May 4, 2007
CE 394K.2 -- Hydrology
Instructor: Dr. David Maidment
Clouds play an important role in both the radiation budget and water balance of the earth. In the radiation budget, clouds regulate the feedback of long wave radiation from the earth and reflect some shortwave radiation from the sun. In the water budget, clouds must form before precipitation can fall. The rate (or intensity) at which precipitation falls can vary widely. The objective of this project is to investigate the relationship between clouds and precipitation intensity.
The comparisons contemplated above require a synthesis of data from very different sources. The basic approach is to obtain data for each parameter over the same time period; and visualize the information in way that encourages spatial comparisons. ArcGIS was selected as the tool for visualizing the data because of its’ unique ability to work with information from several frames of reference. Appendix A provides a detailed outline of the procedure used to make the figures.
Precipitation Intensity & Surface Temperature
Climate data for this project comes from the North American
Regional Reanalysis of climate (NARR), which is produced by
Figure 1 Precipitation Intensity for April 2006
Data from the NARR is distributed in the user-friendly Network Common Data Format (NETCDF) by the National Consortium for Atmospheric Research (NCAR). NETCDF files are useful for climate data because they accommodate multi-dimensional data. That is, data that varies in space and time. NARR data is available on a monthly average basis, or a three-hour basis. Monthly data was chosen for this project to match availability of cloud data.
Cloud information for this project was obtained from the Moderate Resolution Imaging Spectrometer (MODIS) on the satellite Terra. Terra belongs to a system of satellites, operated by NASA, dedicated to observing the earth. The MODIS instrument provides information about many different parameters including:
· Properties of Clouds and Aerosols
· Ocean color
· Atmospheric Water Vapor
· Cloud temperature and pressure
Like climate data, MODIS data is multi-dimensional in nature. The standard file format for MODIS data is the Hierarchical Data Format (HDF), which is a multi-dimensional file format similar to the NETCDF. However, ArcGIS does not currently support HDF files. The data presented here was obtained through the now defunct MODIS Online Visualization and Analysis System (MOVAS). This web-based tool allowed the user to generate maps of individual parameters, and provided a text file output of the data. MOVAS was discontinued after the data for this project were obtained. The current online interface does not provide the export to text file feature.
The physics of how clouds behave and how their behavior results in precipitation is a very complex subject, with its’ own body of literature. For the purposes of this project, a few parameters explain the interactions of interest. “From a macro-physical point of view, a cloud is the result of the chilling of moist air below its dew point.” . A moist air mass cools as it rises because its volume expands due to the attendant reduction in atmospheric pressure. However, the capacity of air to hold water decreases with temperature. Thus the cooler water vapor condenses as the temperature falls. Very small particles, called aerosols, must be present to serve as nucleation sites for condensation. As these nucleation sites become large, they become too heavy and begin to fall. A falling drop may (or may not) hit other drops on the way down. The process of smaller drops hitting larger drops is called coalescence, and it is essentially a Type II settling process. At the same as drops are growing in size by coalescence they are also shrinking by evaporation. Evaporation of cloud drops occurs constantly, because drops have a higher water concentration than the surrounding air. Based on this thought model, a cloud has many different sizes of particles within it at any time. This range of sizes can be expressed as a probability distribution, called a drop size distribution. This drop size distribution can be summarized as an area weighted mean radius :
where re is the effective radius, r is the radius of an individual particle, and n(r) is the particle size distribution. Mason (1952) reviews the physics of natural precipitation processes, wherein drop size is only one important factor . Other cloud properties that could influence precipitation are:
One parameter that combines many properties of clouds is the Optical Thickness. Conceptually, optical thickness is a “…a measure of how opaque a medium is to radiation passing through it” . Mathematically, optical thickness is defined as “the (dimensionless) line integral of the absorption coefficient…along any path in a … medium” . The mathematical definition can be expressed symbolically:
where K is the adsorption coefficient, z is the integration depth, and t is the optical thickness. This definition becomes more meaningful with an understanding of the adsorption coefficient. The adsorption coefficient can be thought of as the cross sectional area per unit volume. Figure 2 illustrates this concept.
Figure 2 Adsorption Coefficient
From the perspective of the incoming radiation, the red particles reduce the cross sectional area of the thin volume. Thus the adsorption coefficient can be thought of as:
where A is the cross sectional area, N is the number of particles, re is the effective radius, and V is volume of the element.
Figure 2 shows reflected radiation as a function of incoming radiation and albebo. The reflected radiation is ultimately what MODIS senses. The albedo will vary with the particle size, moisture content, and radiation wavelength as shown in Figure 3.
Figure 3 Variation of albedo with other parameters 
The reflected radiation will vary with particle size, which will vary with adsorption coefficient. With integration over the cloud depth many of the relevant properties are lumped into a single dimensionless parameter. In sum, optical thickness combines droplet size, water content and cloud height to give a normalized cloud size.
