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COST-EFFECTIVENESS OF THE STREAM-GAGING PROGRAM IN PUERTO RICO AND THE U.S. VIRGIN ISLANDS By Ken Reid U.S. GEOLOGICAL SURVEY Water-Resources Investigations Report 90-4088 San Juan, Puerto Rico 1991 UNITED STATES DEPARTMENT OF THE INTERIOR MANUEL LUJAN JR., Secretary U.S. GEOLOGICAL SURVEY Dallas L. Peck, Director For additional information write to: District Chief U.S. Geological Survey P.O. Box 364424 San Juan, Puerto Rico 00936-4424 Copies of this report can be purchased from: U.S. Geological Survey Books and Open-File Reports Fede(ral Center Boxi25425, Denver, Colorado 80225 CONTENTS Page Abstract.................................................................................................................................................... 1 Introduction.............................................................................................................................................. 1 History of the stream-gaging program in Puerto Rico and the U.S Virgin Islands .......................................................................................................... 2 Present stream-gaging program in Puerto Rico and the U.S. Virgin Islands ......................................................................................................... 3 Uses, funding, and availability of continuous-streamflow data.............................................................. 3 Data-use classes............................................................................................................................... 3 Regional hydrology................................................................................................................ 3 Hydrologic systems................................................................................................................ 3 Legal obligations.................................................................................................................... 9 Planning and design................................................................................................................ 9 Project operation..................................................................................................................... 9 Hydrologic forecasts............................................................................................................... 9 Water-quality monitoring ....................................................................................................... 9 Research.................................................................................................................................. 9 Other....................................................................................................................................... 9 Funding............................................................................................................................................ 9 Frequency of data availability....................................................................................................... 10 Conclusions pertaining to data uses.............................................................................................. 10 Alternative methods of developing streamflow information................................................................. 10 Description of regression analysis .................................................................................................11 Regression results.......................................................................................................................... 12 Summary of second phase of analysis .......................................................................................... 16 Cost-effective resource allocation.......................................................................................................... 16 Discussion of the model................................................................................................................ 16 Description of mathematical program........................................................................................... 17 Application of the model in Puerto Rico and the U.S. Virgin Islands.............................................................................................................. 18 Definition of variance when the station is operating ........................................................... 18 Definition of variance when record is missing .................................................................... 19 Discussion of routes and costs ............................................................................................. 21 Results.................................................................................................................................. 26 Summary of third phase of analysis.............................................................................................. 30 Summary................................................................................................................................................ 30 Selected References............................................................................................................................... 32 in ILLUSTRATIONS Page Figure 1. Map showing geographic setting of Puerto Rico and the U.S. Virgin Islands......................................2 2. Graph showing history of continuous-record stream-gaging stations in operation in Puerto Rico and the U.S. Virgin Islands ................................................................................................................3 3. Map showing location of continuous surface-water data-collection sites in Puerto Rico....................4 4. Map showing location of continuous surface-water data-collection sites in the U. S. Virgin Islands .4 5. Hydrographs for observed and simulated streamflow for sites 50035000 - Rio Grande de Manati at Gales, and 50038100 - Rio Grande de Manati at Highway 2 near Manati, Puerto Rico.................................... 12 6. Graph showing rating curve plotted on logarithmic axes using stfaight-line segments....................... 19 7. Graph showing typical uncertainty function for instantaneous discharge and number of visits for selected stations in Puerto Rico and the U.S. Virgin Islands............................................................. 19 8. Graph showing average standard error per gaging station as a fuijiction of budget.............................. 26 TABLES Page Table 1. Selected data for continuous-record gaging stations for Puerto Rico and the U.S. Virgin Islands, 1984..................................................................................5 2. Data-use, source of funding, and frequency of data availability for continuous-record gaging stations in Puerto Rico and the U.S. Virgin Islands, 1984 ......................................................................................................7 3. Gaging stations used as dependent variables in the regression modeling of daily streamflow at selected sites in Puerto Rico and the U.S. Virgin Islands.................................. 12 4. Summary of calibration for regression modeling of daily streamflow at selected gage sites in Puerto Rico and the U.S. Virgin Islands ......................................................... 13 5. Summary of the autocovariance analysis ..............................................................................................20 6. Statistics of record reconstruction......................................................................................................... 22 7. Summary of the routes that may be used to visit stations in Puerto Rico and the U.S. Virgin Islands ......................................................4.......................................................23 8. Selected results of K-CERA analysis...........................................