Journal of Hydrology 379 (2009) 122–135

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Journal of Hydrology

journal homepage: www.elsevier .com/locate / jhydrol

Spatial and temporal soil moisture and drought variability in the UpperColorado River Basin

Chunling Tang a, Thomas C. Piechota b,*

a Department of Geosciences, Idaho State University, Pocatello, ID 83209-8072, USAb Department of Civil and Environmental Engineering, University of Nevada, Las Vegas, 4505 Maryland Parkway, Box 451087, Las Vegas, NV 89154-1087, USA

a r t i c l e i n f o

Article history:Received 12 June 2009Accepted 28 September 2009

This manuscript was handled by K.Georgakakos, Editor-in-Chief, with theassistance of V. Lakshmi, Associate Editor

Keywords:DroughtSoil moistureWavelet analysis and wavelet coherencySpatialTemporalUpper Colorado River Basin

0022-1694/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.jhydrol.2009.09.052

* Corresponding author. Tel.: +1 702 895 4412; faxE-mail addresses: thomas.piechota@unlv.edu, pie

chota).

s u m m a r y

This research investigates the interannual variability of soil moisture as related to large-scale climate var-iability and also evaluates the spatial and temporal variability of modeled deep layer (40–140 cm) soilmoisture in the Upper Colorado River Basin (UCRB). A three layers hydrological model VIC-3L (VariableInfiltration Capacity Model – 3 layers) was used to generate soil moisture in the UCRB over a 50-year per-iod. By using wavelet analysis, deep layer soil moisture was compared to the Palmer Drought SeverityIndex (PDSI), precipitation, and streamflow to determine whether deep soil moisture is an indicator ofclimate extremes. Wavelet and coherency analysis for the UCRB indicated a strong relationship betweenthe PDSI, climate variability and the deep soil moisture. The spatial variability of soil moisture duringdrought, normal, and wet years was analyzed by using map analysis. Distinct regions showing higher vul-nerability to drought and wet conditions were identified in the spatial analysis. The temporal variation insoil moisture was performed by utilizing map analysis in pre-drought, drought, and post-drought yearsfor four drought events, 1953–1956, 1959–1964, 1974–1977, and 1988–1992. Less than 50% of the basinhad dry conditions (soil moisture anomaly below �10 mm) for the pre-drought years. Soil moistureanomalies were lower than �10 mm for more than 50% of the basin in 15 out of 19 drought years. Gen-erally, droughts did not end until the average soil moisture anomalies increased to positive values for twoconsecutive years.

� 2009 Elsevier B.V. All rights reserved.

Introduction

Droughts are characterized by their severity (average waterdeficiency), magnitude (cumulative water deficiency) and dura-tion. Definitions vary for the different types of drought: agricul-tural, hydrologic, meteorological, and socioeconomic (Dracupet al., 1980). Several drought indices have been defined for charac-terization of drought including the use of soil moisture.

Soil moisture is a significant hydrological variable related tofloods and droughts and plays an important role in the process ofconverting precipitation into runoff and groundwater storage. Asoil moisture deficit results in more infiltration and little runoffwhen followed by precipitation. However, high soil moisture re-sults in overland runoff and possible flooding during intense pre-cipitation. In addition, high soil moisture promotes vegetationgrowth in the summer and this leads to high evapotranspiration.Therefore, soil moisture controls the interaction of the land withthe atmosphere.

ll rights reserved.

: +1 702 895 5464/3936.chota@ce.unlv.edu (T.C. Pie-

The influence of soil moisture on climate variability has re-ceived attention in recent years. Higher soil moisture may resultin higher evaporation and precipitation, and an accurate soil mois-ture representation can enhance precipitation predictability (Kos-ter et al., 2000). Soil moisture information also has potential toimprove seasonal precipitation prediction (Dirmeyer and Brubaker,1999). Timbal and McAvaney (2001) suggested that a high interan-nual variability of soil moisture could potentially play a role inaffecting Australian seasonal climate forecasts, and Reichle andKoster (2003) found that soil moisture could be important for sea-sonal prediction of mid-latitude summer precipitation. Huang et al.(1996) identified that precipitation influenced soil moisture anom-alies and the soil moisture had greater persistence during periodsof low precipitation. Soil moisture has been noted as an indicatorof agricultural potential and available water storage, which re-flected recent precipitation and antecedent conditions (Keyantashand Dracup, 2002). Trenberth and Branstator (1992) stated thatthere are three main contributors to drought: land and sea surfacetemperature, atmospheric circulation, and soil moisture. Changesof each of these parameters were amplified to produce climate ex-tremes such as flood or drought.

