Development of a New Precipitation-Effectiveness Index

Dwain Daniels and Dr. Greg Johnson

This paper describes the methodology used to develop a Thornthwaite Precipitation-Effectiveness Index (PE) geospatial data layer. The equation was originally published in 1931 and requires average monthly temperature and precipitation data. This index is used extensively by the Natural Resources Conservation Service (NRCS) for derivation of the "C" factor for the Wind Erosion Equation and other natural resource applications. In this project, a Precipitation Effectiveness (PE) index is calculated using Parameter-elevation Regressions on Independent Slopes Model (PRISM) data obtained from the NRCS National Water and Climate Center. PRISM is a modeling system that uses point measurements of climate data combined with digital elevation data to generate the gridded monthly climate estimates necessary for deriving PE index values.


The NRCS is currently engaged in changing its way of conducting geospatial business activities. Personnel are starting to work with digital technology as opposed to hard copy documents throughout all levels of the agency. Conversion of existing geospatial tools and applications into the digital realm is one of the challenges faced in this effort. Incorporation of "new" geospatial data into business activities is also a challenge for employees that are new to the technology. "What can these data be used for?" is a common question. This paper examines a combination of these two challenges: using "new"data to produce a digital version of an existing hard copy map that has been in use for many years, and exploring other possible applications.

Estimation of soil moisture is necessary for a number of natural resource and agricultural applications. Soil moisture estimates often are considered to be proportional to the Thornthwaite precipitation-effectiveness (PE) index (ESS, 2000). The PE Index is an attempt to estimate precipitation effectiveness for plant growth. It has been used by NRCS for many years in a variety of applications. The equation is based on work by C.W. Thornthwaite published in 1931 (Thornthwaite, 1931). The PE Index, shown below, is the sum of monthly indices that are calculated with the monthly precipitation (inches) and temperature (F).

PE = å12 115 [P/T-10] 10/9
where P is average monthly precipitation (inches) with 0.5 being the minimum value, and
T is average monthly temperature (degrees F) with 28.4 F being the minimum value used in the calculation.

Figure 1 below is an example of a scanned PE Index map currently being used. It was produced in 1957 with data collected during a 20 to 30 year period prior to 1955. The map was produced at the Cartographic Center in Ft. Worth, Texas. Compilation materials used to create this map are on record as having been destroyed in 1984. Documentation of the specific methods used to create this map has not been recovered.

Annual P-E Index in the Central Great Plains
Figure 1. Annual P-E Index in the Central Great Plains.

One of the uses of the PE Index is the calculation of the climatic factor (C) to characterize wind speed and surface soil moisture used in the Wind Erosion Equation (ESS, 2000). The climate factor (C) is calculated using the equation:

C = 34.48 x V3 / (PE)2
where C is the annual climatic factor,
V is average annual wind velocity, and
34.48 is the constant used to adjust local values to a common base.

The equation below is the general form of the relationship currently used by NRCS to estimate the average annual soil loss (E):

E = f (IKCLV)
where I is the soil erodibility index,
K is the ridge roughness factor,
C is the climactic factor,
L is the unsheltered distance along prevailing wind erosion direction, and
V is the vegetative cover factor.

This illustrates how the C-factor and thus the PE index value are used as important components of conservation planning and are used to derive soil erosivity estimates.

Another use of the PE Index by NRCS is as a soil climate property. In many of the Official Series Descriptions (OSD) for soils in the Great Plains, the PE Index is included as an element of the geographic setting. It is considered an indicator of the potential for plant growth in this region where moisture is frequently the most limiting factor.