|.......................................................27 FACTORS FOR CONVERTING INCH-POUND For the convenience of readers who may prefer to use metric units used in this report, values may be converted by using the Multiply inch-pound units By foot (ft) 0.3048 mile (mi) 1.609 2, square mile (mi ) cubic foot per second (ft /s) 259.0 0.02832 IV UNITS TO METRIC (SI) UNITS (International System) units rather than the inch-pound folk wing factors: To obtain SI units meter (m) kilometer (km) hectare (ha) cubic meter per second (m /s) COST-EFFECTIVENESS OF THE STREAM-GAGING PROGRAM IN PUERTO RICO AND THE U.S. VIRGIN ISLANDS By Ken Reid ABSTRACT This report documents the results of a study of the cost-effectiveness of the stream-gaging program in Puerto Rico and in the U.S Virgin Islands. Data uses and funding from 12 sources are identified for the 50 continuous-record surface-water gaging sites currently (1990) being operated in Puerto Rico and the U.S. Virgin Islands. With a budget of $310,000, the average standard error of estimate of the present operation is 20.6 percent. However, the analysis indicates that with a budget of $500,000, the average standard error of estimate could be reduced to 11.3 percent. The present frequency of visits to continuous- record surface-water data-collection sites is monthly at all but one site in Puerto Rico. The four sites in the U.S. Virgin Islands are visited six times per year. Given a budget of $350,000 (equivalent 1984 dollars), the aver- age standard error could be reduced to 15.6 percent. However, this would require that 20 stations be visited at a frequency of two to three times per month, with the remainder visited as few as six times per year. The logistics required for assigning personnel and vehicles to the field at the computed frequencies would not be feasible. Therefore, the frequency of vehicle and per- sonnel visits would probably be reduced to about twice per month at most sites. This alternate approach could result in a standard error of estimate of about 17 per- cent with a $40,000 increase in the budget. All stations were identified as necessary in the present network, and no stations could be replaced by data simulation using alternative methods, such as re- gression analysis and other simulation means, because these methods tend to be inaccurate. Also, most con- tinuous-record stations are multiple-purpose ones where data are collected for more than one cooperator or Federal agency. There is a need for long-term Index and Benchmark continuous-record discharge stations in Puerto Rico and the U.S. Virgin Islands. These stations are needed on streams draining 1 to 15 square mile areas that are mainly unaffected by the activities of man. Possible sites for such stations are on streams draining areas from Federal and Commonwealth park- land. The data obtained from such areas could be used to discriminate between changes due to man s activities and those due to natural trends. This information is particularly needed where tropical rain forests exist, such as in El Yunque, Puerto Rico. There are no continuous-record stream-gaging stations on Puerto Rico's offshore islands of Vieques and Culebra, and only four such stations exist for the three major U.S. Virgin Islands. Sufficient stations are needed on these islands to obtain information on stream/low, flood peaks, low flows, and quality of water for hydrologic studies leading to an improved under- standing of surface-water availability and quality. INTRODUCTION The U.S. Geological Survey is the principal Fed- eral agency involved in the collection of surface-water data throughout the Nation, the Commonwealth of Puerto Rico, and the U.S. Trust Territories. Streamflow-data collection is a major activity of the Water Resources Division of the U.S. Geological Sur- vey. The data are collected in cooperation with State and local governments and other Federal agencies. The U.S. Geological Survey operates about 7,000 continu- ous-streamflow record gaging stations throughout the Nation. The operation of some of these stations extends back to the turn of the century. In Puerto Rico, about 20 stations have been operated continuously since 1960. Any activity of long standing, such as the collec- tion of surface-water data, should be reexamined at intervals, if not continuously, because of the change in objectives, technology, or external constraints. The last systematic nationwide evaluation of the U.S. Geological Survey's streamflow information program was com- pleted in 1970 and documented by Benson and Carter (1973). In 1983, the U.S. Geological Survey began a 5-year reevaluation of the national stream-gaging pro- gram, and 20 percent of the program is analyzed each year. The objective of this analysis is to define and document the most cost-effective means of furnishing streamflow information. This report documents the analyses of the stream- flow data-collection program in Puerto Rico and the U.S. Virgin Islands (fig. 1). It is organized into five sections. The first section is an introduction to the stream-gaging activities and the current program in Puerto Rico and the U.S. Virgin Islands. The middle three sections each contain discussions of individual steps in the analyses. Because of the sequential nature of the steps and the dependence of subsequent steps on the previous results, conclusions and suggestions are made at the end of each of the middle three sections. The final section summarizes conclusions and recom- mendations. A similar report for the State of Maine (Fontaine and others, 1984) was used as a prototype for this report. Refer to the Maine report for more specific details of the methods used. As the first phase of every continuous-record gag- ing station, an analysis identifies the principal uses of the data and relates these uses to funding sources. Gaged sites for which data are no longer needed, are deficient, or fail to meet user demands, are identified. In addition, gaging stations are categorized by whether the data are available to users in a near real-time sense, on a periodic basis, or at the end of the water year (October through September). The second phase of the analysis is to identify less costly alternative methods of furnishing the needed in- formation. Among these are flow-routing models and statistical methods. The stream-gaging activity no longer is considered a network of observation points, but rather is an integrated information system in which data are provided by measurement and synthesis. The final part of the analysis involves the use of Kalman-filtering and mathematical-programming tech- niques to define strategies for operation of the necessary stations that minimize the uncertainty in the streamflow records for given operating budgets. Kalman-filtering techniques are used to compute uncertainty functions (relating the standard error of estimate of instantaneous discharge to the frequency of visits to the gaging sta- tions) for all stations in the analyses (Fontaine, and others, 1984). A steepest-descent optimization program uses these uncertainty functions, information on practi- cal stream-gaging routes, the various costs associated with sjeam gaging, and the total operating budget to identify the visit frequency for each station that mini- mizes the overall uncertainty in the streamflow data. The slream-gaging program that results from these analyses will meet the expressed water-data needs in the most cast-effective manner. Histoijy of the Stream-Gaging Program in Puerto Rico and the U.S. Virgin Islands The Puerto Rico Water Resources Authority (now the Puerto Rico Electric Power Authority) began stream- flow gaging in Puerto Rico around 1943. The first gaging station was operated in 1943 at Rio Caonillas near Utuado, Puerto Rico. The U.S. Geological Survey, under Public Law 29 (43 U.S.C. 47), began a stream- gaging program in Puerto Rico in 1957. A similar program was begun in 1961 in the U.S. Virgin Islands. The number of continuous-record surface-water sites iiti the U.S. Geological Survey, Water Resources Division, Caribbean District varied from 1 in 1943 and 67"15' 67°00' 66"45' 66"30' 66"15' 66"00' 65*45' 65°30' 65"15' 65"00' 64*45' 64° 30' 18° 30' 18" 15' 18" 00' 17" 45' ATLANTIC OCEAN SAN JUAN i i St. Thomas 10 20 30 KILOMETERS CARIBBEAN &EA 10 20 30 MILES VIRGIN ISLANDS St. Croix Figure 1.