Recent research has focused on the relationship between soilmoisture and the Palmer Drought Severity Index (PDSI) (Palmer,

C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135 123

1965), which is the most widely used index of meteorologicaldrought in the United States. Sheffield et al. (2004) identified thatthe Variable Infiltration Capacity (VIC) drought index based on soilmoisture showed good correlation with the PDSI in the UnitedStates. In evaluating drought in East Hungary, Makra et al. (2005)defined the PDSI as an indicator of soil moisture and this was con-sistent with the study of Szep et al. (2005) that the PDSI is signif-icantly related to soil moisture in East Hungary. Soil MoistureDeficit Index (SMDI) was developed by Narasimhan and Srinivasan(2005). A recent study by Lakshmi et al. (2004) acknowledged thatthe deep layer soil moisture anomaly was a good drought indicatorin the Mississippi River Basin. Therefore, efforts should be madethrough relating soil moisture with PDSI and climate variabilities,to evaluate the potential capability of soil moisture to be a droughtindicator.

Soil moisture interacts with the atmosphere through surfaceenergy and water balances. Poveda and Mesa (1997) analyzed soilmoisture, ENSO (El Niño-Southern Oscillation), and precipitation inColombia and demonstrated that soil moisture accounted for partof the precipitation reduction in tropical South America throughreduction in evapotranspiration and feedback mechanisms. Severalstudies have looked at the temporal variability of soil moisture. Huet al. (1997) examined the temporal function of soil moisture, andsuggested that it was related to infiltration, cloud coverage, precip-itation, and drainage. In evaluating water resources in small catch-ments, soil moisture varied spatially due to water routingprocesses, vegetation, and soil types (Hu et al., 1997). To fullyunderstand the changing dominance of soil moisture in differentregions, its spatial characteristics need to be considered along withthe temporal characteristics. The study presented seeks to evaluateboth the spatial and temporal aspects of soil moisture in extremeclimate conditions.

There are three main objectives in this study. The first objectiveis to generate large-scale, long-term, high-resolution soil moisturebased on model calibration and model verification in the UCRB.Modeling soil moisture is important because the lack of consistenthigh-resolution, large-scale, long-term modeling soil moisture hasprevented certain research, such as the linkages of the soil mois-ture with climate variability. The second objective is to examinesoil moisture as a drought indicator with the main contributionbeing the use of a two-dimensional (time and frequency) waveletanalysis statistical tool in correlating soil moisture with climatevariabilities. The third objective is to improve the understandingof temporal and spatial variations of soil moisture as related todroughts. Soil moisture varies both temporally and spatially inresponse to climate processes over a variety of scales. However,the relative importance of the temporal and spatial soil moistureinfluence on the climate extremes (i.e. droughts) is still poorlyunderstood. Therefore, the comprehensive investigation of spatialand temporal soil moisture on drought will be a significantcontribution.

To attain the research goals, a 1/8� spatial resolution and a tem-poral daily time step soil moisture datasets were generated fromthe Variable Infiltration Capacity Model – 3 layers (VIC-3L). Thenthe modeled soil moisture as a drought indicator was evaluatedby comparing it with the climate variabilities for the UCRB. Spatialvariability of soil moisture was evaluated by map analysis method.Furthermore, the temporal variability of soil moisture was evalu-ated by investigating the soil moisture anomalies during pre-drought, drought, and post-drought years.

Study area

The study area is the UCRB (Fig. 1), which provides water sup-ply, flood control and hydropower to a large area of the southwest

United States. The UCRB drains an area of more than 279,720 km2

in seven states and generates water for 26 million people withinthe basin states and adjoining areas. The elevation, land cover,and soil type maps of the UCRB are presented in Fig. 2. The averageelevation of the UCRB is about 2200 ft. (Fig. 2a). About 40% of theUCRB is covered by barren or sparsely vegetable (Fig. 2b). Fivemain soil types: loam clay, loam sand, sandy loam, silty clay, andsand are in the UCRB (Fig. 2c). The current drought in the ColoradoRiver Basin started in 2000 and has resulted in an accumulativestreamflow deficit of 11 km3 or approximately two years of aver-age streamflow (Piechota et al., 2004). The current drought, com-bined with an increased water supply demand, has severelyaffected the storage of the major reservoirs at the Colorado River.

Data

Soil moisture data

In the United States, the Illinois State Water Survey Departmentstarted to observe soil moisture in the 1980s. Approximately 30stations of observed soil moisture data are available in the UnitedStates and most stations are located in Illinois and Iowa (Robock etal., 2000). Observed soil moisture data are also available from theGlobal Soil Moisture Data Bank (http://climate.envsci.rutgers.edu/soil_moisture). However, no observed long-term soil moisture isavailable in the UCRB. The simulated soil moisture from hydrolog-ical models has been widely used because of the lack of large-scaleand long-term observations of soil moisture. Soil moisture dataused in this study were generated from the VIC-3L model (see sec-tion ‘‘Development of soil moisture dataset”).

The PDSI data

The PDSI was used to represent the severity of dry and wet con-ditions, based on temperature, precipitation, and soil moisture data(Palmer, 1965). The range of the PDSI values is from �4 to +4,which was defined by Palmer (1965) according to a study area incentral Iowa and western Kansas. Positive and negative PDSI valuesindicate wet and dry conditions. The gridded PDSI data is availablefrom the National Climate Data Center of record from 1900 to pres-ent (http://www.ncdc.noaa.gov/oa/ncds.html). Monthly PDSI val-ues for a 50-year span (1950–2000) of the UCRB were used inthis study.

