), so Fig. 13a shows that the rain rate in the mixed-phase simulation is weaker than that in the liquid-only simulation (cf. Fig. 5a).

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Results at t = 20 h of the mixed-phase simulations with z_t = 0 km; values of h_m (km) and U (m s⁻¹) are shown above each column. Rows show (a),(c),(e),(g) the vertical velocities (m s⁻¹) and (b),(d),(f),(h) the cloud water mixing ratios (g kg⁻¹; shaded), rainwater mixing ratios (g kg⁻¹; black contours starting from 0.01 g kg⁻¹ with a contour interval of 0.2 g kg⁻¹), ice water mixing ratios (g kg⁻¹; orange contours starting from 0.01 g kg⁻¹ with a contour interval of 0.02 g kg⁻¹), and snow water mixing ratios (g kg⁻¹; green contours starting from 0.05 g kg⁻¹ with a contour interval of 0.1 g kg⁻¹). Graupel water mixing ratio is negligible in these simulations and is therefore not shown.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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As in Fig. 5, but for the mixed-phase simulations with h_m = 0.7 km and U = 10 m s⁻¹.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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Figure 12b also shows that the inclusion of ice-phase microphysics produces surface precipitation between x = 25 and 50 km, where no surface precipitation forms in the corresponding liquid-only simulation (cf. Fig. 3c). In the mixed-phase simulation, Fig. 12a reveals a strong updraft between z = 3 and 10 km. This updraft leads to the formation of ice crystals (Fig. 12b), which grow and are subsequently converted to snow particles. Because the fall speeds of snow particles are relatively small, they are transported downwind as they fall. When the snow particles fall below the freezing level, they melt and produce surface precipitation at 25–50 km downwind of the mountain peak (Fig. 13a).

Figure 13a shows the rain-rate distributions of the mixed-phase simulations with h_m = 0.7 km, U = 10 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹. When z_t increases from 0 to 0.5 km, the updraft also becomes slightly wider, similar to the liquid-only simulations. However, because the stable layer above the freezing level reduces the depth of the updraft, the updraft-width effect in the mixed-phase simulation is weaker than that in the liquid-only simulation. The updraft-width effect nearly counteracts the vapor-transport effect. Figure 13a therefore indicates that the rain rate in the simulation with z_t = 0.5 km is similar to that in the simulation with z_t = 0 km. As z_t further increases to 1 km, the updraft becomes even wider. Nevertheless, the updraft-width effect is substantially reduced by the stable layer above the freezing level, and becomes weaker than the vapor-transport effect. The rain rate in the simulation with z_t = 1 km is therefore smaller than that in the simulation with z_t = 0.5 km. In the simulations with z_t ≥ 1.5 km, the decelerated region moves upwind, as in the liquid-only simulations. Therefore, Fig. 13a shows that the rain rate near the mountain peak is very small. On the downwind side of the mountain, Fig. 13a reveals relatively large rain rates in the simulations with z_t ≥ 1.5 km. In these simulations, a strong updraft forms below z = 4 km on the downwind side of the mountain. When the snow particles and rain droplets fall through this updraft, they grow and consequently produce a relatively large rain rate. It is worth mentioning that the updraft below z = 4 km is slowly moving downwind.

For a smaller N₂ = 0.8 × 10⁻² s⁻¹, the updraft-width effects are generally weaker. In the simulations with z_t ≤ 1.5 km, the updraft-width effect is weaker than the vapor-transport effect. Figure 13b thus indicates that the rain rate decreases with z_t. In the simulations with z_t ≥ 2 km, the decelerated region moves upwind. Thus, no surface precipitation forms near the mountain peak. Nevertheless, the updraft aloft leads to the formation of ice crystals and consequently produces surface precipitation on the downwind side of the mountain (Fig. 13b). In the simulations with an even smaller N₂ = 0.4 × 10⁻² s⁻¹, the updraft-width effects are even weaker. Figure 13c shows that increasing z_t simply decreases surface precipitation. In all simulations with N₂ = 0.4 × 10⁻² s⁻¹, the decelerated regions do not move upwind.