-- Geographic setting of Puerto Rico and the U.S. Virgin Islands 1944 to 14 in 1950 and decreased to 6 by 1958. Some of the records collected by the Puerto Rico Water Re- sources Authority (PRWRA) are now in the files of the Caribbean District office of the U.S. Geological Survey, Water Resources Division in San Juan, Puerto Rico. The number of sites increased to a maximum of 60 in 1971, then decreased to 34 in 1978. During the 1984 water year, 58 sites were in operation, but by the end of the year, several sites had been discontinued. Fifty con- tinuous surface-water data sites were continued and could be used for the last part of this study. The number of continuous surface-water stations for which records are collected for part or all of each water year since 1943 are summarized in figure 2. - O 30 1940 1945 1950 1955 1960 1965 1970 WATER YEAR 1975 1980 1985 Figure 2.-- History of continuous-record stream- gaging stations in operation in Puerto Rico and the U.S. Virgin Islands. A network of partial-record data-collection sta- tions was begun in Puerto Rico in 1959 to 1960. The purpose of this network has been to define peak-flood characteristics used for highway design, bridge site analyses, delineation of flood-prone areas, and hydrau- lic analyses. The increasing costs of operation and constraints on funds and manpower has resulted in the discontinuation of most of the partial-record peak-flood stations (Lopez and Fields, 1970). Only one partial- record peak-flood station (50115900 Rio Portugues at Highway 14 at Ponce) is now being operated. Present Stream-Gaging Program in Puerto Rico and the U.S. Virgin Islands The Caribbean District of the U.S. Geological Sur- vey is comprised of Puerto Rico and the U.S. Virgin Islands. The region includes an area of 3,605 mi2 (square miles) (including the islands of Vieques and Culebra and other offshore islands. The Caribbean Dis- trict is in the northeast corner of the Greater Antilles and about 1,000 mi (miles) east-southeast of Miami, Florida. The islands of the northeast part of the Greater Antilles form a divide between the Atlantic Ocean to the north and east and the Caribbean Ocean to the south and southwest. The Caribbean District currently (1990) operates 51 surface-water streamflow stations (50 continuous- record discharge sites and 1 partial record crest-stage station site). Four of the surface-water streamflow sta- tions are operated in the U.S. Virgin Islands of which two are on St. Thomas, one on St. John, and one on St. Croix. No benchmark continuous-record streamflow sites have been established on any of the Caribbean District islands. Gage location is shown in figures 3 and 4; and station number, name, drainage area, and period of record of the continuous-record gages are shown in table 1. USES, FUNDING, AND AVAILABILITY OF CONTINUOUS-STREAMFLOW DATA The relevance of a stream-gaging station is defined by the uses that are made of the data that are produced from the station. The uses of the data from each stream- gaging station in the Puerto Rico and the U.S. Virgin Islands were identified from a survey of known data users (table 2). Also included as part of the survey were the sources of funding and the frequency of data avail- ability for each station. The survey documented the importance of each station and identified gaging stations that may be considered for discontinuance. Data-use Classes Data uses identified by the survey are categorized into nine classes as defined below. Regional Hydrology To be useful in defining regional hydrology, the data from a gaging station must be largely unaffected by manmade storage or diversion. In this class of uses, the effects on streamflow are limited to those caused primarily by land-use and climate changes. Large amounts of manmade storage may exist in a basin and stations in such basins are useful, provided the outflow is uncontrolled. These stations are useful in developing regionally transferable information about the relations between stations classified in the regional hydrology category. Forty-four stations in Puerto Rico and the U.S. Virgin Islands are in this category, as listed in table 2. Hydrologic Systems Stations that can be used for accounting, that is, to define current hydrologic conditions and the sources, sinks, and fluxes of water through "hydrologic sys- 67°15' 65°30' 18°30' - ATLANTIC OCEAN ib Doguoo Quebroda Polma I Rio Santiago Rio Blonco Rfo An ton Rulz Rio Huenocoo EXPLANATION SURFACE-WATER STATIONS CONTWI STATION STATION ANALYSIS 0 10 20 KILOMETERS I 0920A CONTINUOUS STREAMFLOW CARIBBEAN SEA 051180^ STATION NOT USED IN THE 17°45' - Figure 3.--Location of continuous surface-water data-collection sites in Puerto Rico. Site numbers on map refer to the third through sixth or eighth digit of station number shown in table 1. 18*25' 18°20' 18 e15' 65° 00* 64" 55' 64° 50' £> SAINT THOMAS ^25204 X^> x^ ^_^ ^*,&y W Q 1 ? KHOXETCTS MILES 2950 17 17°40' 64-50' 64 8 45' SAINT CROIX P 1 2 KILOMETERS i '\ iuus 3450 sites Figure 4.~Location of continuous surface-water data-collection si refer to the third through sixth or eighth digit of station number shown 64° 45' 64° 40' SAINT JOHN EXPLANATION CONTINUOUS STREAMFLOW STATION 64-40' 64-35' EXPLANATION CONTINUOUS STREAMFLOW STATION in the U.S. Virgin Islands. Site numbers on map in table 1. Table 1.--Selected data for continuous-record gaging stations for Puerto Rico and the U.S. Virgin Islands, 1984 [mi , square mile; ft /s, cubic feet per second; *, not used in initial analysis; IND., indetermined; --, not sufficient years of record to compute mean annual flow; PR, Puerto Rico; VI, U.S. Virgin Islands] Station number if * * * * * * * * * * * * 50010600 50011200 50011400 50014800 50015700 50027750 50028000 50028400 50031200 50035000 50038100 50038320 50039500 50043000 50046000 50050900 50051150 50051180 50051310 50053050 50055000 50055650 50056400 50056900 50057000 50061800 50063440 50063500 50063800 50065500 50067000 50071000 50075000 50092000 50106500 Station name Rio Guajataca above Lago Guajataca, PR Rio Guajataca below Lago Guajataca, PR Rio Guajataca above mouth near Quebradillas, PR Rio Camuy near Bayaney, PR Rio Camuy near Hatillo, PR Rio Grande de Arecibo above Arecibo, PR Rio Tanama near Utuado, PR Rio Tanama at Charco Hondo, PR Rio Grande de Manati near Morovis, PR Rio Grande de Manati at Ciales, PR Rio Grande de Manati at Hwy 2 near Manati, PR Rio Cibuco below Corozal, PR Rio Cibuco at Vega Baja, PR Rio de la Plata at Proyecto la Plata, PR Rio de la Plata at Toa Alta, PR Rio Grande de Loiza at Quebrada Arenas, PR Quebrada Blanca at Jagual, PR Quebrada Salvatierra near San Lorenzo, PR Rio Cayaguas at Cerro Gordo, PR Rio Turabo at Borinquen, PR Rio Grande de Loiza at Caguas, PR Quebrada Caimito near Juncos, PR Rio Valenciano near Juncos, PR Quebrada Mamey near Gurabo, PR Rio Gurabo at Gurabo, PR Rio Canovanas near Campo Rico, PR Quebrada Sonadora near El Verde, PR Quebrada Toron ja at El Verde, , PR Rio Espiritu Santo near Rio Grande, PR Rio Mameyes near Sabana, PR Rio Sabana at Sabana, PR Rio Fajardo near Fajardo, PR Rio Icacos near Naguabo, PR Rio Grande de Patillas near Patillas, PR Rio Coamo near Coamo, PR Drainage area (mi 2 ) IND. IND. IND. IND. IND. 200 18. 57. 55. 128 197 15. 99. 54. 200 6. 3. 3. 10. 7. 89. 0. 16. 2. 60. 9. 1. 0. 8. 6. 3. 14. 1. 18. 46 .4 ,6 2 ,1 .1 ,8 ,0 ,25 ,74 ,2 ,89 ,8 ,82 ,4 ,3 ,2 ,84 .01 ,064 .62 ,88 ,96 ,9 .26 .3 Period of record 1984- 1984- 1 1969;1969-1970,1984- 1984- 1984- 1982- 2 1944-58;1959- 1969-71, 1981- 1965- 1 94 6-53, 3 1 95 6-57; 1 l 95 9- 60; 1960- 4 1963-68;1970- 1969- 1973- 5 1958; 1 1959-60;1960- 6 1959;1960- 1977- 1984- 1984- 1977- 1983- 7 1959; 1 1959;1959- 1984- 1971- 1983- 8 1958; 1 1959;I959- 1967- 1983- 1983- 1959-63;1966- 1967-73; 1983- 1979- 10 1960-61;1961- X1 1 945-53; 4 1 953- 62 ; 12 19 62 -66; 197 9 9 1959-65;1966- 1984- Mean annual flow (ft 2 /s) 48. 