Method

The VIC-3L model (Liang et al., 1994; Todini, 1996) was utilizedto simulate soil moisture at a daily time step with a 1/8� spatialresolution for the period 1950–2000 in the UCRB. Then, the rela-tionships between soil moisture and climate variability was evalu-ated by wavelet method. The spatial variability of soil moistureduring drought, normal, and wet years was investigated by usingmap analysis method. Finally, the role of the temporal variabilityof soil moisture during the initiation, persistence, and terminationof drought was evaluated by map analysis. A detailed descriptionof these methods follows.

Development of soil moisture dataset

The VIC-3L model descriptionThe VIC-3L model is a macro-scale water and energy balance

model, based on the Xinnan Jiang Model (Zhao et al., 1980). Thedistinguishing features of the VIC-3L model include the sub gridvariability in soil moisture, land surface vegetation, precipitation,and topography in use of the elevation band. The VIC-3L model

Fig. 1. The UCRB with five streamflow stations from the USGS and five climate divisions from the NOAA.

124 C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135

had been successfully applied over many large river basins withreasonable results (Abdulla et al., 1996). The VIC-3L model is basedon the water balance equation:

DS ¼ p� ET � R� D ð1Þ

where DS is the rate of the change of storage, p the precipitation, ETthe evapotranspiration, R the surface runoff, and D is the subsurfacerunoff.

The VIC-3L model consists of three soil layers, 10 cm for layer 1,30 cm for layer 2, and 100 cm for layer 3. Surface runoff is gener-

ated in the upper two layers by a variable infiltration curve, andbaseflow is produced in the bottom layer (Todini, 1996). The VIC-3L model allows different types of vegetation and land cover. Thesurface land cover types are described by n = 1, 2, 3, . . . N, N + 1(N represents different types of vegetation, and N + 1 representsbare soil). Land cover types are characterized by their Leaf Area In-dex (LAI), canopy resistance, root fraction depth, and soil proper-ties (Liang et al., 1994).

The VIC-3L model typically runs at spatial resolutions varyingfrom 1/8� to 2�, temporal resolutions from monthly to daily time

Fig. 2. Geographical characteristics of the UCRB: (a) elevation map; (b) land cover map; and (c) soil type map.

C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135 125

steps, and is forced by meteorological data, soil data, and vegeta-tion data. The model is coupled to a routing model, which gener-ates streamflow and transports grid cell surface runoff andbaseflow produced by the VIC-3L model to the outlet of that gridcell, and then into the river system (Wood et al., 1997). A morethorough description of the model is given in Liang et al. (1994)and Lohmann et al. (1998).

For soil moisture, Nijssen et al. (2001) reported a good compar-ison between the simulated soil moisture by the VIC-3L and the ob-served soil moisture in central Illinois and in central Eurasia.Another study by Maurer et al. (2001) demonstrated that theVIC-3L modeled soil moisture had a higher persistence than theNCEP (National Center for Environmental Prediction) reanalysisdata for the entire Mississippi River Basins. Stephen et al. (2008)compared the VIC-3L modeled soil moisture with observed soilmoisture in the Lower Colorado River Basin and show that thetwo soil moisture datasets match well.

The VIC-3L model calibrationObserved streamflow. The model calibration was performed be-tween observed streamflow and simulated streamflow. Streamflowstations were identified from the National Water Information Sys-tem Web (NWISWeb) Data retrieval (http://waterdata.usgs.gov/nwis/) of the United States Geological Survey (USGS) (Slack et al.,1993) and monthly average flow rate were retrieved. There areseveral reasons for calibration of streamflow rather than soil mois-

ture. First, long-term observed soil moisture is not available in theUCRB. Second, the output of the VIC-3L model are the main inputsets of the routing model, so calibration of the streamflow whichis the output of the routing model indirectly calibrates the VIC-3L model. Third, the soil moisture parameter is one of the mostsensitive parameters in the calibration of the streamflow. Stream-flow is a spatially integrated response of hydrologic processeswithin a basin, which is important for assessing land surfaceschemes at large spatial scales. The monthly streamflow over a50-year period (1950–2000) for five stations in the UCRB (Fig. 1)(Fall Creek, Piney River, Cisco, Green River, and Lee’s Ferry) wereused for calibration.

Selection of sensitive parameters. The calibration of the VIC-3L mod-el is usually performed by adjusting five parameters (Wood et al.,1997): (a) the maximum baseflow that can occur from the thirdsoil layer (in mm/day) (Dsmax); (b) the fraction of Dsmax wherenon-linear (rapidly increasing) baseflow begins (Ds); (c) the frac-tion of the maximum soil moisture (of the lowest soil layer) wherenon-linear baseflow occurs (Wsmax); (d) the infiltration parameter(binf); and (e) the depth of the second soil layer (d2). Since the max-imum velocity of baseflow (Dsmax) depends on hydraulic conduc-tivity, which can be estimated using the saturated hydraulicconductivity multiplied by the slope of the grid, the fraction ofmaximum soil moisture content of the third layer (Wsmax) is anal-ogous to Ds (Liang et al., 1994; Wood et al., 1997). These three

