1. Mesoscale variability and drizzle in stratocumulus
Kim Comstock
General Exam
13 June 2003

2. EPIC 2001 Sc cruise EPIC 2001 Sc cruise x image courtesy of Rob Wood
EPIC cruise on RHB, six days at WHOI IMET Buoy – primary data set that I’ve been studying
Features to note: large-scale regions of broken and unbroken Sc
These are also sometimes refered to as open and closed cells.
But within these regions there's mesoscale variability
(DEFINE MESOSCALE AS km FOR THE PURPOSES OF THIS ANALYSIS)
this is what we're trying to analyze and understand

3. EPIC 2001 Sc data
Data set
Meteorological measurements on ship and buoy (T, q, U, LW, SST)
Ceilometer
MMCR and C-band radar
GOES satellite imagery
I'll mention just the instruments from which we obtained the data that I'll be talking about today.
Both the Ron Brown and the buoy measured such parameters as T, q, U, downwelling LW rad & SST
The ship was also equipped with a scanning C-band radar.
ETL provided a ceilometer for measuring cloud base and a vertically-pointing mm-cloud-radar.
We also have GOES satellite images, like the one you just saw.

4. Why are Sc important? Areal extent and persistence
Effect on radiation budget
Sc also have a significant effect on radiation
These are low clouds, formed underneath a subsidence inversion, so they are warm, and do not decrease the outgoing LW radiation much, as compared to that from the surface. At the same time, the Sc reflect a significant amount of SW radiation, so they have an overall cooling effect on the atmosphere.
Other dynamics involved: subsidence, LW cooling at cloud top, entrainment, SW warming within the cloud, surface fluxes of heat and moisture, and drizzle (explain).

5. Key parameter: Sc albedo
mean droplet size
CCN  aerosols
cloud thickness
turbulence, entrainment, drizzle
diurnal and mesoscale variations
horizontal variability
mesoscale circulations
drizzle?
A key parameter for climate modelers is the albedo of the Sc. The albedo depends primarily on three things: the mean droplet size in the clouds, the liquid water path or cloud thickness, and the horizontal variability of the cloud layer.
The mean droplet size depends on the number of CCN, which in turn depends on the concentration of aerosols in the region. With more CCN, the cloud will consist of more, smaller drops, thus increasing the cloud’s reflectance (first indirect effect – Twomey 1977). Because it is more difficult for smaller drops to coalesce into drops large enough to fall out as drizzle, the cloud may last longer than a cloud with larger drops (second indirect effect – Albrecht 1989).
Cloud thickness is important because, up to a certain point, the optical depth of a cloud increases with its thickness, and albedo is also related to optical depth. Cloud thickness is maintained by moisture transported via turbulence up from the ocean surface. This turbulent overturning is driven largely by LW rad cooling at the cloud top creating negatively buoyant parcels that sink throughout the BL. The turbulence also drives entrainment, which can serve to thicken the cloud by eroding the inversion and raising cloud top, or to thin the cloud due to evaporation in the entrained dry air. A thick enough cloud will usually drizzle, and drizzle may thin the cloud by removing water. Cloud thickness is subject to diurnal and mesoscale variations.
In terms of albedo, the horizontal variability of the cloud layer relates largely to variation in cloud thickness, though other properties will vary correspondingly as well. This variability is partly controlled by mesoscale circulations (rising, sinking air) and may be affected by drizzle. To understand the inhomogeneity of the cloud, we have to understand the nature of the Sc structure and the life cycle of individual Sc elements.

6. Central Questions
To understand the physical processes that govern variability in Sc albedo, we must answer the following questions:
What is the structure and life cycle of Sc?
What is the role of drizzle in mesoscale variability?
What role does the diurnal cycle play?
structure and life cycle – want to know how much Sc there is, how long it lasts, how thick, which part is drizzling…
drizzle & meso var – we know there’s mesoscale variability, but we don’t know if it’s related to drizzle…
diurnal cycle – an important factor in SE Pacific Sc, can’t ignore it

7. Goals: using EPIC data to address central questions
Determine drizzle cell properties from C-band radar.
Obtain and physically interpret signatures of mesoscale variability from ship and buoy time series.
Estimate amount of drizzle and relate to mesoscale variability.
Analyze diurnal cycle and determine how it modulates all of the above.
structure & life cycle
mesoscale/horizontal variability … dynamics in Sc BL
drizzle…
diurnal…