103 256 362 28. 119 111 267 30. 47 . 218 49. 131 27. 56. 57. 17. 67. 15, 59. ,4 .3 .6 .9 .4 .5 .6 .7 .5 .8 .3 .9 Table 1.--Selected data for continuous-record gaging stations for Puerto Rico and the U.S. Virgin Islands, 1984 Continued Drainage Station Station name number * * * 50108000 50111500 50112500 50114000 50115000 50124200 50129900 50136000 50138000 50144000 50147800 50252000 50276000 50295000 50345000 Rio Descalabrado near Los Llanos, PR Rio Jacaguas at Juana Diaz, PR Rio Inabon at Real Abajo, PR Rio Cerrillos near Ponce, PR Rio Portugues near Ponce, PR Rio Guayanilla near Guayanilla, PR Laguna Cartagena Outflow near Boqueron, PR Rio Rosario at Rosario, PR Rio Guanajibo near Hormigueros, PR Rio Grande de Anasco near San Sebastian, PR Rio Culebrinas at Hwy 404 near Moca, PR Bonne Resolution Gut at Bonne Resolution, St. Turpentine Run at Mariendal, St. Thomas, VI Guinea Gut at Bethaney, St. John, VI Jolly Hill Gut at Jolly Hill, St. Croix, VI area (mi 12. 49. 9. 17 . 8. 18. IND 16. 120 94. 71. Thomas, VI 0. 2. 0. 2. ) 9 8 7 8 82 9 4 1984- 1984- 7 1962 X 1964 X 1964 1981- 1984- Period of record -63; l l 964 ; 1964-70, 1971- ;1964- ;1964- 13 1960-66;1975 12 1959; 1 1959-67;1973- 3 2 49 97 37 1 1963- 1967- 1962- 1963- 1963- 1963- 67;1981;1982- 69; 1978-80; 1982- 67;1982- 68; 1 1962; 1 1969;1982- Mean annual flow (ft 2 /s) 18 35 18, 45 219 309 300 0, I, 0, 0 .4 .1 .0 .1 .21 .04 .072 .027 Monthly discharge measurements only. Daily stage and two to four measurements per month by the Puerto Rico Water Resources Authority. 9 10 11 12 13 Unpublished, available in files of Caribbean Districtoffice and in the "National Water Data Storage" and Retrieval System, Reston, Virginia. Annual maximum discharge only. Occasional measurements only. Measurements only. Low-flow measurements only. Occasional low-flow measurements only. Annual low-flow and occasional measurements only. Occasional low- and peak-flow measurements only. Operated by the Puerto Rico Water Authority. Annual low-flow measurements. Gage-height records only; in files of the Puerto Rico Water Resources Authority. Table 2.--Data use, source of funding, and frequency of data availability for continuous-record gaging stations in Puerto Rico and the U.S. Virgin Islands, 1984 [I, North Coast Limestone project; 2, Puerto Rico Department of Natural Resources (PRDNR); 3, Puerto Rico Environmental Quality Board (PREQB); 4, Puerto Rico Department of Agriculture (PRDOA); 5, Long-term index gaging station, used for water resources review; 6, National Stream-Quality Accounting Network (NASQAN) Station; 7, Rio Grande de Loiza water-supply project; 8, Puerto Rico Aqueduct and Sewer Authority (PRASA); 9, U.S. Corps of Engineers (USCOE); 10, Sediment transport in Rio Grande de Loiza; 11, El Yunque watershed project; 12, Center of Energy and Environmental Research (CEER); 13, Pollution network; 14, G.W. Lajas Valley; 15, Puerto Rico Industrial Development Corporation (PRIDCO); 16, U.S. Virgin Islands Department of Public Works (VIDPW); A, annual; P, periodic; T, telemetry; *, applies to this category; OFA, other federal agencies] Re- gional Hydro- Station hydro- logic number logy systems 50010600 * 50011200 * 50011400 * 50014800 * 50015700 * 50027750 50028000 * 5 50028400 50031200 * 50035000 * 50038100 * 5 50038320 * 50039500 * 5 50043000 * 5 50046000 50050900 * 50051150 * 50051180 * 50051310 * 50053050 * 50055000 * 5 50055650 * 50056400 * 50056900 * 50057000 * 5 50061800 * 50063440 * 50063500 * 50063800 * 50065500 * Data use Planning and design 4 3 3,4 3 3 3 7 7 8,9 8,9 11 11 8 Water quality moni- toring Research 1 1 3 1 1 1 3 3 3 3,6 3 3 3 3,6 2,3,8 2,3,8 2,3,8 2,3,8 2,3,8 3,8 10 3 10 3 12 12 '~ 13 Source of funding Federal OFA Coop program program program 2 2 2 2 2 3,4 3 3,4 3 3 6 3 3 3 3 6 3 9 2,3,8 9 2,3,8 9 2,3,8 9 2,3,8 9 2,3,8 3,8 9 2,3,8 9 3,8 2,3,8 3,8 3 12 12 3 8 Fre- quency of data avail- able A A A A A A A A A A A,P A A A A A A A A A A,T A A A A A A A A A Table 2.--Data use, source of" funding, and frequency of data availability for continuous-record gaging stations in Puerto Rico and the U.S. Virgin Islands, 1984--Continued Data use Station number 50067000 50071000 50075000 50092000 50106500 00 50108000 50111500 50112500 50114000 50115000 50124200 - 50129900 50136000 50138000 50144000 50147800 50252000 50276000 50295000 50345000 Re- gional Hydro- hydro- logic logy systems * * 5 * * 5 * * * 5 * * * - 5 -- --- * * 5 5 * 5 * * * * Planning and design 8 9 4 4 4 3 9 9 3 - - - - 9 3 3 16 16 16 16 Water quality moni- toring Research 9,3 12 3, 6 3 4 4 3 3, 9 14 3 3, 6 3 Source of funding Federal OFA Coop program program program 3 3 9 12 6 3,4 4 4 3 9 3 9 3 3- 4,8, 15 9 3 3,8 6 3 16 16 16 16 Fre- quency of data avail- able A A,P A A A A A A,P A,P A A A A A A A A A A terns," including regulated systems, are designated as hydrologic system stations. They include stations used to gage diversions and return flows, and stations that are useful for defining the interaction of water systems. In Puerto Rico and the U.S. Virgin Islands, 13 continuous surface-water stations are included in this category. The bench-mark and index stations (there are none in Puerto Rico or in the U.S. Virgin Islands) are included in the hydrologic systems category because they docu- ment current and long-term conditions of the hydrologic systems that they gage. Federal Energy Regulatory Commission (FERC) stations and international gaging stations, located on significant rivers that cross national boundaries, would also be included in this category. Bench-mark stations in areas such as El Yunque and Commonwealth parks in both Puerto Rico and its is- lands of Vieques and Culebra and in the U.S. Virgin Islands would provide useful hydrologic data for the assessment of man's activities on streamflow on these islands. Legal Obligations Some stations provide records of flows for the verification or enforcement of existing treaties, com- pacts, and decrees. The legal obligation category contains only those stations that the U.S. Geological Survey is required to operate to satisfy its legal respon- sibility. There are no stations in Puerto Rico and the U.S. Virgin Islands program used for that purpose. Planning and Design Gaging stations in this category are used for the planning and design of a specific project (for example, a dam, levee, floodwall, navigation system, water-supply diversion, hydropower plant, or waste-treatment facil- ity) or group of structures. The planning and design category is limited to those stations that were instituted for such purposes and where this purpose is still valid. Currently, 29 stations in Puerto Rico and no stations in the U.S. Virgin Islands are being operated for planning and design purposes. Project Operation Gaging stations in this category are regularly used, on an ongoing basis, to assist water managers in making operational decisions such as reservoir releases, hydro- power operations, or diversions. The project-operation use generally implies that the data are routinely avail- able to the operators on a rapid-reporting basis. For projects on large streams, data may only be needed every few days. There are no stations in Puerto Rico and the U.S. Virgin Islands that are in current use for this purpose. Hydrologic Forecasts 1 Gaging stations in this category are regularly used to provide information for hydrologic forecasting. The latter includes flood forecasts for a specific river reach, or periodic (daily, weekly, monthly, or seasonal) flow- volume forecasts, which are routinely available to the forecasters on a rapid-reporting basis. On large streams, data may only be needed every few days. No stations in Puerto Rico and in the U.S. Virgin Islands are included in the hydrologic