126 C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135

parameters can be derived from soil textural information, so, theparameters were used with minor adjustment during the calibra-tion in this research. Consequently, the infiltration parameter (binf),and the thickness of the second soil layer (d2) were treated as theprimary calibration parameters (Wood et al., 1997; Su et al., 2005).These two parameters were chosen as the primary calibrationparameters for several reasons. First, sensitivity analysis showedthat binf and d2 were the most sensitive calibration parameters.Second, a change in the thickness of the second layer effects notonly the hydraulic conductivity, but also the maximum storageavailable in the second layer and the water available for transpira-tion. The plant roots can draw water only from the top two soil lay-ers and the baseflow was generated only from the third layer in theVIC-3L model. As a result, the flux of water from the second layerinto the third layer determines how much baseflow will occur.

Of the total 50-year record, a 30-year period (1971–2000) wasutilized for the calibration process, and a 20-year data (1950–1970) was used for validation. Model validation applied the VIC-3L model without changing the calibration parameters (binf, d2) val-ues obtained from calibration. The root mean squared error (RMSE)and linear correlation coefficient (r) were the two calibrationcriteria.

Fig. 3. Monthly observed and simulated streamflow for: (a) Fall Creek station, (b) Piney

Model verificationThe model verification was performed by comparing soil mois-

ture calculated from the VIC-3L model with that from the Distrib-uted Modeling Intercomparison Project (DMIP) of the CPC (ClimatePrediction Center) for five Climate Divisions (33, 298, 299, 300, and337) (Fig. 1) in the UCRB. Soil moisture produced by the CPC hasbeen widely used in climate studies in recent years. The verifica-tion is difficult to perform because different soil layer depths anddifferent soil moisture reservoir sizes were utilized in the CPCand the VIC-3L model. The CPC defined the maximum soil moisturecapacity as 760 mm (Refsgaard, 1997) and the soil was set to onlyone layer with 1.6 m depth. In contrast, the maximum soil mois-ture in the VIC-3L model was equal to the porosity of the soil,and soil moisture storage expressed as a fraction of field capacity.Soil was separated into three layers with a total 1.4 m depth in theVIC-3L model rather than 1.6 m in the CPC. Because of these differ-ences, the verification was carried out by a comparison of the soilmoisture anomaly patterns rather than the absolute storage values.The verification relied upon the correlation between the twodatasets:

rjk ¼COVjk

SjSkð2Þ

River station, (c) Green River station, (d) Cisco station, and (e) Lee’s Ferry station.

C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135 127

where Sj and Sk are the standard deviations of variable j and k,respectively, and COVjk is the correlation between j and k.

To calculate the covariance between the two soil moisture data-sets, the corrected sum of products (SP) which shows the sum ofsquares of variables is defined by:

SPjk ¼Xn

i¼1

ðXij � XjÞðYik � YkÞ ð3Þ

where j is the soil moisture from the VIC-3L model, k is the soilmoisture from the CPC. Xij is the ith measurement of variable j,and Yik is the ith measurement of variable k. Xj is the mean of var-iable j, and Yk is the mean of variable k.

The covariance was then calculated based on SP:

COVjk ¼SPjk

n� 1¼ n

Pni¼1XijYik �

Pni�1Xij

Pni¼1Yik

nðn� 1Þ ð4Þ

Comparison of time series

The next step was to compare soil moisture with other droughtindicators by using wavelet analysis. Methods used to analyze sig-nals for time variation are standard techniques such as Fourier andwavelet analysis. The main problem with the Fourier transform isno time localization of the frequencies are present in the signal(Torrence and Webster, 1999). Wavelet analysis attempts to solvethis problem by decomposing a time series into time/frequencyspace simultaneously. Information on both the amplitude of any

Fig. 4. Comparison of soil moisture anomaly simula

periodic signals within the series and how this amplitude varieswith time is provided by wavelet analysis.

The continuous wavelets transform Wn of a discrete sequence ofobservations xn is defined as the convolution of xn with a scale sand wavelet w(x):

WxnðsÞ ¼

XN�1

n0xn0w �

ðn0 � nÞdts

� �ð5Þ

where n is the localized time index, s is the wavelet scale, dt is thesampling period, N is the number of points in the time series, andthe asterisk indicates the complex conjugate. The wavelet trans-forms Wn(s), at time index n, scale s and with a constant time inter-val were developed (Torrence and Webster, 1999) for all the giventime series (soil moisture of layer 1, layer 2 and layer 3, PDSI, pre-cipitation, and streamflow).

The similarity between the different time series was evaluatedby using wavelet coherency, which was used to identify frequencybands and time intervals where two time series were related (Tor-rence and Webster, 1999). The wavelet coherency Rn is defined as:

R2nðsÞ ¼

jhs�1WXYn ðSÞij

2

hs�1jWXn ðsÞj

2ihs�1jWYn ðsÞj

2ið6Þ

where h i indicates smoothing in both time and scale, WXnðsÞ and

WYnðsÞ are the wavelet transforms of two time series X and Y.