8. MMCR time-height section
dBZ
hourly cloud top
hourly LCL
hourly cloud base
NOTE DIURNAL CYCLE, DRIZZLE
Here's a time-height section from the vertically-pointing MMCR for six days. The time axis is UTC, meaning that each date is at 6pm local time. Overplotted are hourly cloud-top height, from the MMCR, hourly cloud base height from the ceilometer, and hourly lifting condensation level, calculated from surface T and q. The MMCR data is in ~1 min resolution, so you can see the small-scale variability during each day; you can also see the variability in the hourly series.
Also note the strong diurnal signal in cloud top - it rises at night, and sinks during the day, fairly consistently.

9. Quantifying drizzle
We have reflectivity (Z) over a wide area around the ship from the C-band radar, but we want to know rain rate (R) information.
No suitable Z-R relationships exist for drizzle.
We developed Z-R relationships, Z=aRb , from in-situ DSD data at cloud base and at the surface:
aircraft (N Atlantic) and surface (SE Pacific) data
linear least squares regression (log10Z, log10R)
Ideally, we want to know R at the surface.
We have reflectivity data from radars, we want rain rate information.
We compute Z-R relationships because there are none established for drizzle. Use in-situ DSDs. Meth blue from ship and aircraft data from another study (UK Met office, 12 flights in drizzling St/Sc off coast of UK). Calculate linear least squares fit to log10Z-log10R.
Slope of Z-R for convective rain is We find at cloud base, at surface. Significantly different (due to evaporation…?)
Surface DSDs give surface Z-R, Cloud DSDs give us Z-R relat for cloud base… C-band reflectivity data is ~ at cloud base, but we want to find out how much rain hits the surface, for moisture/heat budget

10. Quantifying drizzle - method
Evaporation-sedimentation model
assumes truncated exponential drop-size distribution (DSD) with mean size r
run with various r’s and drop concentrations
Obtain model reflectivity profiles (Z(z)/ZCB) and compare with MMCR profiles.
infer DSD for each MMCR profile
use model to extrapolate cloud base DSD characteristics to the surface (get surface R)
Develop “bi-level” Z-R relationship using cloud base ZCB to predict surface Rs.
We start by estimating a cloud-base Z-R relationship using the MMCR data, via a technique developed by Rob Wood. He ran an evap-sed model with different DSDs (assumed truncated exponential distributions, characterized by mean radius r-bar) and Ns, and found the change of reflectivity below the cloud. Compared results with 20-min avg MMCR profiles to get an approx DSD and N at cloud base.
Put these cloud base DSDs into evap-sed model to determine approx R at surface. Fit curve (as in previous slide) to cloud base Z, surface R to get bi-level Z-R relation

11. Quantifying drizzle - results
Apply bi-level Z-R to C-band cloud reflectivity data to obtain area-averaged rain rate at the surface.
Average drizzle rates for EPIC Sc
0.93 mm/day at cloud base (range 0.3-3)
0.13 mm/day at the surface (range )
Uncertainties due to
C-band calibration (2.5 dBZ)
Z-R fitting procedure
typical DSD?
(ZCB=92Rs0.7)
large uncertainty in area-averaged rain rate due to C-band calibration uncertainty
smaller uncert due to Z-R fitting procedure (~width around Z-R best fit line)

12. Diurnal cycle At night the BL tends to be well mixed (coupled).
During the day, the BL is less well mixed (decoupled).
It tends to drizzle most during the early morning.
RECALL MMCR figure, DIVISION INTO COUPLED, DECOUPLED, DRIZZLING CATEGORIES.
There are other features associated with the diurnal cycle.
First, at night, the BL tends to be well mixed or coupled. At night, there's no solar heating in the cloud layer to offset the LW cooling at the cloud top. This drives strong mixing throughout the BL as negatively buoyant air parcels at the top of the cloud sink toward the surface, also driving more entrainment, and therefore a thicker cloud.
During the day, when there is some SW absorption in the cloud layer, the cloud top cooling effect is not as strong, there's not as much energetic mixing of the BL, so it can become decoupled, separating the surface layer from the cloud layer.
When the cloud thickens, it is more likely for larger drops to form by falling through the cloud and collecting smaller drops. When they get big enough, these drops can fall out as drizzle.
As you saw (will see) in the MMCR vertical profile, there's a great deal of variability that's not associated with the diurnal cycle. Some of it is mesoscale variability that we are trying to analyze and understand, some of it is due to synoptic and aerosol concentrations, about which we do not have very much information.