Materials and Methods

The climatic data used were the gridded mean monthly precipitation and average temperature coverages of the U.S. created using the Parameter-elevation Regressions on Independent Slopes Model (PRISM) developed by researchers at the Spatial Climate Analysis Service (SCAS) at Oregon State University (Daly et al., 2000; Daly et al., 1994). It represents the climatic data of the years 1961 to 1990. Additional information on PRISM can be found on the NRCS web site at, including the description below:

PRISM was developed by Dr. Christopher Daly of Oregon State University and is a hybrid statistical-geographic approach to mapping climate. PRISM uses point measurements of climate data and a digital elevation model (DEM, a digital, gridded version of a topographic map) to generate estimates of annual, monthly and event-based climatic elements. These estimates are derived for a horizontal grid and are compatible for use on Geographic Information Systems (GIS). PRISM is not a static system of equations; rather, it is a coordinated set of rules, decisions and calculations designed to mimic the decision-making process an expert climatologist would invoke when creating a climate map. PRISM was originally developed in 1991 for precipitation estimation, but more recently has been generalized and successfully applied to other climate elements and derived variables, including temperature, snowfall, degree-days (heat units) and frost dates.

Data processing was performed using Esri ArcINFO 8.0® with GRID module and ArcINFO 8.1® Prerelease with Spatial Analyst Extension on a Sun Sparc Ultra 30 with 256 Mb RAM and 504 Mb SWAP.

Celsius temperature data were obtained in an ASCII text file that covered the continental US. Precipitation data in millimeters were obtained in an ASCII text file for the central United States.


PE calculations performed in GRID, where x numerically represents each month, are listed below.

Convert the original temperature data in an ASCII text file to an integer grid:
Asciigrid us_tmax_x us_tmax_x_g int
Calculate monthly mean temperature and convertion from Celsius to Fahrenheit:
Tempx = ((((us_tmax_x_g + us_tmin_x_g) * .01) / 2) * 1.8) + 32
Adjust temperature data to have a minimum value of 28.4 F and less 10 for the index calculation:
Cortempx = con(tempx < 28.4, 28.4, tempx) - 10
Convert the original precipitation data from an ascii text file to an integer grid (geographic extent of these data file covers the central U.S.):
Asciigrid centpptx centpptx_g int
Create integer grid converting millimeter to inches:
Precipx = int((centpptx * .0394))
Convert precipitation from centimeters to inches:
Precx = precipx * .0394
Adjust precipitation data to have a minimum value of 0.5 inches:
Corprecx = con(precx < 0.5, 0.5, precx)
Perform the first steps of the PE index calculation:
Powerx=pow ((corprecx / (cortempx), 1.111)
Perform the final phase of the monthly PE index calculation with the value rounded off to the nearest whole number:
Finalx=int((powerx * 115) + 0.5)
Summation grid with PE index values:
Index = sum(final1, ,final12)

The PE index grid is a summation of the 12 monthly results of the calculation.


Figure 2 below displays a grid of the PE Index derived from PRISM data. Values are classified into 7 groups at break values that have been shown to be indicative of plant growth and soil productivity. The area with values inclusive between 30 to 32 and 44 to 46 were of particular interest.

In Thornthwaite's original paper, PE Index and Temperature Efficiency (TE) Index values were selected to represent zones of vegetation and soil classification. The PE Index value of 32 was used to separate Steppe from Grassland climate and the value of 48 was used to separate Pedocals from Pedalfers in the soil classification terminology of that time.

PE Index Derived from PRISM for Central US
Figure 2. PE Index Derived from PRISM for Central US.

The digital image of the scanned 1957 map was rectified using the State and County boundary intersections as control points. It was then overlaid onto the PRISM derived PE Index for comparison.

The areas on the rectified 1957 map in Kansas that are delineated by contour interval 30 to 32 (red) and 44 to 46 (blue) were digitized as polygons in order to intersect with the PRISM PE index as shown below in Figure 3.

1957 PE Index Map Selected Intervals
PE Index Comparison PRISM with 1957 Map
Figure 3. 1957 PE Index Map Selected Intervals.
Figure 4. PE Index Comparison PRISM with 1957 Map.

Figure 4 displays the polygons as intersected with the PRISM derived PE Index values to examine how well the two geospatial layers matched. There is a difference in both of the range of values examined. Except for a small area in south east Kansas, all of the PE Index values derived from PRISM data are west of the values of the 1957 map. For the area delineated by the contour interval 30 to 32 on the 1957 map, the PE Index values from PRISM data had an average of 35 and ranged from 31 to 41. For the area delineated by the contour interval 44 to 46 on the 1957 map, the PE Index values from PRISM data had an average of 50 and ranged from 45 to 56. This displacement probably reflects a moister climate for the years 1961 to 1990 as compared to the years used to calculate the 1957 data. This difference may also be a result of better data with longer (more consistent and stable) records, as well as better analysis methods.

