SPATIAL EVALUATION OF PRECIPITATION IN TWO LARGEWATERSHEDS IN NORTH-CENTRAL ARIZONA

Boris Poft,1,2 Assefa S. Desta,1 and Aregai Tecle1

The USDA Forest Service established the

Beaver Creek Experimental Watershed PilotProject in north-central Arizona in 1957 andoperated it until 1982. After the Forest Servicediscontinued the project in 1982, Northern ArizonaUniversity's School of Forestry continued tomonitor and do research in two of the largestwatersheds, known as Woods Canyon and Bar M.From 1982 to 1995 only streamflow data areavailable for these watersheds. A weak correlation

between streamflow and precipitation for bothwatersheds was determined by analyzing theUSDA data from 1961 to 1982, using spatialinterpolation methods in ArcGIS. However, thisstudy is a work in progress and the authors are inthe process of using different spatial interpolationmethods in ArcGIS to determine better regressionfunctions between streamflow and precipitation.The objective of this study is to evaluate existinghistorical data using newly available techniquesand technology to obtain new results. Methodsused so far, in ArcGIS, are four different spatialinterpolation methods, namely Inverse DistanceWeighting, Radial Basis Function, and Global andLocal Interpolation.

BACKGROUND AND STUDY SITE

Originally, between 1957 and 1962, the USDAForest Service set up 20 pilot watersheds in theBeaver Creek Experimental Watershed in north-central Arizona. Of the 20 watersheds, 18 rangedfrom 27 to 824 ha. The remaining two watersheds,known as Bar M (Watershed 20) and Woods Can-yon (Watershed 19), are much larger with areas of6620 and 4893 ha, respectively (Baker and Ffolliott1999; see Figure 1). Seventeen of the watersheds,including the largest two, are located in theponderosa pine forest ecosystem. This study usesdata from 39 of the 72 rain gauges the USDA

lUSDA Forest Service Rocky Mtn. Research Station, Flagstaff2School of Forestry, Northem Arizona University, Flagstaff

Forest Service had in place to collect rainfall datain the experimental project (see Figure 1). Theobjective of the Beaver Creek ExperimentalWatershed Pilot Project was to determine theimpacts o.fforest manipulation on water yield. Theultimate desire was to increase the amount of

water available from the forest regions of Arizonafor the growing population in the state.

METHODOLOGY

The data used in the evaluation process for WoodsCanyon (WSI9) consisted of precipitation datafrom 39 rain gauges in the Beaver Creek Experi-mental Watershed for the time period from 1961 to1981. Streamflow data from the Woods Canyonstream gauging station for the same time periodwere used as well. The data are available at a Web

site maintained by the Rocky Mountain ResearchStation and the University of Arizona in Tucson(http:/ / ag.arizona.edu/OALS/watershed/index.html). The data used in the evaluation process forBar M (WS20) consisted of the same precipitationdata used for Woods Canyon from 39 rain gaugesin the Beaver Creek Experimental Watershed from1961 to 1981, and other 1961-1990 precipitationdata from seven additiori.al weather stations eastand south of the Beaver Creek Watershed. This

became necessary because the boundaries of Bar Mextend farther east than the location of any of the39 Beaver Creek rain gauging stations. The stream-flow data from the Bar M stream gauging stationwere used for the time period of 1961-1981. Thestreamflow and precipitation data from the 39Beaver Creek Experimental Watershed rain gaug-ing stations were downloaded from the watershedmanagement Web site given above. Rain data fromthe additional seven weather stations were takenfrom the Global Historic Climate Network data,National Climate Data Center, National Oceanicand Atmospheric Administration, U.S. Departmentof Commerce.

A Trimble GeoExpiorer3 handheld GPS unitwas used to determine the boundary for the two J,iII

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16 Poff, Desta, and Teele

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Rain-gauging Stations.

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Figure 1. The location of the study sites and of the 39 rain gauges used in this study, in the Beaver CreekExperimental Watershed, Arizona.

watersheds (Poff et al. 2005). The GPS data wererecorded in the Universal Transverse Mercator(UTM) system and projected using the NorthAmerican Datum (NAD) of 1927.

Precipitation data were converted into milli-meters where necessary (NOAA data were alreadyin mm) and the rainfall values (1961-1981) wereaveraged for each calendar month for each raingauging station. This produced 12 average valuesfor each station-one for each month of the year.These average values were imported into ArcMap,where their UTMs were calculated. After thegauging stations were spatially referenced, InverseDistance Weighting (IDW), Radial Basis Function(RBF), and Local and Global Interpolation methodswere used to create a precipitation interpolationmap for each month. IDW, which is a local inter-polator, weighs closer points greater than thosefarther away, applying the fundamental assump-tion for spatial interpolation (ESRI 2001), which isthe first law of geography: Everything is related toeverything else, but near things are more relatedthan distant things (Tobler 1970). The second

assumption necessary to using IDW is that thisphenomenon is modeled as a spatially continuousdataset. Even though precipitation values areusually collected as discrete point data, it is safe tomake this assumption with such a dataset.

Even though the data tend to be normally dis-tributed, there is one outlier, which can be seen inthe histogram Voronoi map. Including this outlierin the dataset produced a Kurtosis value of 5.21and a skewness coefficient of -1.00.The Voronoi

map also indicates clustering of values aroundseveral locations, which given the pattern of pre-cipitation is to be expected.