forecast category. Water-Quality Monitoring Only gaging stations where water-quality or sedi- ment-transport monitoring is being conducted, and the streamflow data contribute to the analysis, are desig- nated as water-quality monitoring sites. There are 30 such continuous-record surface-water stations, of which 29 are in Puerto Rico and 1 is in the U.S. Virgin Islands. Four of these stations are National Stream Quality Ac- counting Network (NASQAN) sites, which are part of a U.S. Geological Survey national network designed to define water-quality trends in principal streams. Research Gaging stations in this category are operated for a particular water-resource investigation. Typically, these are operated from 2 to 5 years. There are nine such stations used in support of research activities in Puerto Rico. However, hydrologic analyses are often required for estimating flow characteristics, such as low- and peak-flow frequency prediction for resource studies, and the stochastic statistics used usually require 30 or more years of continuous data to develop reliable models. Other Stations in this category provide streamflow infor- mation for recreational planning, primarily for canoeists, rafters, and fishermen. No stations in Puerto Rico or the U.S. Virgin Islands are in this category. Funding The sources of funding for the Puerto Rico and the U.S. Virgin Islands streamflow-data program are 1. Cooperative program.-Funded jointly by the U.S. Geological Survey and a non-Federal cooperating agency. Cooperating agency funds may be in the form of direct services or money. There are 48 continuous- record surface-water stations in this category with 44 in Puerto Rico and four in the U.S. Virgin Islands. 2. Other Federal Agencies (QFA) program.-- Funds that have been transferred to the U.S. Geological Survey by QFA's. There are nine QFA funded sites in Puerto Rico and none in the U.S. Virgin Islands. 3. Federal programs.-Funds that have been di- rectly allocated to the U.S. Geological Survey for the collection of streamflow or other water-related data. There are four federally funded sites in Puerto Rico and none in the U.S. Virgin Islands. In these categories, the identified sources of funding pertain only to the collec- tion of continuous-streamflow data; sources of funding for other activities, particularly collection of water- quality samples that may be carried out at the site, may not necessarily be the same as those identified in table 2. Funds for the stream-gaging in Puerto Rico and the U.S. Virgin Islands are contributed from 16 sources (head- notes in table 2). Frequency of Data Availability Frequency of data availability refers to the times at which the stream-flow data may be furnished to the users. Data can be furnished by direct-access telemetry equipment for immediate use, by periodic release of provisional data, or in publication format through the annual data reports for Puerto Rico and the U.S. Virgin Islands (Curtis and others, 1985). These three catego- ries are designated in table 2 as T, P, and A, respectively. Data for all 50 stations in the current Puerto Rico and U.S. Virgin Island program, are made available through the annual report. Data are available for one station on a real-time basis; at four stations, quarterly; and at two stations every 2 months. Conclusions Pertaining to Data Uses A review of table 2 shows that all stations have at least one use, and most of the continuous-record sur- face-water stations in Puerto Rico, and the U.S. Virgin Islands have multiple uses. Most of the stations are used continuously for accounting and hydrologic operations. Although the stations may have been established for a single purpose, the data are available for other projects. As an example, gaging stations at Quebrada Sonadora near El Verde (50063440), and Quebrada Toronja at el Verde (50063500) in Puerto Rico are research stations in the Caribbean National Forest that will probably be discontinued at the end of the project. Both stations are in a tropical rainforest area minimally affected by cul- tural activities and are located at relatively high elevations (1,230 and 876 feet, respectively). Data for such stations in tropical areas are scarce but needed for comparison with streamflow affected by cultural ac- tivities. The information from such sites can be used to evaluate environmental changes and their effects on the surface I water, ground water, and quality of water of small bjasins. There is a need to continue these sites indefinitely and to establish additional similar sites in other areas of Puerto Rico and the U.S. Virgin Islands. ALTERNATIVE METHODS OF DEVELOPING STREAMFLOW INFORMATION T ic second phase of the analyses of the stream- gaging program is to investigate alternative methods of providing daily streamflow information, instead of op- erating continuous-flow gaging stations. The objective of this )art of the analyses is to identify gaging stations where jilternative technology, such as flow routing or statistical methods, could provide accurate estimates of daily mean stream flow. There are no accuracy guide- lines for the data; therefore, judgment is required in deciding whether the accuracy of the estimated daily flows would be adequate for the intended purpose. Tie data uses at a station affect whether or not information can potentially be provided by alternative methods. For example, those stations for which flood hydrogfaphs are required in a real-time sense, such as hydrologic forecasts and project operation, are not can- didates for the alternative methods. Likewise, there might be a legal obligation to operate an actual gaging station that would preclude using alternative methods. The primary candidates for alternative methods are sta- tions that are operated upstream or downstream from other siations on the same stream. The accuracy of the estimated streamflow at these sites may be adequate if flows zre highly correlated between sites. Alternative methocs could also be employed at gaging stations in similar Islands watersheds, located in the same physiographic and climatic area. All stations in the Puerto Rico and the U.S. Virgin stream-gaging program were categorized as to their pDtential for utilization of alternative methods. Because of time limitations in this study, only the re- gression method (described below) was applied to five station 5 that best met the criteria as candidates for simu- lation. The categorization of gaging stations and the application of the specific methods are described in sub- sequent sections of this report. Hydrologic flow routing methods were not applied because there are very few pairs of stations on the same stream where they might work, and regression analysis provides similar results. Eiesirable attributes of a proposed alternative method are (1) the method needs to be computer- oriented and easy to apply; (2) the method needs to have an available interface with the WATSTORE Daily Val- ues Fil e (Hutchison, 1975); (3) the method needs to be technically sound and generally acceptable to the hydro- 10 logic community; and (4) the proposed method needs to provide a measure of the accuracy of the simulated streamflow records. The regression method has these attributes. Description of Regression Analysis Simple and multiple regression techniques can be used to estimate daily flow records. Unlike hydrologic routing, regression methods are not limited to locations where an upstream station exists on the same stream. Regression equations can be used to compute daily flows at a station (dependent variable) from measured daily flows at another station or combination of stations (independent variable). The independent variables in the regression analyses can include stations from differ- ent watersheds. The regression method is easy to apply, provides indices of accuracy, and is widely used and accepted in hydrology. The theory and assumptions of the method are described in numerous textbooks such as those by Ezekiel