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<br />FL Ogd~n n Ill./ Journal of Hydrology 228 (2000) 82-/00
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<br />FL Ogd~11 rl al./ Journal of Hydrolot.Y 228 (2000) 82-JOO
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<br />than when using ZH alone. Another important dual
<br />polarization radar observable is the differential propa-
<br />gation phase shift t/)op (degrees) (Sachidananda and
<br />Zmi.::, 1986). The specific differential propagation
<br />phase shifl, K[lp (degreeslkml is given by one half
<br />the spatial gradient of the ctJop_ The tPoP signal is
<br />quite noisy. so a low-pass filter was used to smoolh
<br />!pop along each ray. The parameter Kop is useful in
<br />hydrometeorology, because it is insensitive 10 hail,
<br />independent from measurements of the reflectivity
<br />factor, and nearly linearly proponionallo high rainfall
<br />rates ($achidananda and Zmic, 1986).
<br />In a smdy of radar-rainfall estimation errors using
<br />difft:rent radar observables, Chandrasekar et al. (1993)
<br />estimated the fracliona! standard deviation (FSD) of
<br />lwon!y rainfall rate estimate to be 45% for rates up to
<br />]0 mm/h and increases to 55'1'c- when Iherate is as high
<br />as 150 mmlh. When lH and lOR was used in combina-
<br />tion 10 estimale the rain rate, FSD was 60% for rates
<br />up 10 10 mmlh and 25% for higher rales. When using
<br />Kill' as an estimalor, Ihey estimated FSD values of 80,
<br />25 and 15% for rainfall rates of 20,80 and 200 mmlh,
<br />respectively. Gorgucci et al. (1994) emphasized that
<br />conventional rainfall rate estimates using lH and ZoR
<br />are unstable when lOR values are !ow due to measure-
<br />ment errors. They suggested a robust estimator which
<br />uutperfonn conventional estimators particularly al
<br />very low and very high rainfall rates. Chandrasekar
<br />(]997) refined that estimator.
<br />The three radar observables mentioned above were
<br />used to estimate the rainfall rate from the polarimetric
<br />radar data. Each observable was used within the range
<br />where it is believed to be physically related to the
<br />rainfall rate. Dual polarization rainfall rate estimates
<br />were obtained according to the following multi-para-
<br />meter algorithm:
<br />If KDI' > 1.:!50lkm and ZH > 40.0 dBZ the rainfall
<br />rate (mmlh) is calculated using the relation by Ryzh-
<br />kov and Zmic (1995):
<br />
<br />R(Kop,2D1.) = 52.0KSp~f>Zu~+n
<br />
<br />If the above conditions are not met, but lOR> -0.5,
<br />then the relationship developed by Chandrasekar
<br />(1997) is u;,ed:
<br />R(Z[)l~,Zt!l = I 17 x JO-C(Z::,~t~)(JO-OAO~ Zu..) (4)
<br />
<br />If neither of the above conditions are true, then
<br />
<br />~
<br />
<br />with redislribution (Ogden and Saghafian, 1997). The
<br />model can be used 10 simulate single events, or comin-
<br />uous periods of record. CASC2D accepts rainfall
<br />input at any number of painls in space with any
<br />temporal resolution, which allows the model to
<br />readily accept radar-rainfall estimates.
<br />Infiltration into the soil is oplionally modeled using
<br />either the Green and Ampt (191 I) method, or the
<br />Green and Ampt Redisuibution (GAR) method
<br />(Ogden and Saghafian, 1997). The GAR technique
<br />is similar to the method described by Smith et al.
<br />(1993), with the assumption of rectangular soil moist-
<br />ure profiles and the addition of an analytically-derived
<br />unsalUrated capillary head term (Ogden and Saghafian,
<br />1997). The GAR option allows accurate simulation of
<br />infiltralion when there are muhiple ponding periods.
<br />The original Green and Ampt (1911) equalion is:
<br />
<br />the Battan (1973) Z-R relation given in Eq. (2) is
<br />applied.
<br />The polarimetric radar measurements are spaced
<br />125 m along the radar beam. Rain rate estimates
<br />were produced by compUling mean values of 2H.
<br />20R and KDf> over seven adjacent radar measuremenls
<br />(bins), and applying the abqve polarimelric algorithm.
<br />These rainfall estimales are then gridded to a hexago-
<br />nal grid with the centers of hexagons 707 m apart,
<br />which is approximalely the beam width of the radar
<br />over the Spring Creek watershed. Hexagonally
<br />centered grids were selected to reduce Ihe bias due
<br />10 grid orientation. Rain gage accumulations were
<br />compared with the nearesl radar pixel. The polari-
<br />metric hourly radar accumulations compare very
<br />well wilh hourly rain gage accumulations, as shown
<br />in Fig. 3. The slope of the best-fit regression line
<br />through the polarimetric hourly rainfall estimates is
<br />0.991, indicating thai the polarimetric rainfall algo-
<br />rithm produces unbiased hourly precipitation esti.
<br />mates compared with the gage observations.
<br />Therefore, there is no need 10 multiply the dual polar-
<br />. ization estimates by any factor (bias adjustment).