One application of the PE Index may be to provide a guide to refining the delineation of certain soil climate boundaries. Soil Taxonomy (SSS, 1999) has detailed criteria for soil moisture regimes. Soil moisture and temperature can be measured directly; however, air temperature and precipitation records from weather stations are used to estimate the regime boundary locations. The four moisture regimes pertinent to this part of the country and at this scale are Aquic, Udic, Ustic, and Aridic. The Aridic and Ustic regimes are subdivided into Typic and Intergrades to adjacent regimes. The moisture regimes were established to approximate the major crop growing areas of the Great Plains. The Aridic-Ustic boundary is expected to separate the areas that require irrigation for crop production. The boundary between the Aridic Ustic intergrade with the Typic Ustic regime is approximately the line where a fallow year is needed in the crop rotation to achieve optimum crop production. The Ustic-Udic boundary is expected to separate areas where moisture is a limiting factor for crop production.

Base maps were sent to the state NRCS representatives for line placement (SSQAS, 1994). Figure 5, shown below, displays the Typic Ustic moisture regime boundary in Texas overlain on the PRISM derived PE Index. This moisture regime boundary fits between the PE values of 31 and 44 very well.

Typic Ustic Soil Moisture Regime Boundary over PE Index (PRISM) in Texas
Figure 5. Typic Ustic Soil Moisture Regime Boundary over PE Index (PRISM) in Texas.

Another use of the PE Index is in defining climatic ranges for individual soil series and evaluation of within-series range of characteristics. The extent of individual soil series can be used to intersect with the PE Index values. The potential use of this index will be in prediction of the spatial extent of selected soil properties, such as depth to carbonates or pH as they occur across the extent of the Series. Also, if verified, this climatic index may be a tool to further geographically define an individual soil series productivity potential.


The PE Index calculated using PRISM data appears to be worthy of further study for a number of conservation applications currently using values derived from older data and methods. One possible application is the refinement of selected moisture regime boundaries used for soil classification. When compared to early versions of the PE Index, a difference exists that may illustrate clearly climate variability over time, or the difference may be a result of longer more stable records and better analysis methods being used.


We would like to thank Paul Finnell, Soil Data Quality Specialist, NRCS, Salina, Kansas and Michele May, Cartographer, NRCS, Ft. Worth, Texas.


Daly, C., G.H. Taylor, W.P. Gibson, T.W. Parzybok, G.L. Johnson and P.A. Pasteris. 2000. High-quality spatial climate data sets for the United States and beyond. Trans. of the American Society of Agricultural Engineers. 43(6): 1957-1962.

Daly, C., R.P. Neilson and D.L. Phillips. 1994. A statistical-topographic model for mapping climatological precipitation over mountainous terrain. J. Appl. Meteor. 33:140-158.

Ecological Sciences Staff. 2000. National Agronomy Manual 3rd Ed Exhibit 502-8a. NRCS-USDA.

Soil Survey Quality Assurance Staff. 1994. Soil Climate Regimes of the United States. National Soil Survey Center, NRCS-USDA.

Soil Survey Staff. 1999. Soil Taxonomy: A basic system of soil classification for making and interpreting soil surveys. NRCS, USDA. Handbook-436, Washington D.C.

Thornthwaite, C.W. 1931. The Climates of North America According to a New Classification. Geog. Review. 21: 633-655.


Author Information

Dwain Daniels, CPSS
Soil Scientist
National Cartography and Geospatial Center
Federal Center, Bldg. 23
501 W. Felix Street
Fort Worth, Texas 76115
(817) 509-3358

Dr. Greg Johnson
Applied Climatologist
National Water and Climate Center
101 SW Main, Suite 1600
Portland, Oregon 97204
(503) 414-3017