13. Coupled BL U T cloud thickness 410 ± 60 m cloud base 930 ± 30 m
RESULTS OF ANALYSIS PRESENTED AT CLOUDS SEMINAR.
Here's a coupled cloudy element, not drawn to scale. We expect the cloudy element to be about 30 km across (from satellite imagery), but the BL is only about 1 km deep. Mean properties... small standard deviation (in all properties: cloud base height, cloud thickness, T, q, etc.)
T and U in quadrature - convergence where it's warm: warm, rising air; divergence where it's cooler: cooler, sinking air. A direct circulation. T and q were not well correlated, but we did show the slightly more moist warmer air in the thermodynamics plots, so it's likely that the rising air is warm and moist, sinking air is cooler and drier.
~ 30 km

14. Decoupled BL cloud thickness 310 ± 110 m cloud base 930 ± 60 m
Moving on to the decoupled BL, the surface layer and the cloud layer have separate circulations, so it is difficult to say from the surface series what is happening in the cloud layer.
[Moyer & Young (1994) found for FIRE data that coupled & decoupled situations were very similar… we will try to see if this is the case… but I suspect it isn’t entirely because the cloud tends to be much thinner and occasionally disappear…]
Mean properties... thinner cloud than coupled case, with a larger standard deviation, but the cloud base is at about the same height.

15. Drizzling BL cloud thickness 415 ± 150 m cloud base 890 ± 110 m
Things are also complicated in this situation. We expect some decoupling, partly because the LCL and cloud base are far apart frequently during drizzling episodes. Also, in a drizzling situation, latent heat of condensation warms the cloud layer while evaporation cools the subcloud layer, this can stabilize the BL and lead to decoupling. However, because the drizzle cells last for such a long time, we know there must be some coupling, or source of moisture from the surface. In some regions, Cumulus clouds form at the top of the surface layer, bringing moisture into the Sc above (for example in ASTEX in the north Atlantic). This is not the case here, so there must be some other type of coupling mechanism.
The drizzling clouds have the same mean thickness as the coupled category, but the standard deviation is 2-3 times greater, meaning there are thick bits that are drizzling and thin or clear patches in between. The cloud base is lower and more variable as well.

16. Mesoscale variability
Goes 8 Visible
19 October
0545 Local Time
WANT TO EXPLORE RELATIONSHIP BTWN DRIZZLE AND ENHANCED MESOSCALE VARIABILITY TO THE EXTENT POSSIBLE WITH THIS DATA SET. Here’s an example of how they are associated…
Here is an example of MV in both the horizontal and the vertical, where you can see drizzling episodes. The satellite image was taken at almost 6 am local time, and I've circled the position of the ship at that time in red. The yellow lines correspond to the approximate cloud advection path during the previous and following six hours. The previous path, from midnight to 6 am is shown in vertical profile from the MMCR in the middle figure, while the following six hours after the satellite image is shown in the bottom MMCR figure. Times are in local time, and the MMCR data only extends to 150 m.
So in the first six hours, we can see a lot of drizzle and variable conditions, during the broken/patchy (variable) cloud conditions. When the cloud becomes more uniform (~9am), there is less drizzle and less variability (though it is still present - you can see, perhaps, some cloudy elements - rising top, lowering base). So we can associate MV and drizzle, but we can't yet pinpoint which is the chicken and which is the egg.

17. Summary of previous work
Though the diurnal signal is dominant, mesoscale structure is an integral part of the dynamics of the Sc BL.
BL time series classified as coupled, decoupled or drizzling.
There is a significant amount of drizzle in the SE Pacific BL, and it is associated with increased mesoscale variability
This is what I’ve already done…
BL is either coupled, decoupled or drizzling  somewhat different dynamics associated with each
 IN ORDER OF INCREASING INHOMOGENEITY
lots of drizzle & evaporation in this BL