<br />From Fig. 3, it is clear that the uncalibrated polari-
<br />metric rainfall estimates are significantly more accu-
<br />rate than the uncalibraled single-polarization WSR-
<br />88D rainfall estimates of this storm based on the
<br />operulional algorithm in use at the Cheyenne, Wyom-
<br />ing, WSR-88D on 28 July 1997. The polarimetric
<br />radar-rainfall eSlimates are also considered superior
<br />to rain gage measuremenls because of their finer
<br />spacellime resolution.
<br />
<br />f~K.[H,(\- 8,) + 1]
<br />
<br />where:fis the infiltration rate (ur): K, the soil satu-
<br />rated hydraulic conductivity (UT): H. the Green and
<br />Ampt capillary head term (L): 8. the soil effective
<br />porosity (dimensionless); 8, the soil initial water
<br />content (dimensionless); F the cumulative infiltrated
<br />depth (L).
<br />Eq. (5) was used to model infiltration during the
<br />storm that occurred during the evening of 28 July
<br />1997, because of high initial soil moislUre contents,
<br />and the lack of significant periods of rainfall hiatus.
<br />Once ponding occurs in CASC2D, surrace water is
<br />accumulated in each model grid cell until the specified
<br />retention depth for Ihat cell is exceeded. Thereafter,
<br />the overland flow is routed in two orthogonal direc-
<br />tions using Manning's equalion with the diffusion
<br />wave form of the de St. Venant equations to estimate
<br />the friction slope. When overland flow reaches a
<br />model grid-cell that contains a defined channel, the
<br />flow is passed inlo Ihe channel and routed using a one-
<br />dimensional. explicit, diffusive-wave routing lech-
<br />nique. A full description of the current capabilities
<br />of CASC2D is given in Ogden (1998).
<br />
<br />8. Hydrologic model CASC2D
<br />
<br />(3)
<br />
<br />CASC2D (Julien et aI., 1995; Ogden. 1998) is a
<br />physically-based, distributed-parameler, fiilite-differ-
<br />ence hydrologic model that simulates infiltration
<br />excess (Hononian) runoff. CASC2D operates on a
<br />digital elevation model of the watershed, using square
<br />grids that Iypically range from 10 to 120 m on a side.
<br />The original formulalion of CASC2D was reponed in
<br />Julien et a!. (1995). The original CASC2D formula-
<br />tion has been significantly enhanced with the addition
<br />of continuous soil moisture accounting (Ogden and
<br />Senarath, 1997), a variety of channel cross-seclions
<br />(Ogden, 1994), and Green and Ampt infiltration
<br />
<br />Water levels in Horsetooth Reservoir (Fig. 2) are
<br />
<br />9, Calibration of CASC2D on Horsetooth
<br />watershed
<br />
<br />(5)
<br />
<br />recorded digitally every 15 min. The first storm on the
<br />morning of 28 July had a significant effecl on the
<br />Horsetooth watershed; between 08:30 and 11:30
<br />MDT Ihe water surface elevation in Horsetooth Reser-
<br />voir rose approximately 7 cm more Ihan Ihe amount it
<br />would have due solely to CST project diversions. This
<br />indicates Ibal approximately 1 cm of runoff occurred
<br />from the contributing area. Radar observations from
<br />the morning of 28 July suppon the assenion that a
<br />significant storm passed over the watershed.
<br />The soil hydraulic parameters published in Ihe
<br />NRCS county soil survey are approximate values;
<br />actual values must be obtained by calibration. During
<br />the second storm during the evening of 28 July, the
<br />water surface elevation in Horsetooth Reservoir rose
<br />by 37 em belween 18:30 and 22:30 MDT. This rise
<br />exceeds that due to CBT diversions by 35 cm. indical-
<br />ing a basin-average runoff of approximately 5 cm
<br />from Ihe contribuling area. Given that the morning
<br />stonn on 28 July produced significant runoff, it is
<br />reasonable to assume that it saturated the upper few
<br />cm of the soil column. At Ihe beginning of the evening
<br />stonn, the upper soil layer was likely near saturation.
<br />This condition presents a unique' opponunity for cali-
<br />braling the soil hydraulic conductivity field of the
<br />watershed. Under high initial water content condi-
<br />tions, the Green and Ampt equation (5) states Ihat
<br />infiltration rates are very close to the saturated hydrau-
<br />lic conductivity of the soil, and that soil capillary head
<br />plays a minor role. The occurrence of the significant
<br />storm during the morning on 28 July allows a one-
<br />parameler calibr.lIion of the dominant soil hydraulic
<br />propeny (saturated hydraulic conductivity), because
<br />the soils were nearly saturated at the beginning of
<br />the evening SlDnn.
<br />After reviewing the characteristics of the soils in
<br />the Horsetooth walershed they were assigned one of
<br />six textural classifications. The ephemeral stream
<br />network in the Horsetooth watershed (Fig. 2) was
<br />modeled assuming trapezoidal cross-sections. The
<br />polarimetric radar-rainfall fields were used as model
<br />input during Ihis calibration.
<br />The runoff into the reservoir was simulated for a
<br />period of 10 h (14:00-24:00 MDT). The observed rise
<br />in the reservoir level was caused by three separate
<br />sources: CBT diversion inflows (10 ml/s), direct
<br />runoff inlo the lake, and direct rainfall. Each source
<br />was considered. The soil hydraulic conductivity
<br />
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