WXYn ðsÞ is the cross-wavelet spectrum of X and Y which is defined as:

WXYn ðsÞ ¼WX

nðsÞWX�

n ðsÞ ð7Þ

ted from the VIC-3L model and from the CPC.

128 C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135

where (�) means the complex conjugate. The intent of the waveletcoherency analysis is to determine how well soil moisture repre-sents hydrological drought in the UCRB.

Spatial variability of soil moisture during droughts

To evaluate the spatial variability of soil moisture, map analysiswas performed on the 50 year period which was divided intodrought, normal, and wet years. In this study, the PDSI value of�1 was selected as the threshold. Drought was defined as the con-secutive years during which the PDSI variable was continuouslybelow �1. The normal years were defined as the years with thePDSI values between �1 and 1. The wet years were identified asthe PDSI greater than 1. This resulted in 19 drought, 14 normal,and 17 wet years over the 50-year records which is consistent withthe study of Timilsena et al. (2006). Secondly, gridded yearly aver-age soil moisture and soil moisture anomaly for the drought, nor-mal, and wet years were calculated. Finally, maps displaying thetemporal and spatial variability of soil moisture were developed.

Temporal variability of soil moisture during droughts

As discussed above, there are 19 drought years and four droughtevents over a 50-year record. In general, two years before and afterthe drought were chosen for the pre-drought and post-droughtanalysis, so the soil moisture anomaly response before and aftera drought event could be evaluated. A total 19 drought years, 8pre-drought years, and 8 post-drought years were evaluated inthe map analysis. Secondly, the areas were defined as in dry, nor-mal, and wet conditions based on soil moisture anomalies, andused the following classification scheme: dry condition (soil mois-ture anomaly below �10 mm), normal condition (soil moistureanomaly between �10 mm and 10 mm), and wet condition (soil

a

b

0

40

80

120

160

200

1950 1955 1960 1965 1970 19

Time

soil

mos

itur

e (m

m)

Layer 1(0-10cm) Layer2(

0

40

80

120

160

200

240

1950 1955 1960 1965 1970 1

soil

moi

stur

e (m

m)

soil moisture (298) soil mois

Fig. 5. Modeled soil moisture for the UCRB: (a) 50-year monthly average soil moi

moisture anomaly greater than 10 mm). The percentages of the ba-sin in different conditions were calculated for pre-drought,drought, and post-drought years.

Results

Calibration results

The results of the calibration are presented in Fig. 3, which com-pares the monthly modeled streamflow with the observed stream-flow at Fall Creek, Piney River, Green River, Cisco, and Lee’s Ferrystations from 1950 to 1960. The maximum error between thesedata sets is less than 5% for the UCRB. The monthly hydrographsclosely match the observations, which indicates very low flowsduring November–April and high flows during May–October forthe five stations. The model simulations capture the time of thepeak flows, but overestimate the flows in 1950, which could possi-bly be due to the initialization of the model.

Soil moisture verification

The CPC soil moisture datasets used for verification were gener-ated from observed precipitation and temperature (Refsgaard,1997). Model verification was carried out for each Climate Division(Fig. 1) and the entire UCRB. Only the verification results of thewhole UCRB for period 1950–2000 were represented in Fig. 4.The comparisons of the two soil moisture datasets demonstratedsimilar results for the five Climate Divisions as those for the wholeUCRB in Fig. 4a. A comparison revealed that the seasonal cycles insoil moisture were well captured and the two models matched rea-sonably well. The soil moisture anomaly in the CPC tended to behigher than that of the VIC-3L model for the period 1967–1972and lower for the period 1977–1981. The VIC-3L model predicts

75 1980 1985 1990 1995 2000

10-40cm) Layer3(40-140cm)

975 1980 1985 1990 1995 2000Timeture (300) soil moisture (337)

sture; (b) yearly average soil moisture of layer 3 for three Climate Divisions.

C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135 129

soil moisture values 1.5% lower than the data from the CPC. Fig. 4bpresents the scatter and correlation of the monthly soil moistureanomalies from the CPC and the VIC-3L model. The scatter plotillustrates a relatively high correlation of 0.82 between the CPCand the VIC-3L soil moisture anomalies. The correlations for thefive Climate Divisions (not shown) were 0.80, 0.78, 0.81, 0.83,and 0.83, respectively.

Soil moisture in the UCRB

The VIC-3L model soil moisture is presented in Fig. 5. The dailytime scale modeled soil moisture of layer 1, layer 2, and layer 3 wasaveraged to monthly values and displayed in Fig. 5a. The soil mois-ture of layer 1 shows a higher frequency of variation and this maybe attributed to the structure of the VIC-3L model where layer 1soil responds to precipitation immediately and has a smaller infil-tration capacity, in comparison with the layer 2 and layer 3 soil.The highest amplitudes variation with lowest frequencies occurred

Fig. 6. Wavelet power spectrum of the six time series: (a) soil moisture of layer 1, (b) soiprecipitation. The scale of the power spectrum is a log2 representation of the power spe

in the layer 3. This suggests that extreme climate occurs at longertime scales and the soil storage is higher in the deeper soil layer.Soil moisture data varied from 12.9 mm to 23.4 mm for the layer1, 37.2 mm to 70.5 mm for the layer 2, and 106.0 mm to216.7 mm for the layer 3. Soil moisture values for the layer 2 andlayer 3 show some drastic reduction for certain drought years,for example, 1964–1966 and in the late 1970s. The maximum soilmoisture deficit in layer 3 occurred during the late 1990s, whichprovides insight to drought characterization, coincided with thecurrent drought studied by Piechota et al. (2004).