18. Future work
Compare Sc mesoscale structure with previous studies of mesoscale cellular convection (MCC)
Further examine radar data for 2-D and 3-D information
circulations (also use DYCOMS II and possibly TEPPS Sc)
compositing/tracking
Analyze buoy time series for mesoscale variability in relation to “drizzle”.
Here’s what I’m going to do to try to explore and describe the dynamics and properties of the Sc that relate to its albedo.
…inputs to/comparisons with LES models … GCM parameterizations
Analyze buoy air-sea DT time series
*** find additional evidence to relate drizzle & mesoscale variability

19. MCC comparisons
Compare our coupled cell with closed cell from Rothermel and Agee (1980) q
Here’s an example of a study of closed-cell MCC by Rothermel & Agee (1980) during AMTEX-75. Our coupled cell results are in basic agreement with this model. Other examples that we can compare our results with are Agee & Lomax’s (1978) open cell from the same study, and Moyer & Young’s (1994) study of closed cells from FIRE.
If existing models compare well with our results at the surface, we can essentially extrapolate our results to the cloud layer using previous ideal models. Also, the SE Pacific Sc have not been extensively studied before. By comparing our results w/ results from other regions, we can determine if dynamics are similar or different in different Sc regions. (Important to know also for climate models – would be most convenient if all Sc regions were the same…)
Showed in previous talk: comparison w/ old conceptual model of closed cell and our coupled cell {Rothermel and Agee looked at aircraft data from AMTEX-75 in a cold-air outbreak in the East China Sea. They flew through closed cells, which are akin to our coupled case. They have warm, moist, rising air in the center of the cell, and drier, sinking air on the edges. They also have this funky double temperature wave, which is a strange artifact of their data collection. For the most part, we are in agreement.}
Agee and Lomax (1978) made a sketch of an idealized open cell using sounding data (RH, theta, theta-v). (But, just as Rothermel and Agee used flights beneath 2 cells, Agee and Lomax used 2 soundings.)

20. Radial velocities
EPIC C-band volume-scan radial velocities are probably unusable due to pointing errors associated with these scans.
Vertical RHI scans appear less susceptible to error, so the radial velocity data (in the RHIs) may be useful for qualitatively looking at 3-D circulations in the BL.
TEPPS volume scans and DYCOMS II vertically-pointing radar data are other possibilities.
DATA: RHI’s from EPIC, possibly volume scans from TEPPS, MMCR from DYCOMS II
WHY: Ideally we want circulations from (radial velocity) open/closed cells
want to understand physics in Sc open/closed cells & how drizzle affects circulations (& cloud cover, thickness…)
RHI scans 6x/hour

21. 0
90
180
270
15 km
30 km
Example
C-band volume scan at 1 degree, out to 30 km radius
reflectivity ranges from –12 (cutoff) to ~25 in this image
1 mm/hr corresponds to ~ 16 dBZ (from MMCR CB Z-R: Z = 16 R ^ 1.2)
note 0, 90, 180 and 270-degree directions (N E S W)

22. EPIC Sc RHIs 17 October 2001 1058 UTC
2 km
19 km 0
90
180
Ere are vertical RHI scans to the N E S and W, between about 2 and 19 km away from the radar. You can see high-reflectivity cells, especially in the 0 and 270 (N and W) directions…
270
dBZ

23. EPIC Sc RHIs 17 October 2001 1058 UTC
2 km
19 km 0
90
180
These are the same RHI’s, but with radial velocity (positive away from the radar).
You can see drizzle cells modifying the cloud top / circulation conditions “modification of dynamic environment by drizzle”.
I am going to look at a number of examples qualitatively to find consistent behaviors surrounding drizzle cells. The examples will be selected from coupled/decoupled/drizzling times if possible. This will supplement our findings from the time series data in describing the dynamics of the Sc BL. It may also give us further insight into the relationship between mesoscale variability and drizzle. …
hopefully will help us to understand the chicken and the egg problem in a QUALITATIVE manner
If I look at TEPPS, I can also look at RHI’s, but it may be simplest to look at PPI’s within the cloud layer. For each of these I can subtract the mean radial velocity at each location in the circle (assuming there is sufficient reflective material to calculate a mean) and then look at the residual radial velocities for evidence of convergence/divergence. TEPPS, though, had situations of Cu rising into the Sc, from which much of their drizzle came. So the dynamics might be somewhat different.
270
m/s

