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Spatial and temporal precipitation characteristics over a large gaged network.

During 1961, a watershed research study was initiated by the USDA-Agricultural Research Service in the central reach of the Washita River basin in Oklahoma [ILLUSTRATION FOR FIGURE 1 OMITTED]. This project, recommended in Senate Document 59, was established to determine the impact of USDA-Natural Resource Conservation Service (formerly the Soil Conservation Service) upstream conservation programs on the main stem of a river basin (USDA-ARS staff 1983). The major conservation treatment applied was the installation of approximately 2,500 flood retarding structures on the tributaries of the Washita River.

A central reach of the river was chosen as the study area because no flood retarding structures had been installed in the area. The experimental design for the study focused on determining the runoff and sediment regimes of the river and tributaries before treatment and then continuing measurements long enough after treatment to establish the possible changes in the runoff and sediment yields. Seven main stem and 12 tributary runoff and sediment measuring stations were established beginning in 1961. Also, a 168-station network of weighing-recording precipitation gages was installed (Nicks 1971). Eventually, 50 watersheds were established ranging in size from a few hectares on unit source areas to 2,940[km.sup.2] (1,135[mi.sup.2]) for the entire study reach. Additional precipitation stations were installed on the small watershed, which increased the total to 230. Shown in Figure 2 are the final locations of precipitation, runoff, and sediment stations. The base precipitation measuring network was operated in the 168-station configuration from September 1961 until October 1986.

Data collected from the rain gage network have been used for many precipitation studies. In addition to its primary role of providing measured rainfall inputs to each of the sub-drainage areas, other important uses of the data include calibration of radar precipitation rate with surface measurements (Brandes and Wilson 1987), depth-area-duration relationships (Nicks and Igo 1980) and development of synthetic rainfall generators (Nicks 1974; Nicks and Gander 1994). Furthermore, with the advent of global change investigations involving spatial and temporal scaling of climate inputs, measurements of precipitation characteristics from sparse to dense scales have become important. Dense network data such as these can provide a link between climate station spacing and smaller scale measurements.

Watershed topography and network design

Topography of the area is characterized by rolling plains cut by deeply eroded valleys. The predominant topographic features are the Washita River and associated flood plains, which comprise 10% of the area. Maximum relief is approximately 153m (500ft) from the northwest corner of the network to the Washita River flood plain near Anadarko. Rainfall distribution throughout the year is bimodal with peak monthly amounts during May and September. Most precipitation falls as rain (98%) with an average of 5 (2%) days a year with sleet or snow. Normal mean annual precipitation across the network from west to east ranges from 710mm to 840mm (28in to 33in). Stations of the basic network were spaced across the area on a 5 x 5[km.sup.2] (3 x 3[mi.sup.2]) grid rotated clockwise approximately 5 [degrees] from true north [ILLUSTRATION FOR FIGURE 2 OMITTED].

Large variations in annual precipitation have been observed nearly every year. Table 1 lists the annual precipitation amounts for each year with maximum and minimum station amounts. Differences between the maximum and minimum gages average 409 mm (16 in) with a mean separation of 51 km (32 mi). These differences in maxima can be attributed to the occurrence of large storms centered near the maximum station location during the year. In most years the difference between the maximum and minimum station was more than half the mean annual amount.

Annual point precipitation ranged from 547mm (22in) in 1966 to a high of 1,031mm (41in) in 1973. The number of wet days during a year in the network domain averaged 124. During the 24-year period, wet days ranged from a low of 85 days in 1980 to 150 days in the following year, 1981. Contrastingly, at a single gage (gage 100) near the center of the network the annual number of wet days averaged 68. During the 24-year period, 1962 to 1985, 2,979 days of precipitation were measured by the network. A maximum point 24-hour rainfall of 236mm (9in) was observed for a storm in October 1983. The maximum observed intensity of 328mm/hr (13in/hr) [109mm (4.3in) in 20 minutes] was observed during one storm in May 1968.