The variation of the yearly averaged soil moisture was studiedfor the five Climate Divisions, however, only the results of threeClimate Divisions (298, 300, and 337) were presented in Fig. 5b.High soil moisture occurred from 1982 to 1983; this may due towet conditions derived by the El Niño event. All Climate Divisionsshow a decrease in soil moisture for several periods, for instant, theyear 1956 and 1963, the late 1970s and the 1980s, and the late1990s.

l moisture of layer 2, (c) soil moisture of layer 3, (d) the PDSI, (e) streamflow, and (f)ctrum value.

ig. 7. Wavelet coherency between: (a) the PDSI and soil moisture of layer 1, (b) theDSI and soil moisture of layer 2, and (c) the PDSI and soil moisture of layer 3.

Table 1Coherency between the six time series: soil moisture of layer 1, soil moisture of layer2, soil moisture of layer 3, the PDSI, precipitation, and streamflow.

Coherency (95%significant)

Soil moisturelayer 1

Soil moisturelayer 2

Soil moisturelayer 3

Soil moisture layer 1Soil moisture layer 2 0.9Soil moisture layer 3 0.82 0.87PDSI 0.84 0.86 0.88Streamflow 0.83 0.85 0.87Precipitation 0.85 0.87 0.86

130 C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135

Comparison of soil moisture and drought indicators

Wavelet analysis was conducted on six time series: soil mois-ture of layer 1, soil moisture of layer 2, soil moisture of layer 3,streamflow at Lee’s Ferry, precipitation, and the PDSI in the UCRB.The wavelet power spectrum for these six time series are pre-sented in Fig. 6, which shows the temporal fluctuation of the vari-ables over the entire 50-year period. For soil moisture of layer 1,layer 2, and layer 3 (Fig. 6a–c), the power is widely distributed,with peaks in the 1-year, 4–8 year and the 8–16 year bands. The1-year frequency band in the soil moisture of layer 1 coincideswith the annual cycle precipitation (Fig. 6f). The wavelet resultsof the PDSI display a dominant feature of a high spectrum for theperiod of 4–8 year, representing the periodicity of 4–8 years fre-quency cycle coincides with El Niño events. Variance changes sim-ilar to the soil moisture are found in the PDSI (Fig. 6d), andstreamflow (Fig. 6e) over the 4–8 year and the 8–16 year bandswhich means that the soil moisture is closely linked to the PDSIand streamflow. Over the entire range of frequencies and timeperiods, the most similar wavelet power spectrums are for soilmoisture of layer 3 and the PDSI. There is a significant covariancebetween them in the 4–8 year band. This is expected since the PDSIis partially computed based on soil moisture values. Furthermore,Lakshmi et al. (2004) found similar results for the Mississippi RiverBasin.

To further investigate the similarities of the six time series,wavelet coherency was performed between all of the time series.Fig. 7 depicts the wavelet coherency of soil moisture of layer 1 withthe PDSI (Fig. 7a), soil moisture of layer 2 with the PDSI (Fig. 7b),and soil moisture of layer 3 with the PDSI (Fig. 7c). The waveletcoherency between soil moisture of layer 1 and the PDSI is greaterthan 0.8 for most times in the 1–2 year band, and it exceeds 0.85during the intervals from 1965 to 1980. The coherency betweensoil moisture of layer 2 and the PDSI demonstrates high valuesfor in the 2–4 year band and in the 4–8 year band. The soil mois-ture of layer 3 and the PDSI identify significant coherency in the4–8 year band and the 8–16 year band, with relatively low coher-ency outside of these periods, which indicates that the soil mois-ture is strongly correlated to the PDSI at the similar frequencypatterns as the El Niño (every 3–7 years). The changes in the PDSIand soil moisture of layer 3 appear with high coherency from 1955to 1985.

Table 1 summarizes the coherency between the six time seriesof 95% significant level. Similar to the comparisons made in Fig. 7,the coherence between the soil moisture of layer 1 and the soilmoisture of layer 2 is 0.9. This represents the high amount of inter-flow between these two soil layers. The PDSI and the soil moistureof layer 3 are coherent at 0.88. This suggests that the soil moistureof layer 3 could be utilized as an indicator of extreme climate con-ditions (e.g., droughts and floods). Lastly, precipitation and the soilmoisture of layer 3 have a moderate coherency (0.85) that furtherhighlights the usefulness of the soil moisture of layer 3 as an indi-cator of hydroclimatic conditions. The coherency between precipi-tation and the soil moisture of layer 1, precipitation and the soilmoisture of layer 2 are 0.85 and 0.87, respectively. This may bedue to the quick response of the layer 1 and layer 2 soils to theprecipitation.

