Simulation Results

Selected time-series and mean profiles of different cloud properties averaged over the horizontal (x - y) plane (referred to as layer averages) and then time averaged over the last hour (5h) will be shown. Comparison between the two runs will be presented and compared with the available observational data. In general the model requires about 2 h to produce the initial cloud and establish the resolved-scale turbulence. Thus, we will only look at various fields after the spin-up period.

Figure 3 shows selected time-sequences from both runs. The local height of the inversion is determined by linearly interpolating grid values of total water mixing ratio r_t to 1.8 g kg^-1, which gives the corresponding interpolated inversion height in a column. The inversion height, z_i, (Figure 3a) is then defined as the horizontal average of these inversion height values; this is in general not a model level. The average rate of change of z_i is calculated later to give the time resolution of the entrainment velocity w_e ( =dz_i/dt - w_sub) and averaged over the last 3 h of simulation for comparison with the estimate from observations. z_i shows a steady increase with time for both runs except that z_i is higher in the N250 run, suggesting stronger mixing at the inversion. Liquid water path, LWP (Figure 3b) is very similar for much of the simulation in both runs except for the last hour when LWP is about 10% higher in the N250 run. The reduction in LWP for N30 is associated with the increase in the surface drizzle flux (Figure 3c). The column maximum value of (w'w')^1/2 labeled $\sigma_w$ in Figure 3d does not show strong correlation with either the LWP or surface drizzle flux although during the last 40 minutes of the N30 simulation, the decrease in $\sigma_w$ may correspond to the depletion in LWP resulting from drizzle, and the feedback to dynamics incurred by drizzle [Stevens et al., 1998]. Note that this reduction in LWP and $\sigma_w$ occurs despite the fact that the drizzle flux is approximately constant (Figure 3c), so that the response appears to be due to the integrated amount of drizzle rather than the increase in the drizzle rate [see also Feingold et al., 1999]. However, the time-averaged $\sigma_w$ over the last 3 h of simulation (not shown) is about 5% higher in the N250 run, indicating significant dynamical response and more vigorous eddies.

It is known that the CCN concentration determines cloud droplet number concentration N_d. The dependence of cloud optical depth $\tau$ and cloud albedo A on N_d has long been established for nonprecipitating clouds [e.g., Platnick and Twomey, 1994] and for drizzling clouds [e.g., Feingold et al., 1997]. In this study, the change in CCN concentration is mainly from above-cloud air parcels containing higher concentrations of CCN entrained into the cloud layer, and through mixing at the cloud top. Figure 4 shows the layer averages of CCN concentration (N_ccn, potential drop number that can be activated in the cloud layer), drop concentration (N_d), and unscavenged CCN concentration (N_unscavenged) at different simulation times for the N250 run (see equation 2 in the model section for a detailed explanation). N_ccn is quickly doubled from the initial value in the cloud layer, while it stays low below cloud at 2 h (solid line). It is interesting to note that the maximum N_ccn in the cloud layer never exceeds 60 cm^-3 over the last 3 hrs of the simulation; instead higher values brought in by entrainment and turbulent mixing at the cloud top are continuously mixed throughout the entire boundary layer. Consequently, the CCN concentration is fairly well-mixed throughout the boundary layer by the end of simulation (long-dashed line). Note that the constant value of 30 cm^-3 used for the N30 run is drawn for reference (solid vertical line). The maximum N_d is on the order of 55 - 60 cm^-3. The near zero N_unscavenged = N_ccn - N_d (Figure 4c) indicates that almost all of N_ccn in the cloud layer are activated to form droplets (N_d), while above and below the cloud layer, N _unscavenged is identical to N_ccn. It can be seen that cloud top grows with time (Figure 4), in agreement with Figure 3a.

Snapshots of the layer-averaged N_d, effective radius r_e, drizzle rate, liquid water content LWC, and vertical velocity variance <w'w'> at 5 h for both runs are shown in Figure 5. Also plotted in Figure 5 is the LWC and droplet concentration from different probes used in the observations. For comparison purposes, the droplet number concentration N_d is plotted again in Figure 5a. The maximum value of N_d for N30 is about 30 cm^-3, only half of that for N250. Within the cloud region, N_d is approximately constant with height, consistent with observations in the Arctic [e.g., Curry, 1986] and in the marine boundary layer [e.g. Duynkerke et al., 1995]. The increase in droplet concentration is correlated with the increase in N_ccn for N250. As the air containing higher CCN concentration is entrained into the cloudy boundary layer, the CCN are quickly activated to form droplets. Note that the measured N_d, derived from the FSSP-100 (dotted line), have a maximum of 105 cm^-3, i.e., much higher then the modeled value. This should be borne in mind when comparing other modeled variables with observations.