24. Comparison with DYCOMS II
Anticipate receiving DYCOMS II aircraft data (vertically-pointing MMCR data and time series)
look for circulations associated with closed cells and drizzling conditions
look at variability associated with drizzle (flight RF02)
We will look at (similar) vertically-pointing MMCR data from DYCOMS II flights off the coast of CA. We will look at reflectivity and radial (vertical) velocity data from their cloud radar to find circulations associated with non-drizzling and drizzling conditions.
I may also look at time series of T, q, U, w, etc for several flights. I may be able to separate the time series into coupled/decoupled/drizzling time periods and look for similarities to EPIC findings in the surface layer (e.g. increased variance associated with drizzling conditions).
Here is an example of downward-pointing reflectivity from the most-drizzly flight to show that some of the conditions in DYCOMS were similar to those in EPIC.

25. C-band composite Cell 1 Cell 2
Back to 2-D C-band reflectivity data from EPIC: Here’s a 2-D volume, with Cell #1 shown at various times throughout its life. Cell #2 is also highlighted. The tracking for these sample cases was essentially performed by hand.
Advection performed through 2-D maximum correlation analysis with each successive C-band image.
***Through compositing studies (or cell-cut-out / tracking by hand) we can obtain structure and life-cycle information***

26. Compositing/tracking: preliminary results
Examples from tracked drizzle cells
Time avg PDF of dBZ
Average reflectivity
Time (hr UTC)
dBZ
Example of 3 cells (first two shown on previous slide) – similar histograms, but first is fading, second growing, third growing then fading. The lifetimes of these cells overlaps – will need to look at some other examples from another day to ensure that we get a representative sample.
We’re trying to understand what is the same and what is variable about these drizzle cells.
***Through compositing studies (or cell-cut-out / tracking by hand) we can obtain structure and life-cycle information*** such as typical strength & size of drizzle cells, life cycle information
CAN ALSO LOOK AT RAIN RATE vs AREA  will see that the highest R (dBZ) comes from a small fraction of the area
We may try to use a more automated method to track drizzle cells and/or cloud elements from satellite data (if can get thresholds right) is presented in Williams and Houze This algorithm IDs features with [for example: reflectivity] greater than some threshold.
Compares adjacent time steps t and t+dt. If features overlap by [threshold] %, they are the same feature. This % can be of either the feature in the first or second time step, in the cases of decay or growth. The features can split or merge.
WHY (threshold dependent results:) automated procedure to get *sizes, and some lifetime information (w/in C-band limit), number of cells, splits and mergers, behavior of drizzle cells - further describe structure and life cycle of Sc open cells
ALSO try to use on 1-hr satellite images … can compare with sizes of cells from radar, potentially longer data set – more info, sizes more directly related to albedo (a.o.t. drizzle), possibly more info on lifetimes
(PDFs of size, strength to compare with models (?), correlate drizzle cell strength and size… )

27. Drizzle’s signature
Air-sea temperature difference appears to be a good indication of drizzle occurring in the area.
As we noted previously, we see more variable cloud conditions associated with drizzle - this leads to a lower cloud fraction, on average.

28. Drizzle’s signature
Here are two time series from the ship, again in UTC time. The bottom plot shows C-band area-averaged reflectivity data, with the -5 dBZ threshold indicating when it's drizzling in the area. On top, we have the difference between SST and air temperature. When this difference is large (say, above 2 degrees C, indicated by the line), that means there is a substantial amount of evaporation, probably caused by drizzle. You can see that when it's drizzling, the air-sea temperature difference is large - it is also highly variable.

29. Drizzle climatology
Will apply air-sea DT analysis to year-long buoy time series to determine
frequency and persistence of drizzle
diurnal cycle information
cloud fraction associated with drizzle
Longwave radiation can be used as a proxy for cloud fraction in the buoy data series.
relationship to satellite images
From the ship series, we compared air-sea temperature difference "drizzle" signals with cloud fraction from the ceilometer to try to determine something about the increased variance. But with the buoy, we have to look at the long-wave radiation to get cloudy vs. non-cloudy time periods - provides a reasonable cloud fraction over time (tested on ship data where I could compare cloud fraction and LW-estimated cloud fraction).
So the next step in this analysis is to apply the air-sea temperature difference to the long buoy series in conjunction with the cloud fraction signals to hopefully glean more information about drizzle and mesoscale variability over longer periods of time.
WANT further evidence to associate drizzle w/ incr mesoscale variability & more intermittent cloud cover (open cells)