Spatial variability of soil moisture

Fig. 8 represents soil moisture maps, displaying the 50-yearaverage gridded soil moisture (Fig. 8a), the average soil moistureanomaly for the drought years (Fig. 8b), the normal years(Fig. 8c), and the wet years (Fig. 8d). There were six regions withlow soil moisture in Fig. 8a, four of them, regions 1–4, were locatedin the western-central UCRB. These regions are mostly located in

FP

the Colorado plateau with barren or sparse vegetation (Fig. 2b). Re-gion 1 had the lowest average soil moisture, where the average soilmoisture was below 20 mm. Another two regions, regions 5 and 6,with lower soil moisture, were identified in the lower portion ofthe basin, with barren or sparse vegetation (Fig. 2b) and sandy soils(Fig. 2c). The soil moisture in Climate Division 33 was higher thanthat of other Divisions. The deep loam clay soil (Fig. 2c) is the major

Fig. 8. Soil moisture and soil moisture anomaly maps for the UCRB: (a) Yearly average soil moisture over the 50-year periods; (b) average soil moisture anomaly for thedrought years; (c) average soil moisture anomaly for the normal years; and (d) average soil moisture anomaly for the wet years.

C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135 131

soil type and the needle leaf forest (Fig. 2b) comprises most part ofthis Division. Three regions, regions 7, 8, and 9, with high soil mois-ture stand out. Region 7 was in the upper corner of the basin,which is affected by snow melt. Regions 8 and 9, along the eastof the basin, are also affected by snow melt and have more vegeta-tion, which leads to deep, dark, and rich soils.

Three maps (Fig. 8b–d) shows the spatial patterns of soil mois-ture anomalies for different time periods: drought, normal, andwet years. When taken together, the three maps display a spatialpicture of the changes of soil moisture anomalies for three differ-ent periods. Two regions, regions 1 and 2 (Fig. 8b), were identifiedwith lower soil moisture anomaly over the drought years. These re-gions are mostly covered by shrub land, and some areas are com-prised of barren or sparse vegetation. The soil moisture anomalyduring the drought years ranged from �40.00 mm to 0 mm withthe averaged value of �12.7 mm.

The soil moisture anomaly displays a lower variation with low-er amplitudes in the normal years (Fig. 8c), in which the averagesoil moisture anomaly was 0.7 mm. Two distinct regions (Fig. 8d)were identified as being sensitive to wet conditions. These two re-gions have a similar spatial concentration in comparison with the

significant regions in the drought map (Fig. 8b). The response pat-tern of vegetation to drought and wet conditions may contribute tothe sensitivity of the soil moisture anomaly to the drought and wetconditions.

Temporal variability of soil moisture

The soil moisture anomalies in three periods: pre-drought,drought, and post-drought years for two drought periods wereidentified and displayed in Figs. 9 and 10. Yearly average soil mois-ture anomalies for all four drought periods are showed in Table 2.The percentages of regions in dry, normal, and wet conditions forthe pre-drought, drought, post-drought years are also displayedin Table 2.

For the pre-drought year of 1951, over 66% of the UCRB experi-enced dry conditions (soil moisture anomaly below �10 mm) (SeeFig. 9). However, in 1952, only 16% of the basin had dry conditions.Sheffield et al. (2004) noted that the surface was dry but the deeperlayer soil was wet in 1952 due to long-term variation in climate.During the drought period (1953–1956), over 50% of the basinhad negative soil moisture anomalies. Lower soil moisture anom-

132 C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135

aly might have played a major role in accelerating the widespreadof the drought. The average soil moisture anomaly reached a his-torical low value of �26.13 mm, and 83% of the basin had dry con-ditions. The sudden increase of the soil moisture anomalies anddecrease of dry regions in 1957 were due to the spring rain in

Fig. 9. Soil moisture anomaly with the percentage of dry regions for the pr

1957 (Sheffield et al., 2004). Less than 50% of the basin had nega-tive soil moisture anomalies in two post-drought years (1957and 1958). Average soil moisture anomalies increased to positivevalues (Table 2) in 1957 and 1958, which signaled the end of thefour year drought.

e-drought, drought, and post-drought periods of the year 1951–1958.

C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135 133

The drought of the years from 1988 to 1992 (Fig. 10c–g) costmore than $30 billion losses over the United States and has beenconsidered to be one of the worst disaster in US (Trenberth andBranstator, 1992). The main factors in the development of thisdrought were the combination of the sea surface temperature,associated with the La Niña and the feedback of soil moisture with

Fig. 10. Soil moisture anomaly with the percentage of dry regions for the p

precipitation (Trenberth and Branstator, 1992). The two pre-drought years had only 10% of the basin in dry conditions. How-ever, more than 50% of the basin had dry conditions for three outof the five drought years. The average soil moisture anomalieswere negative for the five drought years. The soil moisture beganto increase with wet conditions across the southern to the central

re-drought, drought, and post-drought periods of the year 1986–1994.