Pattern analysis

Analysis of rainfall patterns were performed using the daily (24-clock hour) data from 593 storms with maximum gage rainfall amounts of [greater than] 25mm (1 in). The objective of this analysis was to derive characteristics of daily rainfall patterns that might be useful in developing a spatially dependent stochastic rainfall generator. Point precipitation generators have been developed in the past that provide spatially independent daily precipitation inputs for many uses including hydrologic, erosion, and water quality models applied to small watersheds (Nicks and Gander 1994; Richardson and Nicks 1990; Richardson et al. 1987). Techniques used by these generators to represent daily point amount and wet-day dry-day sequences may be adequate, but these generators are limited in their use for generating inputs for large basins such as the Washita River or its tributary watersheds. Techniques are needed to enable continuous simulation of precipitation pattern generation similar to the point data provided by existing generators. However, basic data on pattern size, shape, frequency of occurrence, and other characteristics must be developed.

A x and y coordinate system was established with its origin at the lower left corner of the network [ILLUSTRATION FOR FIGURE 2 OMITTED] and x and y coordinate distances calculated for each gage. These distances multiplied by the corresponding rainfall amount were used to derive a rain-weighted centroid of the rain pattern by

[X.sub.c] = [summation of] [r.sub.i][x.sub.j]/[summation of] [r.sub.i] (1)


[Y.sub.c] = [summation of] [r.sub.i] [y.sub.i]/[summation of] [r.sub.i] (2)

where [X.sub.c] and [Y.sub.c] were the centroid coordinates, [r.sub.i] was the gage amount, [x.sub.i] and [Y.sub.i] were the x and y distances from the origin to gage i, for i = 1, ..., 168.
Table 1. Network mean, maximum, and minimum annual; daily mean; and
number of days of precipitation; differences between maximum and
minimum gage and distance separating them

       Annual   Max.   Min.           Daily   Separation
Year    mean    gage   gage   Diff.   mean     distance    Days
        (mm)    (mm)   (mm)   (mm)    (mm)       (km)

1962     723     959    565    394    5.52        64        131
1963     513     707    380    327    4.43        20        116
1964     730     936    581    355    5.66        35        129
1965     674     958    500    458    5.15        45        131
1966     547     743    322    421    4.93        62        111
1967     665     844    539    305    5.04        47        132
1968     860    1088    681    406    6.33        31        136
1969     697     898    528    370    5.24        34        133
1970     568     868    386    482    4.86        88        117
1971     760     899    610    289    6.67        48        114
1972     581     817    390    427    4.69        59        124
1973    1031    1309    831    477    7.87        59        131
1974     807    1025    636    389    7.77        26        104
1975     889    1146    757    389    6.79        33        131
1976     588     725    484    241    5.25        72        112
1977     688     928    533    395    5.42        52        127
1978     656     861    409    452    5.34        69        123
1979     772    1100    515    585    6.78        83        114
1980     578     726    475    251    6.81        33         85
1981     831    1050    537    513    5.55        62        150
1982     809    1086    560    526    5.95        55        136
1983     882    1091    713    378    6.79        28        130
1984     698     892    397    495    5.37        52        130
1985     982    1232    730    502    7.50        75        131
MEAN     730     954    544    410    5.90        51        124
Table 2. Distribution of major axis of 593 daily rainfall patterns
by class interval

Class                         Number              Accumulated
interval                    of events              frequency

0-75                           443                   0.747
76-150                          92                   0.902
151-225                         27                   0.948
226-300                          8                   0.961
300-375                          5                   0.970
375-450                          2                   0.973
451-525                          4                   0.980
[greater than]525               12                   1.000

Principal component analysis (Cooley and Lohnes 1962) was employed to develop pattern statistics and distribution of rainfall pattern characteristics. A variance-covariance matrix of rainfall amounts weighted by distance from the pattern center was calculated, as given in equations 1 and 2, for each of the 593 storms. Principal components, standard deviation of major and minor axis, direction cosines, and eccentricity of the pattern were derived for each storm. Figures 3 and 4 show the accumulated distributions of daily rainfall pattern eccentricity and direction of the major axis from true north, respectively. The distribution of length of the standard deviation of the major axis is listed in Table 2.