b. h_m = 1.5 km and U = 10 m s⁻¹

Figure 12c shows the vertical velocity of the mixed-phase simulation with h_m = 1.5 km, U = 10 m s⁻¹, and z_t = 0 km. In this simulation, the higher mountain exerts a stronger orographic forcing, which overcomes the effect of the stable layer above the freezing level. The vertical velocity in the mixed-phase simulation is hence almost the same as that in the liquid-only simulation (cf. Fig. 6a). Figure 12c suggests that the updraft over the upwind slope extends above the freezing level, resulting in the formation of ice crystals (the ice water mixing ratio is so low that it does not appear in Fig. 12d). These ice crystals quickly grow and become snow particles (Fig. 12d), the melting of which consequently produces rainwater. In this mixed-phase simulation, the formation of precipitation is accelerated due to the presence of ice-phase microphysics. The mixed-phase simulation thus needs a shorter time to produce precipitation. For the simulations with z_t = 0 km, Fig. 14a shows that the surface precipitation occurs farther upwind in the mixed-phase simulation than in the liquid-only simulation (cf. Fig. 7a). On the downwind side of the mountain, Fig. 12c also reveals a strong updraft aloft. Ice crystals therefore form, leading to the formation of snow particles. These snow particles are also transported downwind as they fall. Therefore, they melt and produce rain droplets at 25–50 km downwind of the mountain peak (Fig. 12d). In addition, most of the rainwater is evaporated before the rain droplets fall to the surface. Thus, Fig. 14a shows that the rain rate is small on the downwind side of the mountain.

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As in Fig. 5, but for the mixed-phase simulations with h_m = 1.5 km and U = 10 m s⁻¹.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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Figure 14a shows the effect of varying z_t on rain-rate distributions of the simulations with h_m = 1.5 km, U = 10 m s⁻¹, and N₂ = 1.2 × 10⁻² s⁻¹. The rain rates in the simulation with z_t = 0 and 0.5 km are similar, as in the liquid-only simulations. However, unlike the liquid-only simulations, where the decelerated region moves upwind when z_t ≥ 1.5 km; in the mixed-phase simulations, the decelerated region moves upwind when z_t ≥ 1 km. Figure 14a thus indicates that the rain rate near the mountain is much smaller in the simulations with z_t ≥ 1 km than in the simulations with z_t < 1 km. In the simulations with N₂ = 0.8 × 10⁻² s⁻¹, Fig. 14b shows that the rain rate does not change as z_t increases from 0 to 0.5 km, and decreases as z_t further increases to 1 km, similar to the liquid-only simulations. In the liquid-only simulations, the decelerated region moves upwind only when z_t = 2.5 km; while in the mixed-phase simulations, the decelerated region moves upwind when z_t ≥ 1.5 km. Figure 14b thus indicates that the rain rate becomes much smaller when z_t ≥ 1.5 km. In the simulations with N₂ = 0.4 × 10⁻² s⁻¹, Fig. 14c reveals that the rain rate decreases with z_t, similar to the liquid-only simulations (cf. Fig. 7c). In all the mixed-phase simulations with h_m = 1.5 km and U = 10 m s⁻¹, Fig. 14 indicates that the rain rates are small on the downwind side of the mountain.

c. h_m = 1.5 km and U = 20 m s⁻¹

Figure 12e shows the vertical velocity of the mixed-phase simulation with h_m = 1.5 km, U = 20 m s⁻¹, and z_t = 0 km. It can be seen that the updraft over the upwind slope is much shallower than that in the liquid-only simulation (cf. Fig. 8a). Figure 12f reveals that ice-phase microphysics is active in this simulation. As mentioned before, the presence of ice crystals accelerates the formation of precipitation. For the simulations with z_t = 0 km, Fig. 15a shows that precipitation occurs farther upwind in the mixed-phase simulation than in the liquid-only simulation (cf. Fig. 9a). The precipitation efficiently removes moisture. The upwind atmosphere becomes drier, and hence has a larger N. According to linear theory, the vertical wavelength is inversely proportional to N (Lin 2007, 109–112). Therefore, Fig. 12e indicates that the updraft over the upwind slope in the mixed-phase simulation is shallower than that in the liquid-only simulation.

Figures 15 shows the rain-rate distributions of all the simulations with h_m = 1.5 km and U = 20 m s⁻¹. Comparing with Fig. 9, it is found that the response of rain rate to both N₂ and z_t in the mixed-phase simulations is similar to that in the liquid-only simulations, except that the surface precipitation occurs farther upwind in the mixed-phase simulations.