and Fox (1930), Draper and Smith (1966), and Kleinbaum and Kupper (1978). The application of re- gression methods to hydrologic problems is described and illustrated by Riggs (1973) and Thomas and Benson (1970). Only a brief description of the regression analy- ses is provided in this report. A linear regression model of the following form is commonly used for estimating daily mean discharges: Yj = Bo + T Bj Xj + ei (1) where Yi= daily mean discharge at station i (dependent variable); Xj= daily mean discharge(s) at n station(s) j (independent variables), these values may be lagged to approximate travel time between stations i andj; Bo and BJ = regression constant and coefficients; and ei = the random error term. The above equation is calibrated using observed values of Yi and Xj (B0 and Bj are estimated). The observed daily mean discharges can be retrieved from the WATSTORE Daily Values File (Hutchison, 1975). The values of discharge for the independent variables may be observed on the same day as discharges at the independent station or may be for previous or future days, depending on whether station j is upstream or downstream of station i. During calibration, the regres- sion constant and coefficients (B0 and Bj) are tested to determine if they are significantly different from zero. A given independent variable is retained in the regression equation only if the variable's regression coefficient is significantly different from zero. The regressions are calibrated using one period of time and verified or tested using a different period of time, to obtain a measure of the true predictive accuracy. The calibration and verification periods must be repre- sentative of the expected range of flows. The equation can be verified in two ways: (1) plotting the residuals (difference between simulated and observed discharges) against both the dependent and the independent vari- ables in the equation, and (2) plotting the simulated and observed discharges over time. These tests are intended to determine whether the linear model is appropriate or some tranformation of the variables is needed and whether there is any bias in the equation. These tests might indicate; for example, that a nonlinear regression equation is appropriate, or that the regression equation is biased in some way. The use of regression to produce a simulated re- cord at a discontinued gaging station causes the variance of this record to be less than the variance of an actual record of streamflow at the site. The reduction in vari- ance is not a problem if the only concern is deriving the best estimate of a given daily mean discharge record. If, however, the simulated discharges are to be used in additional analyses where the variance of the data are important, least-squares regression models are not ap- propriate. Hirsch (1982) discusses this problem and describes several models that preserve the variance of the original data. A two-level screening process was applied to gag- ing stations in Puerto Rico and the U.S. Virgin Islands, to evaluate the potential for use of alternative methods. The first level was based only on hydrologic considera- tions. The only concern at this level was whether it was hydrologically possible to simulate flows at a given station from information at other gages. The first-level screening was subjective; there was no attempt at that level to apply any mathematical procedures. Those sta- tions that passed the first level of screening were then screened again to determine if the simulated data would be acceptable in view of the data uses in table 2. Even if simulated data were not acceptable for the given data uses, the analyses continued. This was done under the assumption that the data uses may change in the future. Where data uses required continuation of gaging, how- ever, the result was predetermined. Although alternative methods were technically possible, they were unaccept- able given the present uses of the data and the accuracy of simulated daily values obtained for sites with the best simulated figures of daily discharges. 11 Regression Results Regression methods were applied at streamflow stations shown in table 3 that exhibited high coefficients of correlation (at least 0.85) with other stations in the initial analyses. The initial results showed that regres- sion methods would be unacceptable at many of the possible sites. Stations for which the initial correlation were not promising were eliminated from further con- sideration. Those stations with high correlations are listed in table 4. The data for the correlations were converted to logarithmic form. Formulas from these correlat ons are in logarithms (Log) to the base ten for- mat, as presented in table 4. The purpose of developing these formulas was to use them to compute synthetic daily discharge figures that could be compared to dis- charges in the Daily Values File (Hutchison, 1975). The percentage of time that the simulated streamflow is within ;5, 10, and 15 percent of actual streamflow is listed ir served c ischarges at two stations are plotted in figure 5. Table 3.~Gaging stations used as dependent variables in selected sites in Puerto Rico and the U.S. Virgin Islands [mi , square miles; Period of record, table 4. Hydrographs for simulated and ob- the recession modeling of daily streamflow at water years corsidered for the regression analysis] Station number 50031200 50035000 50038100 50071000 50114000 Station name Drainage area (mi2) Rio Grande de Manati near Morovis, PR 55.2 Rio Grande de Manati at Ciales, PR 128 Rio Grande de Manati near Manati, PR 197 Rio Fajardo near Fajardo, PR 14.9 Rio Cerrillos near Ponce, PR 17.8 Period of record 1965-84 1960-84 1970-84 1961-84 1964-84 50035000 OBSERVED 50038100 MAY JUNE juur 1984 AUG. SEPT. Figure 5.~Hydrographs for observed and simulated streamflow for sites 50035000-Rio Grande de Manati at Ciales, and 50038100-Rfo Grande de Manati at Highway 2 near Manati, Puerto Rico. MAY JUNE JULY 1984 AUG. SEPT. 12 Table 4 . --Summary of calibration for regression modeling of daily streamflow at selected gage sites in Puerto Rico and the U.S. Virgin Islands Station number and name Model Percentage Percentage Percentage Calibration of simulated of simulated of simulated period flow within flow within flow within (water years) 5 percent of 10 percent of 15 percent of observed observed observed 50031200-Rio Grande de Manati near Morovis, PR November through May-- Log Q0312 = -0.1153 + 0 0.2152 Log .8331 Log Q0350 + Q0381 .7556 Log Q0350 + Q03820 .9312 Log Q0350 .8747 Log Q03832 .6845 Log Q0350 + Q0381 18.1 18.7 17.0 17.5 51.2 1979-84 1979-84 1979-84 1979-84 1979-84 50035000-Rio Grande de Manati at Ciales, PR May through November-- Log Q0350 = -0.2472 + 1.02483 Log Q0381 25.8 18.4 59.1 1979-84 Table 4.--Summary of calibration for regression modeling of daily streamflovr at selected gage sites in Puerto Rico and the U.S. Virgin Islands--Continued Station number and name Percentage of simulated Model flow within 5 percent of observed Percentage of simulated flow within 10 percent of observed Percentage of simulated flow within 15 percent of observed Calibration period (water years) 50038100-Rio Grande de Manati at Highway 2 near Manati, PR 50071000-Rio Fajardo near Fajardo, PR November through May-- Log Q0381 = 0.3191 + 0.7404 Log Q0350 + 0.2276 Log Q0395 Log Q0381 = 0.4399 + 0.8859 Log Q0350 Log Q0381 = 0.8647 + 0.8294 Log Q0395 May through November-- Log Q0381 = 0.3248 + 0.7414 Log Q0350 0 .2117 Log Q0395 Log Q0381 = 0.4657 + 0.8736 Log Q0350 Log Q0381 = 0.8928 + 0.7692 Log Q0395 November through May-- Log Q0710 = -0.3459 + 0.8213 Log Q0638 + 0.2258 Log Q0655 + 0.3230 Log Q1150 Log Q0710 = 0.6642 + 0.2707 Log 1125 + 0.6160 Log 1150 May through November-- Log Q0710 = 0.4637 + 0.4709 Log Q1125 + 0.3936 Log Q1150 Log Q1150 5.4 .4 45. 10.5 17. 19.4 14. 