The results of this project are presented in the following five maps, depicting the months of January through May of 2006. Precipitation intensity is shown as the colored map, cloud optical thickness is shown with contours, and temperature is shown by symbol size. Precipitation intensity is depicted in units of kg/m2/s to avoid the need to distinguish between liquid and frozen precipitation. Assuming water has a density of 1000 kg/m3, a precipitation intensity of 1 kg/m2/s is equivalent to 1 mm/s. As discussed above, optical thickness is dimensionless. Temperatures are shown in units of Kelvin.
January 2006 shows significant precipitation in the
February 2006 shows a similar pattern as January. Precipitation is stronger in the South, and is accompanied by a well-defined area of high optical thickness. The northern area of high thickness and low precipitation is still present, though precipitation is slightly higher and the thickness is lower. February temperatures for this area are lower than January, possibly inhibiting cloud formation.
In March, surface temperatures begin to increase, causing
larger areas of high precipitation. The
areas of high intensity rainfall which extend from
As the map indicates, April can be severe weather season for
the middle of the
The distribution of precipitation intensity in May is very
different from the other months. The
Pacific Northwest seems to have much less rainfall, while the
To compare precipitation intensity over areas with similar optical thickness, zonal statistics were calculated for areas within optical thickness contour 20. Each month had between 20 and 30 different areas of optical thickness 20. The average over each area was calculated, and then averaged again on an area weighted basis. The result is monthly average precipitation intensity for areas with an optical thickness of at least 20. These calculations include areas of higher optical thickness because lower contours enclose higher contours.
Average intensity seems relatively constant for optical thickness contour 20. This result is somewhat unexpected, because of the areas of high thickness and low precipitation present during the winter months.
This analysis shows some correlation between optical thickness and precipitation intensity. In each map, areas of high intensity precipitation have a higher optical thickness. However some regions of high optical thickness occur without much precipitation, thus reducing the correlation between the parameters. On a visual basis, correlation seems to increase with the seasonal increase in temperature.
This subject area has many opportunities for future work, especially as more data becomes available. Future work might consider the correlation between precipitation intensity and optical thickness in a more quantitative way using geostatistical methods. Also, comparisons between the parameters on a shorter time scale could provide better insight into the mechanics of the process.
i. Precipitation Rate
ii. Temperature at Surface
i. The website used for this project was:
ii. Creating similar maps for different dates will require extracting the optical thickness data from the hdf file. See the duke website for one possible way to do this: http://code.env.duke.edu/projects/mget/wiki/HDF%20SDS%20to%20ArcGIS%20Raster%20tool
i. Using ArcCatalog, right click to create a New Personal Geodatabase, and right click to create a New Feature Dataset called “Basemap”
ii. Use coordinate system GCS_1984 for the coordinates, because this is the datum used by the NARR data
Using ArcMap, open an ArcGIS template for the
ii. Right Click on the states feature class use Data>Export Data to put the states into the Basemap feature dataset created above
Go to the following website to get the coordinates of
the geographic center of the
ii. Save these points to a dbf file using Excel
iii. Open a new ArcMap document
iv. Use Tools>Add X-Y Data to add the center points to ArcMAP
1. Import the coordinate system from the Basemap feature dataset to the center point data
v. Right Click on the center point events and use Data>Export Data to put the points into the Basemap feature dataset created above
i. This step sets the spatial reference for the map
i. Select a contour interval of 2 so that the map has enough information to see the surface, but not so much that it’s unreadable
ii. Set the path to store the shapefile of the contours in the appropriate directory
i. Specify the appropriate netcdf file and variable
ii. The netcdf file should have variables “x” and “y”. Use these variables as the X dimension and Y dimension, respectively.
i. Use the States feature class for the Zone Dataset
ii. Join the output table to the zone layer
i. The purpose of this step is to facilitate showing temperature information for regions already delineated on the map.
ii. Point at the center of each state (joined to the state attribute table, which joined to the zonal statistics table for temperature)
iii. Optical Thickness displayed as contours
iv. Precipitation Intensity displayed as a raster
i. Scale: 1:30,000,000
ii. Enable the Clip to Shape option and specify a lat/lon box similar to 10N to 60N and -133W to -63W
i. The formatting options for each type of data layer are accessed the same way:
1. Right Click on the data in the Table of Contents and select Properties, then select the Symbology tab and select
ii. Center Points
a. Show: Quantities>Graduated Symbols
i. Value: Select the mean value from the joined zonal average
ii. Normalization: none
c. Classification: Equal Interval
iii. Optical Thickness Contours
a. Show: Features>Single symbol
b. Select an appropriate lineweight and color
a. Check to Label features in this layer
b. Label Field: Contour values
c. Placement Properties: Horizontal
iv. Precipitation Rate
a. Show: Stretched
b. Choose an appropriate color ramp
c. Strech Type: Standard Deviations with n=2
a. Show: Features>Single symbol
b. Select an appropriate lineweight and color