Correlating Mathis Discharge to Estimated Stage at Calallen 



Data from the concurrent periods shared by the Mathis and Calallen gauges (daily records from January 1940 

 through July 1950, and October 1989 dirough December 1999) were used to correlate Mathis discharge to Caktikn 

 stage. Prior to this correlation, several modifications to the original Mathis data set were made. 



First, the travel time of flow events was examined for the period of conctirrent data between the Mathis and 

 Calallen gauges. Based upon this analysis, the average travel time for flow events in the Nueces River to travel 

 from Mathis to Calallen was determined to be about two days. The entire Mathis data set was therefore 

 corrected by delaying each daily flow value by 48 hours. When analyzed individually, however, the actual travel 

 time for the flow peak of any one flow event, which depends greatly upon the characteastics of the individual 

 flood event, has been estimated to take as many as 5 days (Ward 1985). The average correction was used 

 because individual correction of each flow event was not possible for the entire data set due to the absence of 

 daily stage data at Calallen for the period of 1950 through 1989. 



Second, the resulting data set was corrected to account for channel losses in the reach between the Mathis and 

 CalaUen gauges. HDR Engineering, Inc., et al. (1991) calculated an average loss rate of 0.1243% per river 

 kilometers, or a total of 7.0% for the entire 56.3 km reach between Lake Corpus Christi and Calallen Dam. 

 This rate was based on field measurements reported by the United States Geological Survey (1968), and is 

 representative of the loss rate during periods of normal water deliveries with minimal intervening flows. The 

 distance between the Mathis and Calallen gauges is only 54.6 km, sUghdy shorter than between the two dams, 

 which resulted in only a 6.8% loss rate. A conservative arbitrary value of 8.5 m'/s (300 cfs) was used to 

 represent the upper limit of " minim al intervening flow". Daily Mathis values below this limit were corrected by 

 a loss of 6.8%. Stream flow losses for daily values in excess of 8.5 m'/s were assumed to be constant at 

 0.58 mVs (20.4 cfs), or 6.8% times 8.5 mVs. 



Third, the resulting data set was corrected to account for the estimated total daily municipal and industrial 

 withdrawals made from the Nueces River at or before Calallen Diversion Dam. Estimated total annual 

 withdrawals for every tenth year of the period of record were derived from a number of sources (Homer & 

 Shifrin Consulting Engineers 1951, Bureau of Reclamation 1971, Corpus Christi 1990), and then estimated for 

 each intervening year assuming a linear relationship between the decade totals. Each total annual withdrawal 

 amount was then divided by an average monthly percentage of water use for the Coastal Bend area (Bureau of 

 Reclamation 1971), and the resulting values converted from total volume to average daily flow. These daily 

 values, which represent the estimated daily municipal and industrial withdrawal for that month and year, were 

 then subtracted from the modified Mathis data set. The daily correction values range from 0.20 to 0.25 m'/s 

 (7 to 9 cfs) in 1940, and from 4.36 to 6.20 mVs (154 to 219 cfs) in 1999. 



Once the Mathis data set had been thus corrected, the relation between this discharge data and published 

 CalaUen stage data was determined through linear regression (Figure 5). Daily values greater than 2.44 m (8.0 ft) 

 from the unpublished Calallen data were also used. In addition, one point was added to the data set as an 

 estimate of the extreme condition. The largest daily flow value recorded at Mathis was 3,539 m'/s (125,000 cfs) 

 on September 25, 1967, and was a result of the massive flooding caused by Hurricane Beulah. This event 

 occurred during the period for which there is no available stage data at Calallen, but other sources have 

 reported that the Nueces River at Calallen crested at 5.02 m (16.48 ft) the same day (Corpus Christi Times 

 1967). 



This relationship therefore allows the use of Mathis daily discharge data as the independent variable to solve for the corresponding 

 estimated daily stage at Calallen. The entire corrected Mathis discharge data set was then converted to estimated 

 stage at Calallen using this relation. 



There are three primary limitations to this method of correlating Mathis and Calallen gauge data. First, as 

 previously discussed, travel times for each flow event vary, which compromises the temporal accuracy of the 

 estimations. The inability to correct each flow event in the record for travel time requires the acceptance of this 

 error. Second, although there is very litde additional watershed below Mathis and above Calallen (only 559 

 km'^, some locally intense storms produce flow events at Calallen that are not recorded at Mathis. This 

 relational difference between the Mathis and Calallen gauge data sets is especially high for tropical storm events 

 that move onshore from the Gulf. Finally, stage data for the Nueces River at Calallen is not available for values 

 in excess of 4.13 m (13.55 ft) (which roughly correspond to a discharge of about 50,000 cfs at Mathis), requiring 

 extrapolation for higher discharge values. 



C-8 ^* Analysis of the Historic Flow Reffme of the Nueces River into the Upper Nueces Delta 



