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1. Stratiform Precipitation Fred CarrCOMAP NWP Symposium Monday, 13 December 1999

2. Stratiform precipitation is the precipitation produced by large-scale vertical motions. Specifically, it is the precipitation produced by large-scale, dynamic ascent of stably stratified, saturated air. (Such precipitation is normally grid-scale, resolvable by the model grid.) The forecast amount of stratiform precipitation can be estimated simply by lifting a parcel along a moist adiabat. First we will look at an equation used to estimate stratiform precipitation and then apply it to an example. Think about how each of the components of the equation functions, and how it physically affects the precipitation process. Stratiform Precipitation

3. Stratiform Precipitation • Ignoring cloud microphysical processes, precipitation is simply the sum of the condensation produced in parcels lifted from all the model vertical layers within the cloud. The final form of an equation to estimate stratiform precipitation (P) is: • In this equation rsis the change in the saturation mixing ratio through a model layer (which takes into account the water being squeezed out of this layer),  is the vertical motion within the layer (which provides the rate at which condensation is occurring). The  symbol says that we are summing the following term over each model layer from the pressure level at the cloud top (ptop) to the pressure level at the cloud bottom (pbot). The negative sign means that as rs decreases (as air is lifted to higher and cooler levels), water vapor is condensing and precipitation is being formed.

4. Stratiform Precipitation • Note that this equation is a simplification of those actually used. In addition to ignoring the details of precipitation formation, we are also using pressure coordinates to keep things simple.

5. To demonstrate how the equation works, we will generate a precipitation forecast from actual data collected for Portland, Maine from 00 UTC, 7 April 1982, when a 15-inch snowfall occurred. Step 1 We begin by dividing the atmosphere into 100 hPa layers in the vertical (as illustrated in the near right) and assuming that little precipitation comes from above 400 hPa. These will represent our model layers. Step 2 We first need to obtain the saturation mixing ratios in each model layer, so we will examine the sounding data on a Skew-T diagram (above right) from 00 UTC, 7 April 1982 for Portland, Maine. Saturation at all levels is indicated by the dewpoint line (in green). Stratiform Precipitation

6. Step 3 The next component of the equation for which we need information is the vertical motion. We will assume a parabolic profile of , with=0 at 1000 hPa and 200 hPa (see above left). We will base the parabola on a maximum value of -10 microbars/sec at 600 hPa, which was predicted by the model for that day. Stratiform Precipitation

7. Step 4 Now we can begin to create a table which includes values for all the components of the precipitation equation. First we can obtain the temperature for each 100 hPa from the sounding (sounding is in red, temperature lines are in aqua.) Stratiform Precipitation

8. Step 5 Once we have temperature, we can determine rs by reading the value of the saturation mixing ratio line (in light blue) intersecting the temperature line at each layer boundary. Stratiform Precipitation

9. Step 6 We can then compute the rs that will result from lifting the parcel 100 hPa at each level. To find that value, follow the moist adiabat (in dark blue) up to the next model pressure level. Stratiform Precipitation

10. Step 7 With these values in place, we determine rs (change in rs through the layer) by subtracting the second rs value from the first. This value is assigned to the mid-point of the layer. Stratiform Precipitation

11. Step 8 The vertical velocity for the mid-point of each layer is determined from the profile we created at the beginning of the exercise. ( is given in microbars/sec) Stratiform Precipitation

12. Step 9 To complete the solution to the equation below, we find the product of  and rs for each layer and then multiply the sum by -1/g. This yields a precipitation value of 4.44 b sec/m. The units can be reduced to kg/m2 /sec which is more meaningful for precipitation measurement. Total= -43.38 Stratiform Precipitation

13. Stratiform Precipitation • Precipitation quantities are more familiar in units of centimeters and inches per day. In these units the result is 3.8 cm or 1.5 inches of liquid per day. If we use a 10:1 snow to liquid ratio, this would yield about 15 inches of snow, which was what was observed that day.

14. Stratiform Precipitation • Although the vertical velocity profile was fabricated in this case, the profile used was reasonable for a strong synoptic scale system. • This calculation is somewhat involved when illustrated step by step, but a computer can do it very quickly. Most models today, however, will include additional effects such as: • evaporation of precipitation • precipitation efficiency effects such as accretion rates, collection, aggregation, and coalescence • the physical differences between liquid and ice (e.g., the latent heat of fusion is greater than the latent heat of condensation)

15. Stratiform Precipitation • This exercise also suggests how errors can occur in precipitation forecasts. In order to make the best possible forecast we would have to know the following characteristics throughout the vertical extent of the atmosphere where the precipitation process is occurring: • low-level moisture (to determine the cloud base) • cloud interior temperatures (so the saturation mixing ratios and condensation rate can be determined) • vertical motion at every level • All of these fields have large mesoscale variability and are not measured well, so even the initial conditions aren’t well suited for an accurate precipitation forecast. This should suggest to you why precipitation forecasts in NWP are so difficult, even if we ignore the more complicated effects of convection.