Pattern eccentricity, a measure of the roundness of the pattern, ranged from 0.1 to 0.98. Values of 0.1 represent an elongated pattern while values near 1.0 represent near circular shapes. The majority of the patterns, 379, were in the range from 0.8 to 1.0, indicating that most likely pattern shape is slightly elongated. Eccentricity E is

E = [{([P.sub.[1.sup.2]] - [P.sub.[2.sup.2]])/[P.sub.1]}.sup.0.5] (3)

where [P.sub.1] is the major axis length and [P.sub.2] the minor axis length in km.

The distribution of major axis lengths given in Table 2 ranged from 10 to 857km (6 to 530mi). The maximum length may not be representative of rainfall for this region because it is well beyond the domain of the network. However the majority of the patterns, 443, are less than 75km (47mi) which is within the network dimensions. The distribution of major axis direction shown in Figure 4 indicates the most likely orientation of the major axis of the pattern to be between 0 to 90 degrees.

Summary and conclusions

Annual precipitation statistics of a large, dense measuring network located in the Southern Great Plains are presented to show the spatial characteristics of rainfall over a 3,900[km.sup.2] (1,506[mi.sup.2]) area. Analyses were performed to derive distributions of major axis length, direction, and eccentricity of 593 daily rainfall patterns. The majority of the patterns had eccentricities of more than 0.80 indicating rounded shapes. The most likely major axis length was less than 75km (47mi) oriented between 0 90 degrees.

The pattern characteristics presented here are only a few of those that would be needed to generate spatially dependent precipitation in a manner similar to a point rainfall generation methods now being used. However, such analysis may point out the complexity inherent in generating pattern of precipitation useful in continuous simulation modeling. Many other variables may be required, such as the gradient of a rainy day across an area in order to justify the rainfall gradient for amount. A considerable amount of analysis remains to be done.


Brandes, E.A., and J.W. Wilson. 1987. Measuring storm rainfall by radar and rain gage. In: E. Kessler (ed.) Instruments and Techniques for Thunder Storm Observation and Analysis. p. 171-189. University of Oklahoma Press, Norman, Oklahoma.

Cooley, W.W., and P.R. Lohnes. 1962. Multivariate Procedures for the Behavioral Sciences. John Wiley and Sons, New York, NY. 211 pp.

Nicks, A.D. 1971. Agricultural Research Service precipitation facilities and related studies. USDA-ARS, #41-176. pp. 71-81.

Nicks, A.D. 1974. Stochastic generation of the occurrence, pattern, and location of maximum amount of daily rainfall. Proceedings, Symposium Stat. Hydrol. Misc. Publication #1275. pp. 154-171.

Nicks, A.D., and F.A. Igo. 1980. A depth-area-duration model of storm rainfall in the Southern Great Plains. Water Resource Research 16(5):939-945.

Nicks, A.D., and G.A. Gander. 1994. CLIGEN: A weather generator for climate inputs to water resource and other models. 5th International Conference on Computers in Agriculture. Computers In Agriculture 1994. ASAE publication 3-94.pp. 903-909.

Richardson, C.W., and A.D. Nicks. 1990. Weather generation description. In: A.N. Sharpley and J.R. Williams (eds.) EPIC - Erosion/Productivity Impact Calculator: 1. Model Documentation. USDA Technical Bulletin No. 1768. pp. 93-104.

Richardson, C.W., C.L. Hanson, and A.L. Huber. 1987. Chapter 2. Climate generator. In: J.R. Wight and J.W. Skiles (eds.) Simulation and Utilization of Rangelands. Documentation and User Guide. USDA-ARS, ARS 63, pp. 3-16.

USDA-ARS Staff. 1983. Hydrology, Erosion, and Water-Quality Studies in the Southern Great Plains Research Watershed Oklahoma, 1961-78. USDA-ARS, Agricultural Reviews and Manuals, ARM-S-29, 175 pp.

Arlin D. Nicks is an agricultural engineer, USDA-Agricultural Research Service, National Agricultural Water Quality Laboratory, Durant, OK 74702.
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Title Annotation:Special Issue: Water Research and Management in Semiarid Environments
Author:Nicks, Arlin D.
Publication:Journal of Soil and Water Conservation
Date:Sep 1, 1995
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