The average rainfall value for August forWoods Canyon was used for a more in-depth in-vestigation after the interpolation output for eachmonth using the IDW method had been reviewed.Because these values were collected during themonsoon season they provide adequate data forstatistical analysis.

Global and local trends such as latitude

(global), as well as elevation and aspect (local), caninfluence the spatial distribution of precipitation. It

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Spatial Evaluation of Precipitation in Watersheds 17

. Woods Canyon 81BarM

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Figure 2. A bar graph showing the mean volume of precipitation for each month for the two watersheds (convertedfrom cu m back to average mm distributed over the entire watershed).

is safe to assume that elevation and consequentlytemperature are factors causing a trend, given thatthe gauging stations used to collect this informa-tion are distributed along the elevation gradient ofthe Mogollon rim.

IDW, local, and global polynomial interpola-tions were run with a power of 1 for reasons ofsimplicity. The neighborhood search was set toinclude at least 10 neighbors for all interpolations,whereas we included 15 for the Radial BasisFunction (RBF),the IDW, and the local polynomialinterpolation. We selected 39 neighbors (or allgauging stations) for the global polynomial inter-polation. These helped to compare the differentmethods to each other at the same (default) set-tings whenever possible.

The 24 IDW output maps (12 each for WoodsCanyon and Bar M) as well as the two watershedpolygons were converted into raster layers with aresolution of 50 x 50 m cells. This allowed the useof 3D spatial arithmetic to calculate precipitationvolume in cubic meters for each month for each

watershed resulting in a total of 12 values for eachwatershed (see Figure 2). Next these values wereused to predict streamflow based on precipitationvolume calculated by IDW for each watershed.The results of the linear, quadratic, and cubicregression functions are shown in Figures 3 and 4.

RESULTS

The global polynomial interpolation is theleast exact interpolation, because it uses the entiredataset to make its predictions and shows valuesthat are different from the measured values. How-ever, it does show a trend in the level of precipita-tion. It indicates that precipitation increases fromsoutheast to northwest. This trend is also indicatedby the local polynomial interpolation, whose pre-dicted values more closely resemble the measuredones. The results obtained using both the IDW andRBF,better represent the measured data than thoseobtained using the polynomial interpolations.Even though the results in the former two methodsare relatively similar to each other, there are

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Figure 3. Linear, quadratic, & cubic regression curves of fitting the Woods Canyon data; the cubic line has the best fit.

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Spatial Evaluation of Precipitation in Watersheds

noticeable differences. These differences are due to

the way each method calculates the interpolation.The r2 values of the three different regression

functions are given in Table 1. The cubic regressionfunctions show the highest r2 values for bothwatersheds-D.60 for Bar M and 0.59 for Woods

Canyon.

CONCLUSION

The r2 values generated by the regressionfunctions are not high enough to be very reliable.

"However, they show that there is a correlationbetween streamflow and precipitation and thatstreamflow data can be used, in this case, to"predict" precipitation for the years and monthsfor which precipitation data are missing. In thefuture, the authors will use the above methods todetermine the relationship between streamflowand precipitation; hence this study is considered awork in progress. There are other geostatisticaltechniques to be used, such as Kriging andCokriging, as well as the transformation of dataand the elimination of outliers. Another possibilitywould be to run these techniques on a month bymonth basis instead of the mean values for 20

years. The goal is to use such techniques to find amore reliable correlation (higher r2 value) betweenstreamflow and precipitation in order to "predict"precipitation based on streamflow data with ahigher accuracy and reliability for the water years1982-1994.

Interpolation in general, but IDW or RBF inparticular, can be very useful geostatistical toolsfor predicting values in areas where adequate dataare not available or when it is difficult to predictvalues in the past. Precipitation is a prime ex-ample. Areas can be divided into relatively small

19

cells to accurately calculate the average precipita-tion for different time periods for each of thesecells. Local or global polynomial interpolation canbe used to identify trends such as elevation or "

temperature gradients. All methods of interpola-tion can also be used to identify global or localoutliers, which, in turn, can influence our data ifnot taken into consideration. In other words,interpolation is a tool that can be successfullyapplied in today's decision-making processes.

Table 1. The r2 values for linear, quadratic, and cubic re-gressions for the two watersheds.

REFERENCES CITED

Baker, M. B., Jr., and P. F. Ffolliott. 1999. Interdiscipli-nary land use along the Mogollon Rim. In History ofWatershed ResearCh in the Central Arizona High-lands, compiled b}' M. B. Baker, Jr. USDA ForestService General Technical Report RMRS-GTR-29, Ft.Collins, CO.

ESRI. 2001. Using ArcGISTMGeostatistical Analyst. ESRI,Redland, CA.

Poff, B., D. S. Leao, A. Teele, and D. Neary. 2005. Deter-mining watershed boundaries and area using GPS,OEMs, and traditional methods: A comparison. Pro-ceedings of the 7th Biennial Conference of Researchon the Colorado Plateau. USGS Plateau Field Station,

" Northern Arizona University, Flagstaff, November2003. University of Arizona Press, Tucson.

Tobler, W. 1970. A computer movie simulating urbangrowth in the Detroit region. Economic Geography46(2): 234-240.

Type of Function Woods Canyon BarM

Linear .359 .205Quadratic .548 .521Cubic .558 .601