1979-84 Table 4 . --Summary of calibration for regression modeling of daily streamflow at selected gage sites in Puerto Rico and the U.S. Virgin Islands--Continued Station number and name Model Percentage of simulated flow within 5 percent of observed Percentage of simulated flow within 10 percent of observed Percentage of simulated flow within 15 percent of observed Calibration period (water years) 50114000-Rio Cerrillos near Ponce, PR November through May-- Log Q1140 = 0.3183 + 0.4412 Log Q1125 + 0.4805 Log Q1150 + 0.0389 Log Q0920 Log Q1140 = 0.3587 + 0.4416 Log Q1125 + 0.4976 Log Q1150 22.4 42.1 55.1 1984-84 May through November Log Q1140 = 0.4202 + 0.4740 Log Q1125 + 13.6 0.3815 Log Q1150 + 0.0341 Log Q0920 Log Q1140 = 0.4657 + 0.4709 Log Q1125 + 14.8 0.3936 Log Q1150 45.5 1979-84 Most of the combinations of stations tested pro- duced unacceptable results. The most common reason for poor correlation and regression results in the Puerto Rico and the U.S. Virgin Islands probably relates to orographic effects. The central mountain range of Puerto Rico induces higher precipitation along the northern coast, and creates a rain shadow along the southern coast. Also, along the northwest coast of Puerto Rico, streamflow relations are effected by a coastal karst limestone belt where there is a substantial exchange of water between the streams and the aquifer. Intense rainfall associated with tropical storms have no typical pattern and can cause extensive flooding in any part of the islands, even in areas with low average an- nual rainfall. On the south coast of Puerto Rico, many streams lose water to the alluvial aquifer and correlation of flows between stream sites generally is poor. On the offshore islands of Puerto Rico (Vieques, Culebra, and Mona) and in the U.S. Virgin Islands, the amount of surface water data collected is not adequate for analyzing mean- ingful correlations. However, streamflow conditions similar to Puerto Rico probably exist in the smaller islands on a reduced scale, because similar charac- teristics in geography, geology, and weather occur in the islands of Culebra, Vieques, St. Thomas, St. John, and St. Croix. However, there are almost no data available for statistical evaluations of surface-water hydrology in these areas. The results of regression analyses for selected combinations of streamflow sites are summarized in table 4. The differences between observed and simu- lated streamflows for discharges that are within 5, 10, and 15 percent of actual flow are given in percentage of simulated flows. Summary of Second Phase of Analysis For the purposes of this study, acceptable accuracy is defined as 90 percent or more of the regression esti- mated streamflows being within 15 percent of the measured flow. None of the stations studied were within the range of acceptable accuracy for the applica- tion of alternative methods. At only two stations, Rio Grande de Manati at Ciales (50035000) and Rio Grande de Manati at Highway 2 near Manati, Puerto Rico (50038100), were the regression models able to predict flows close to acceptable limits (fig. 5). From Novem- ber through May, estimated flows at the two gages were within 15 percent of the measured flows 65 and 71 percent of the time, respectively. From May to Novem- ber, estimates were within 15 percent of measured flows 59 percent of the time at site 50035000, and 80 percent of the time at site 50038100. For periods of missing record, the regression procedures may be useful for estimating discharge record, but further verification of the calibrated model is needed. Simulation of streamflow in Puerto Rico and the U.S. Virgin Islands may be a suitable alternative in those few instances where the inaccuracies of simulated infor- mation! is acceptable, or where data for periods of missing record are needed. In these instances, the stream] low computed from a model should be compared with 01 her methods, and the best results used on the basis o* experience and judgment. COST-EFFECTIVE RESOURCE ALLOCATION Discussion of the Model A set of techniques called K-CERA (Kalman filter- ing for Cost-Effective Resource Allocation) was develo )ed by Moss and Gilroy (1980) to study the cost- effectiveness of networks of stream gages. The original application of the technique was in the analysis of a streamflow network operated to determine water con- sumption in the Lower Colorado River Basin (Moss and Gilroy, 1980). Because of the water-balance nature of that study, minimization of the total variance of errors of estimation of annual mean discharges was chosen as the measure of effectiveness of the network. This total vari- ance is defined as the sum of the variances of errors of mean annual discharge at each site in the network. This measure of effectiveness is utilized on the large rivers and streams where discharge and, consequently, poten- tial erirors (in cubic feet per second) are greatest. Although this measure may be acceptable for a water- balanck network, considering the many uses of data collected by the U.S. Geological Survey, concentration of effort on large rivers and streams is undesirable and inappropriate. Tihe original version of K-CERA was, therefore, altered to include, as optional measures of effectiveness, the sufris of the variances of errors in estimating the following streamflow variables: annual mean dis- charge^ in cubic feet per second; annual mean discharge, in percent; average instantaneous discharge, in cubic feet per second; or average instantaneous discharge, in percent (Fontaine and others, 1984). The use of percent- age errors effectively assigns equal weight to large and small streams. In addition, instantaneous discharge is the basic variable from which all other streamflow data are derived. For these reasons, this study used the K- CERA techniques with the sums of the variances of the percentage errors of the instantaneous discharges at con- tinuously gaged sites as the measure of effectiveness of the dala-collection activity. 16 The original version of K-CERA did not account for errors contributed by missing stage or other correla- tive data that are used to compute streamflow. Missing correlative data are more likely to increase with fewer service visits to a stream gage. A procedure for dealing with the missing record has been developed (Fontaine and others, 1984) and was incorporated into this study. Brief descriptions of the mathematical program used to minimize the total error variance of the data- collection activity for given budgets and of the application of Kalman filtering (Gelb, 1974) used to determine the accuracy of a stream-gaging record are presented by Fontaine and others (1984). For more detail on either the theory or the applications of the K-CERA model, see Moss and Gilroy (1980) and Gilroy and Moss (1981). Description of Mathematical Program The K-CERA methodology considers the cost ef- fectiveness of a network of stream gages. This is determined by the total variance uncertainty, in either the annual mean discharge or the instantaneous dis- charge at all sites involved in the stream-gaging program, and by the cost of achieving that uncertainty. For the present study, the measure of uncertainty at each site was taken to be the variance of the percent of error in the instantaneous discharge. (See Fontaine and oth- ers, 1984). The first step in estimating a site-specific uncer- tainty function (a relation between variance and number of visits to the site) is to determine a logarithmic dis- charge rating curve relating instantaneous discharge to gage height for each station involved in the stream- gaging program. The sequence of discharge residuals (in logarithmic units) from this rating (the discharge measurement minus the rating value) is analyzed as a time series. The second step is to fit a lag-one-day autoregres- sive model to this temporal sequence of discharge residuals. The three parameters obtained from this analysis are: (1) the measurement variance - a measure of the variability of a current-meter measurement at the site, (2) the process variance - a measure of the variabil- ity about the rating in the absence of