Table 2Yearly Average soil moisture anomalies and percentage of basin had dry, normal, andwet conditions for the pre-drought, drought, and post-drought for four droughtevents.

Catalog Years ASMA (mm) Normal (%) Dry (%) Wet (%)

1953–1956 droughtPre-drought 1951 7.85 22 66 12

1952 8.66 40 16 44

Drought 1953 �14.15 36 58 61954 �16.78 32 65 31955 �19.08 24 73 31956 �26.13 15 83 2

Post-drought 1957 0.45 34 43 231958 8.8 41 14 45

1959–1964 droughtPre-drought 1957 0.45 34 43 23

1958 8.8 41 14 45

Drought 1959 �17.04 28 69 31960 �6.3 48 39 131961 �8.22 44 47 91962 0.66 45 26 291963 �16.56 29 65 61964 �21.98 18 80 2

Post-drought 1965 0.45 46 28 261966 5.68 50 14 36

1974–1977 droughtPre-drought 1972 18.96 44 39 17

1973 6.24 26 10 64

Drought 1974 �12.86 35 57 81975 �11.39 43 52 51976 �18.14 25 73 21977 �37.25 10 90 0

Post-drought 1978 6.32 47 20 331979 23.37 23 8 69

1988–1992 droughtPre-drought 1986 17.01 32 10 57

1987 12.61 39 10 51

Drought 1988 �5.56 37 25 381989 �15.47 32 64 41990 �33.58 16 81 31991 �19.89 34 54 121992 �1.02 43 22 35

Post-drought 1993 30.28 30 2 681994 0.37 60 21 19

134 C. Tang, T.C. Piechota / Journal of Hydrology 379 (2009) 122–135

basin. Wet conditions prevailed in the UCRB with 68% classified aswet conditions in 1993. Sheffield et al. (2004) also found the sim-ilar results that 70% of the UCRB had recovered from the severedrought in 1993. Additionally, averaged soil moisture anomalieswere positive (Table 2), and less than 30% of the basin had dry con-ditions in the two post-drought years.

Conclusion

This research presented a simulation of soil moisture by theVIC-3L model at a 1/8� resolution and a daily time step over a50-year period in the UCRB. This simulation offered a spatiallyand temporally long-period, high-resolution soil moisture datasetfor the UCRB. The observed and simulated soil moisture valueswere in reasonably good agreement and differences between sim-ulated and observed streamflow never exceeded 5% during the val-idation period. The model verification was performed bycomparing simulated soil moisture from the VIC-3L model withthat from the CPC center. During the verification test, it was note-worthy that the two soil moisture datasets showed similar vari-ability and the correlation between them was relatively high

(0.82). The 50-year simulations over the UCRB indicated that theVIC-3L model was able to produce the streamflow and soil mois-ture quite well.

The simulated soil moisture was related to the PDSI, stream-flow, and precipitation by utilizing wavelet and coherency analysisin the UCRB. The wavelet coherency analysis presented the rela-tionships between six time series (soil moisture of layer 1, layer2, and layer 3, the PDSI, streamflow, and precipitation). The soilmoisture of layer 3 showed high correlation with the PDSI (0.88)and this suggests that soil moisture may be a good drought indica-tor or a central variable for characterizing the hydrologic status forthe UCRB.

Then the study identified the spatial and temporal variability ofsoil moisture in response to drought events using 50-year soilmoisture data (1950–2000) in the UCRB. In the spatial analysis, re-gions identified with more sensitivity to wet and dry conditionswere the western-central parts of the basin. In general, regionswith lower soil moisture were associated with the barren or sparsevegetation and sandy soil. The regions with high soil moisture areconsistent with high vegetation density (needle leaf forest).

The temporal soil moisture conditions were evaluated by exam-ining soil moisture in three different periods: pre-drought,drought, and post-drought of four drought events. The results fromthe 35 maps created for the temporal analysis demonstrated thatthe average soil moisture anomalies were negative for the droughtperiods. Also, the droughts did not end until two consecutive yearsof positive soil moisture anomalies. For pre-drought years, soilmoisture anomalies decreased for two drought events (e.g.,1974–1977, and 1988–1992). However, for another drought events(e.g., 1953–1956, and 1959–1964), soil moisture did not have neg-ative anomalies prior to the drought. This may be due to the se-quence of the drought impacts identified by Andreadis andLettenmaier (2006). The sequence begins with meteorological(precipitation) drought and as its duration increases, agricultural(soil moisture) drought, and then hydrological (streamflow)drought follow. For drought periods, more than 50% of the basinhad dry conditions for 15 out of 19 drought years. For post-droughtperiods, greater than 50% of the basin had normal and wet condi-tions, and the average soil moisture anomalies were positive forall the 10 post-drought years, which indicate that only one yearwith positive average soil moisture anomaly was not enough toend a drought.

Acknowledgements

This research is supported by the US National Science Founda-tion award CMS-0239334 and Cooperative Agreement EPS-0814372, and the National Oceanic and Atmospheric Administra-tion under award NA070AR4310228.

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