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As in Fig. 5, but for the mixed-phase simulations with h_m = 1.5 km and U = 20 m s⁻¹.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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d. h_m = 0.7 km and U = 20 m s⁻¹

Figure 12g shows that lee waves also occur in the mixed-phase simulations with h_m = 0.7 km, U = 20 m s⁻¹, and z_t = 0 km. Actually, lee waves occur in all the mixed-phase simulations with h_m = 0.7 km and U = 20 m s⁻¹. Because the updraft over the upwind slope are mostly below the freezing level, Fig. 12h shows that ice crystals hardly form in the nominally mixed-phase simulations. Therefore, Fig. 16 shows that the rain rate in the mixed-phase simulations is almost the same as that in the liquid-only simulations (cf. Fig. 11).

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As in Fig. 5, but for the mixed-phase simulations with h_m = 0.7 km and U = 20 m s⁻¹.

Citation: Journal of the Atmospheric Sciences 76, 12; 10.1175/JAS-D-19-0115.1

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6. Upwind movement of the decelerated region

Table 2 shows that the decelerated region moves upwind in 5 out of the 12 simulated combinations of h_m, U, and N₂ (Table 1). In addition, the upwind movement occurs in these 5 combinations no matter whether ice-phase microphysics is included or not. We define the smallest z_t with which the simulated decelerated region moves upwind as z_t,c. Table 2 lists the values of z_t,c and the corresponding values of N₂z_t,c/U for the 5 combinations. For the liquid-only simulations, the simulated critical values are generally close to the theoretical value. For the mixed-phase simulations, the simulated critical values are close to the theoretical values except for the two combinations with h_m = 1.5 km and U = 10 m s⁻¹ due to more complex microphysical effects on the effective stability.

Table 2.

Simulated critical values of N₂z_t,c/U. Only the combinations of h_m, U, and N₂ that produce an upwind movement of decelerated region are shown. The values outside the parentheses are for the liquid-only simulations while those in the parentheses are for the mixed-phase simulations.

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7. Summary

Nearly moist-neutral flows are frequently observed in orographic precipitation events. Previous studies of nearly moist-neutral flow either assumed the whole atmosphere to be saturated or assumed a constant relative humidity. However, there are times when we observe subsaturated, low-level layers below the saturated, nearly moist-neutral, upper-level layers. In this study, a series of idealized 2D simulations are performed to study the response of orographic precipitation to the Brunt–Väisälä frequency N₂, and depth z_t of the subsaturated low-level layers. The effects of cross-mountain wind speed U and cloud microphysics are also investigated.

The response of orographic precipitation is partially controlled by a nondimensional parameter N₂z_t/U. When N₂z_t/U exceeds a critical value, the decelerated region on the upwind slope of the mountain moves upwind, leading to a shallow and weak updraft near the mountain peak. The surface precipitation therefore becomes very weak near the mountain peak. The critical values of N₂z_t/U determined from the simulations are close to that derived from linear theory (i.e., 1.6).

When N₂z_t/U is smaller than the critical value, increasing z_t has two competing effects. On the one hand, increasing z_t decreases the amount of vapor transported to the mountain, and tends to decrease surface precipitation. This effect is the vapor-transport effect. On the other hand, increasing z_t enhances flow blocking. This increases the width of the updraft on the upwind side of the mountain, and tends to increase surface precipitation. This effect is the updraft-width effect. When the vapor-transport effect dominates, surface precipitation decreases with z_t. When the updraft-width effect dominates, surface precipitation increases with z_t.

When N₂, z_t, and the microphysics scheme are fixed, increasing the maximum mountain height h_m or U generally increases the surface precipitation. However, when h_m = 0.7 km and U = 20 m s⁻¹, the simulations produce lee waves, which substantially reduces the surface precipitation. In addition, due to the difference in initial profiles and the inclusion of ice-phase microphysics, the surface precipitations in the mixed-phase simulations are generally different from those in the liquid-only simulations. Nevertheless, in the mixed-phase simulations, the response of surface precipitation to subsaturated low-level layers is similar to that in the liquid-only simulations.