The layer averaged effective radius r_e, defined as the ratio between the third and second moments of the drop distribution (Figure 5b), provides evidence that N250 produces smaller cloud drops than N30. With less drops competing for the available water vapor in the N30 run, drops grow to sizes considerably larger and fall to the subcloud layer, where r_e is significantly higher for N30 than for N250. Note that the values of r_e become progressively less meaningful as the moments tend to zero at heights below 50-100 m.

In the N250 run the drizzle rate (Figure 5c) has a maximum of 2.2 mm day^-1, mainly in the cloud layer with almost no drizzle reaching the surface. In the N30 run, however, the maximum is barely two thirds of that of N250 in the cloud layer, but approximately 16% of the maximum reaches the ground. The lower drizzle rates within the cloud are a result of depletion of cloud water through a more active drizzle process.

The differences between the LWC (Figure 5d) for N30 and N250 are characteristic of the differences between drizzling and non-drizzling clouds [e.g., Stevens et al., 1998]; In N250, LWC is about 21% higher in the layer near cloud top and lower near cloud base and in the subcloud layer compared with the N30 run. Drizzle effectively redistributes the liquid water downward with some losses occurring in N30 through sedimentation to the surface.

The dynamical response is significant at this time of the simulation, as expressed by higher <w'w'> for the N250 run (Figure 5e).

Figure 5f shows that the maximum observed LWC is in the range from 0.16 g m^-3 (King and Gerber probe) to 0.26 g m^-3 (FSSP-100). The modeled LWC averaged over the last 3 h of simulation (not shown) is on the order of 0.3 g m^-3. The higher value of LWC and the lower value of N_d predicted by the model have implications for the cloud radiative response, as shown later.

It is evident in Figure 5 that the increase in CCN concentration through entrainment results in larger N_d, smaller drop sizes, and less drizzle reaching the ground, [e.g., Albrecht, 1989]. The results shown in Figure 5 are consistent with Olsson et al. [1998], who found that higher CCN concentrations produced a cloud with larger cloud top LWC, larger number concentrations, and smaller droplets in their cloud-resolving simulations of warm-season arctic stratus.

The impact of the entrainment of CCN into the cloud on the cloud optical properties is evaluated in Figure 6. Optical depth (in the visible) is defined as

$$\tau \approx \int_{z_b}^{z_t} \int_0^{\infty} 2 \pi r^2 n(r,z) dr dz,$$ (3)

where n(r) defines the drop spectrum with respect to radius r, z_b is cloud base, z_t is cloud top, and the extinction efficiency has been assumed to be equal to 2. Albedo is calculated using the simple relationship between cloud albedo A and optical depth given by Bohren [1987].

$$A \approx \frac{(1-g)\tau}{2 + (1-g)\tau}$$ (4)

where g is the scattering asymmetry factor (Twomey, 1991). At small $\tau$, A is approximately linearly dependent on $\tau$ and therefore A is positively correlated with $\tau$. Both A (Figure 6a) and $\tau$ (Figure 6b) increase steadily from the beginning of the simulation. According to Twomey [1974], $\tau$ scales with N_d^1/3 for clouds of similar r_l. Figure 5a indicates that N_d(N250)/N_d(N30) $\approx$ 60/30 = 2, so that their optical depth ratio should scale by 2^1/3=1.26. Figure 6b indicates that at 200 min, before N30 LWP has begun to lose significant water $\tau$(N250)/$\tau$(N30) $\approx$ 9.5/7.5=1.27 so that there is excellent agreement with this simple scaling law when the runs have similar LWP. Notice that the differences between the two runs grows larger with time. In the case of N250, A is roughly 7% higher at 120 min and is about 12% higher at 300 min of simulation, while $\tau$ is 14% higher at 120 min and 33% higher at 300 min. This is related to the depletion in liquid water in N30 which reduces both $\tau$ and A.