30. Buoy data Example of SST-Ta for 15 September 2001 satellite overpasses
Here’s an example of a random day in the buoy series. It appears to be drizzling during the night and early morning (.5 = 6 am, .75 = noon)
We’ll look at satellite overpasses at 5:45 am (IR), 8:45 am, 11:45 am and 2:45 pm (VIS) to look at the cloudiness associated with drizzle…

31. Buoy data GOES 8 IR 1145 UTC WHOI BUOY
5:45 am, IR image, (recall it has recently begun to drizzle), image is cut off (we’ll be getting better data), but I can see a slight clearing region surrounding the buoy
WHOI BUOY

32. Buoy data GOES 8 Vis 1445 UTC WHOI BUOY
8:45 am, VIS image, substantial drizzle, open-cell conditions
WHOI BUOY

33. Buoy data GOES 8 Vis 1745 UTC WHOI BUOY
11:45 am, slacking drizzle, starting to become closed-cell again
WHOI BUOY

34. Buoy data GOES 8 Vis 2045 UTC WHOI BUOY
2:45 pm, no drizzle, closed-cell conditions
This type of visual analysis can be performed to confirm ‘drizzle indicator’s’ validity ALSO relationship between open cells (enhanced variability) and drizzle. Perhaps ~ 10 cases would be sufficient. But there are time periods when it does not drizzle for several days, and a few of these would be interesting to look at as well, to see if there is less mesoscale variability (flip side of the coin).
WHOI BUOY

35. Schedule Date Goal Summer 03 Submit Z-R paper
Compositing & sizing of drizzle cells
Summer-Fall 03
Contribute to broken cell/drizzle paper
Fall 03
Submit mesoscale variability paper
Winter-Spring 04
C-band radial velocity analysis
Spring-Summer 04
DYCOMS II data analysis
Summer-Fall 04
Satellite – time series analysis
Winter 05
Finish

37. LW as a proxy for cloud fraction
LW-sTa4 (W/m2)
Ship 6 days – LW – sigma*Ta^4 (to try to remove effects caused by change of height of cloud base…)
pick –50 W/m^2 as a threshold between cloudy/non-cloudy
calculate hourly cloud fraction to compare with ship ceilometer hourly cloud fraction (good)
[ALSO WANT TO KNOW HOW REPRESENTATIVE EPIC 6-DAYS WERE… can compare cloud thickness and fraction with TRMM satellite 3-monthly means, and, eventually cloud fraction and drizzle frequency from buoy]

38. C-band reflectivity (gray scale)
Drizzle and open cells
GOES image (color) and
C-band reflectivity (gray scale)
GOES image only
I mentioned in my proposal that I will be working with Sandy on relating increased drizzle to open cells. This is an example that she made, showing reflectivity from the C-band radar overlayed on reflectance from a GOES satellite image. In this case, the reflectivity got quite high (over 17 dBZ). With images like these we will show that higher reflectivities/rain rates tend to occur during the broken cloud / open cell conditions rather than closed cell / unbroken cloud conditions.

39. (Less) drizzle and closed cells
GOES image (color) and
C-band reflectivity (gray scale)
GOES image only

40. Evaporation-sedimentation model
r (mm)
N (#/L)

41. C-band Sc Volume Scan

42. MCC – closed cell
Moyer
&
Young
1994

43. Tracking algorithm Williams and Houze 1987
A more automated method to track drizzle cells and/or cloud elements from satellite data (if can get thresholds right)
Algorithm IDs features with [reflectivity] greater than some threshold.
Compares adjacent time steps t and t+dt
If features overlap by [threshold] %, they are the same feature. Parts b and c show that this % can be of either the feature in the first or second time step, in the cases of decay or growth.
Parts d and e show examples of a split and a merger.
WHY (threshold dependent results:) get sizes, tracks, lifetimes (w/in C-band limit), number of cells, splits and mergers, behavior of drizzle cells
further describe structure and life cycle of Sc open cells
ALSO try to use on 1-hr satellite images … can compare with sizes of cells from radar, potentially longer data set – more info, sizes more directly related to albedo (a.o.t. drizzle), possibly more info on lifetimes
Williams and Houze 1987