Precipitation Intensity


Cloud Physics


Brad Eck


May 4, 2007


The University of Texas at Austin

 CE 394K.2 -- Hydrology

Instructor: Dr. David Maidment



Table of Contents



Data Sources

Cloud Physics and Remote Sensing

Results and Discussion

Conclusions and Future Work


Appendix A: Procedural Outline




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.


Data Sources


Precipitation Intensity & Surface Temperature


Climate data for this project comes from the North American Regional Reanalysis of climate (NARR), which is produced by the National Center for Environmental Prediction.  The NARR product combines the latest algorithms for climate prediction with historical measurements of climate data to create a spatially continuous dataset of more than 400 variables.  Figure 1 shows an example of NARR data displayed by the Integrated Data Viewer.


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. 


Cloud Physics and Remote Sensing


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.” [1].  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 [2]:


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 [3].   Other cloud properties that could influence precipitation are:

  • Height
  • Temperature
  • Pressure
  • Moisture content


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” [4].   Mathematically, optical thickness is defined as “the (dimensionless) line integral of the absorption coefficient…along any path in a … medium” [5].  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 [6]


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.


Results and Discussion


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 Pacific Northwest, and lighter precipitation in the South and over the Northeast.  These areas of high rainfall intensity are associated with higher values of optical thickness (around 24).  The map also shows areas of high optical thickness (34) just north of North Dakota, but this area has very little precipitation.  This effect is probably due to temperature, as air can hold less water as it cools.  At low enough temperatures, water vapor might condense on aerosols, but not coalesce into large enough particles to fall to the ground.





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 Texas to Ohio, are reminiscent of the large lines of thunderstorms that move through the Midwest in the springtime.



As the map indicates, April can be severe weather season for the middle of the USA.  Areas of high intensity rainfall occur with high optical thickness values.   As the surface temperatures rise, the northern area of high thickness and low precipitation as disappeared.  Also, the optical thickness values in the Pacific Northwest have decreased from previous months.  The optical thickness as the northwestern corner of the contiguous United States was 24 for January and March, but is only 18 for April.



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 Eastern USA is nearly covered with rainfall.  The closed contours representing high optical thickness over the Northwest have disappeared along with the precipitation.


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. 


Conclusions and Future Work


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.



[1]        Ludlam, F.H. Introduction to [3]


[3]        Mason, B.J. The Physics of Clouds. Oxford University Press,1957.



[6]        King et. al., “Remote sensing of cloud, aerosol, and water vapor properties from the Moderate Resolution Imaging Spectrometer (MODIS),” IEEE Trans. Geosci. Remote Sens. 30, 2-27 (1992).


Appendix A: Procedural Outline


  1. Preliminaries
    1. This appendix does not describe every mouse click required to make the maps, but rather lists the major steps.  Some familiarity with ArcGIS is assumed.
    2. ArcGIS menu sequences and tools (from ArcToolbox) are in boldface type
    3. NARR data use the GCS_1984 coordinate system, so all of the map components use these coordinates
  2. Get NARR Data
    1. Download site:
    2. A detailed tutorial for using the site is available
    3. Download NARR monthly file from thredds server, using the netcdf server to create netcdf files that contain the parameters of interest:

                                                               i.      Precipitation Rate

                                                             ii.      Temperature at Surface

    1. Select the option to add lat/lon values if necessary
  1. Get MODIS Data
    1. The data for this project were obtained using the now non-existent website called MOVAS (short for MODIS Online Visualization and Analysis System). Select the parameter and geographic region of interest, and click the button to generate a text file.

                                                               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:


    1. Save the text file as a database IV file (.dbf) using Excel
  1. Create Basemap
    1. Geodatabase

                                                               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

    1. United States

                                                               i.      Using ArcMap, open an ArcGIS template for the United States using File>New… and select the ConterminusUSA map on the USA tab

                                                             ii.      Right Click on the states feature class use Data>Export Data to put the states into the Basemap feature dataset created above

    1. State Centers

                                                               i.      Go to the following website to get the coordinates of the geographic center of the United States:

                                                             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

  1. Optical Thickness Contours
    1. Open a new ArcMap document, and add the Basemap feature dataset

                                                               i.      This step sets the spatial reference for the map

    1. Add optical thickness data obtained from MODIS for a given month using Tools>Add X-Y Data



    1. Create a raster from these points using Spatial Analyst>Interpolate to Raster>Kriging


    1. Create contours to represent the surface shown by the Kriged raster using Spatial Analyst>Surface Analysis>Contour

                                                               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



  1. Average Temperatures
    1. Open a new ArcMap document, and add the Basemap feature dataset
    2. Open the Multi-dimension toolbox and select the tool to Make NetCDF Raster Layer

                                                               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.



    1. Calculate the average temperature for each state using Spatial Analyst>Zonal Statistics

                                                               i.      Use the States feature class for the Zone Dataset

                                                             ii.      Join the output table to the zone layer


    1. Join the StateCenters feature class to the States feature class using the State Name field

                                                               i.      The purpose of this step is to facilitate showing temperature information for regions already delineated on the map.



    1. Save the ArcMap document
  1. Finalize and Format the Map
    1. Add the precipitation intensity information using the Make NetCDF Raster Layer of the Multi-dimension toolbox.
    2. At this point the map should contain all of the data to be displayed

                                                               i.      The United States

                                                             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

    1. Switch to Layout view, and right click on the dataframe and select properties.  This control over the display so multiple maps are comparable

                                                               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



    1. Formatting

                                                               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

1.      Symbology

a.       Show: Quantities>Graduated Symbols

b.      Fields

                                                                                                                                       i.      Value: Select the mean value from the joined zonal average

                                                                                                                                     ii.      Normalization: none

c.       Classification: Equal Interval

                                                            iii.      Optical Thickness Contours

1.      Symbology

a.       Show: Features>Single symbol

b.      Select an appropriate lineweight and color

2.      Labels

a.       Check to Label features in this layer

b.      Label Field: Contour values

c.       Placement Properties: Horizontal

                                                           iv.      Precipitation Rate

1.      Symbology

a.       Show: Stretched

b.      Choose an appropriate color ramp

c.       Strech Type: Standard Deviations with n=2

                                                             v.      States

1.      Symbology

a.       Show: Features>Single symbol

b.      Select an appropriate lineweight and color

  1. Zonal Average Intensity
    1. Use the Selection>Select by Attribute tool to select all of the 20 contours



    1. Export the selected contours to a new shape file by right clicking on the item and selecting Data>Export Data
    2. On the Spatial Analyst>Options tab set the analysis extent to the displayed area.  Since the display was set earlier using the Data Frame properties, this ensures that the same area is used for the calculations.
    3. Use the Spatial Analyst>Zonal Statistics tool to average the precipitation intensity over the areas of contour 20



    1. Open the summary table in Excel, and compute an area weighted average of the mean values.