Since entrainment is a key element of this study, the entrainment rate w_e(the growth rate of the cloud-top height) is computed as the average dz_i/dt - w_sub over the last 3 h of the simulation period. Recall that the imposed w_sub is about -0.25 cm s^-1 at the inversion. The estimation of w_e is also provided with observational data based on the jump model [De Roode and Duynkerke, 1997], $w_e=\overline{(w'r'_t)_{z_i}}/\Delta r_t$, where $\Delta r_t$ is the jump of the mean total water across the cloud top and $\overline{(w'r'_t)_{z_i}}$ is the total water entrainment flux right beneath the inversion height. As shown in Table 1, the model results (3 h average) are slightly larger, but compare reasonably well with the observation.

Layer-averaged droplet spectra, n(r) are shown in Figure 7 at 5 h and compared to observed spectra. The observed spectra were measured with a forward scattering spectrometer probe (FSSP-100) and a one-d optical array probe (260X) mounted on the Meteorological Research Flight (MRF) C-130. The FSSP-100 detects particles with a diameter range of 2 - 47$\mu m$ and has a resolution of about 3 $\mu m$. The 260X probe measures particles in the diameter range 12.5 - 812.5 $\mu m$ and has a resolution of about 25 $\mu m$. Specific calibrations were also made for the instruments used in this experiment. Because the aircraft samples drop spectra along a flight track that is not necessarily representative of the entire cloud we have opted to compare spectra at similar LWC rather than at similar flight altitudes. Figure 7 indicates that broad features of the drop spectra are reasonably well captured by the model, e.g., the mode of the spectrum is usually in the correct position. In Figure 7a the modeled mode is at about 3 $\mu$m as opposed to 5 $\mu$m. The source of the 3 $\mu$m mode has been traced to droplet activation occurring just above cloud base. The most notable differences lie in the tendency for the model to overpredict the number concentration of drops in the range 15 $\mu$m <r< 80 $\mu$m. At the largest drop sizes (100 $\mu$m) the 260X tends to show higher concentrations than predicted by the model. This ``concavity" in the 260X drop spectra may indicate the presence of ice particles or melted ice particles. Observed spectra often have a significantly stronger mode than the modeled spectra. Examination of the data shows that when this occurs, the observed N_d$\approx$ 100 cm^-3 compared to the typical 60 cm^-3 modeled here. The higher N_d indicate stronger competition for vapor and limited growth so that the differences are consistent with our understanding of droplet growth through condensation and collision-coalescence.

Modeled and observed shortwave downwelling fluxes at the surface (F^-_s) are shown in Figure 8a. F^-_s decreases with time in response to the increase in albedo (cloud shortwave reflectance) and optical depth $\tau$ (Figure 6b) for both simulations. Note that F^-_s is systematically lower for the increased CCN (N250) run than for the lower CCN (N30) run. This is consistent with the work of Curry et al. [1993], who studied the Arctic radiative response to changes in cloud optical properties. They found that increased numbers of CCN cause a larger number of smaller droplets and as drop sizes become smaller, cloud reflectivity increases, reducing the incoming shortwave flux. The observed values of F^-_s are higher than the modeled ones although they do show a similar trend to the modeled values, indicating that the observed cloud was probably thickening over the course of the measurement period. Considering the fact that the observed N_d are sometimes as high as 100 cm^-3 (Figure 5a), one might have expected lower transmission through the observed cloud and therefore an observed F^-_s that is lower than both model results. However, an integration of the observed LWC profiles (Figure 5f) yields a LWP somewhat less than the modeled one and since to first order $\tau \approx 1.5 LWP/r_e$ the lower LWP reduces $\tau$ and A, and increases F^-_s. (A reduction in r_e due to the larger N_d is not sufficient to offset this.) Longwave downwelling fluxes at the surface (not shown) are identical between both runs and the observed value of $\approx$ 280 W m^-2.

The total cloud top radiative cooling exhibits an irregular periodic variation for both runs (Figure 8b), but differences are clearly present. A number of features are noteworthy. The maximum cooling is about -50 K day^-1 for the N250 run, and about -30 K day^-1 for the N30 run. From Figures 8b and 8c, it can be seen that the maximum entrainment is correlated with reduced cooling rates. The correlation between the entrainment and the cloud-top cooling may be attributed to the following: cloud-top cooling promotes turbulence and entrainment and when the entrainment is vigorous, the enhanced mixing of warmer and dries air from above leads to a reduction in the cloud-top cooling.