measurement error, and (3) the lag-one-day autocorrelation coefficient (RHD) - a measure of the memory in the sequence of discharge residuals. These three parameters determine the variance, Vf, of the percentage error in the estima- tion of instantaneous discharge whenever the gage height data at the site is available for use in the rating equation. Kalman filter theory, along with the assump- tion of a first-order Markovian process, is used to determine this variance, Vf, as a function of the number of discharge measurements per year (Moss and Gilroy, 1980). If the gage height data at the site is not available, the discharge may be estimated by correlation with nearby sites. The correlation coefficient shows the lin- ear relations ( pc ) between streamflows with seasonal trends removed (detrended) at the site of interest and detrended streamflows at the other sites. The fraction of the variance of the streamflow at the primary site that is *y explained by data from other sites is p£ . The coefficient of variation of daily streamflows at the primary site, in percent is taken to be 365 Cv = 100 (2) where CTI is the square root of the variance of daily discharges for the ith day of the year and joi is the expected value of discharge on the ith day of the year. Thus the variance, Vr, of the percentage error during periods of reconstructed streamflow records is and the variance, Ve, of the percentage error during periods when neither primary correlative data nor recon- structed streamflow from nearby sites is available, is Ve = Cv2 . (4) If the fraction of time when primary correlative data are available is denoted by e f and the fraction of time when secondary streamflow data are available for reconstruction is er and ee = 1 -£f -tr , the total per- centage error variance, VT, is given by Vr + EeVe. (5) The fraction uptime, e f, of the primary recorders at the site of interest is modeled by a truncated negative exponential probability distribution, which depends on T, the average time between service visits, and the recipro- cal of the average time to failure when no visits are made to the site. The fraction concurrent downtime of the primary and secondary site is found by assuming independence of downtime between sites (Fontaine and others 1984). The variance, VT, given by equation (5), which is a function of the number of visits to each site, is deter- mined in the stream-gaging network. For a given site visitation strategy, the sum of the variance, VT, over all sites is taken as the measure of the uncertainty of the network. The variance, VT, given by equation (5) is one measure of the spread of a probability density function, 17 gT. The function, gT, is a mixture of three probability density functions - gf, gr, and ge - each of which is assumed to be a normal, or Gaussian, probability den- sity with a mean equal to zero and the variance, Vf, Vr, and Ve, respectively. Such a mixture is denoted by gT = efgf+e r gr + e e ge. (6) In general, the density gT will not be a Gaussian probability density and the interval from the negative square root of VT to the positive square root of VT may include much more than 68.3 percent of the errors. This will occur because, while e e may be very small, Ve may be extremely large. Actually, this standard error interval may include up to 99 percent of the errors. To assist in interpreting the results of the analyses, a new parameter, Equivalent Gaussian Spread (EGS), was introduced by Fontaine and others (1984). The parameter EGS specifies the range in terms of equal positive and negative logarithmic units from the mean that would encompass errors with the same a priori probability as would a Gaussian distribution with a standard deviation equal to EGS; in other words, the range from -1 EGS to +1 EGS contains about two-thirds of the errors. For Gaussian distributions of logarithmic errors, EGS and standard error are equivalent. EGS is reported herein in units of percentage and an approxi- mate interpretation of EGS is "two-thirds of the errors in instantaneous streamflow data will be within plus or minus EGS percent of the reported value." Note that the value of EGS is always less than or equal to the square root of VT and ordinarily is closer to Vf, which is the measure of uncertainty applicable during periods of no missing record the greatest portion of the time. The cost portion of the input to the K-CERA meth- odology consists of determining practical routes to visit the stations in the network, the costs of each route, the cost of a visit to each station, the fixed cost of each station, and the overhead associated with the stream- gaging program. The next step is to determine the frequency of visits to each of the gages for periodic maintenance, rejuvenation of recording equipment, or required peri- odic sampling of water-quality data. All these costs, routes, constraints, and uncertainty functions are then used in an iterative search program to determine the number of times that each route is used during a year. The objectives of the program are the following: (1) the budget for the network should not be exceeded, (2) at least the minimum number of visits to each station should be made, and (3) the total uncer- tainty in the network should be minimized. This allocation of the predefined budget among the stream gages is taken to be the optimal solution to the problem of cost-effective resource allocation. Due to the high dimensionality and non-linearity of the problem, the optimal solution may really be "near optimal." (See Moss aid Gilroy, 1980, or Fontaine and others, 1984, if greater detail is desired.) Application of the Model in Puerto Rico and the U.S. Virgin Islands The operation of the existing network was ana- lyzed by the K-CERA techniques to consider alternative operative funding and collection of field data. The re- sults of this phase of the analysis are described in the remainder of this section. The model assumes the un- certainty of discharge records at a given gage to be derived from three sources: (1) errors that result be- cause I he stage-discharge relationship is not perfect (applies when the gage is operating), (2) errors in recon- structing records based on data from another gage when the primary gage is not operating, and (3) errors inherent in estimated discharge when the gage is not operating and no correlative data are available to aid in record reconstruction. These uncertainties are measured as the variance of the percentage errors in instantaneous dis- charge. The proportion of time that each source of error applies depends on the frequency at which the equip- ment is serviced. Definition of Variance When Station is Operating Tie model used in this analysis assumes that the difference (residual) between instantaneous discharge (measurement discharge) and rating curve discharge is a continuous first-order Markovian process. The underly- ing probability distribution is assumed to be Gaussian (normal) with a zero mean and the variance of this distribution is referred to as process variance. Because the totyl variance of the residuals includes error in the measurements, the process variance is defined as the total variance of the residuals minus the measurement error variance. Computation of the error variance about the stage- discha^ge relation was performed in three steps. A long-tejrm rating was defined, generally based on meas- urements made during three or more water years, and deviations (residuals) of the measured discharges from the rating discharge were determined. A time-series analysis of these residuals defined the 1-day lag (lag- one) autocorrelation coefficient and the process variance required by the K-CERA model. Finally, the error vari- ance h: defined within the model as a function of the lag-on 5 autocorrelation coefficient, the process and measurement variances, and the frequency of discharge measurements. 18 Long-term applicable rating curves were defined for each station used in the evaluation. In some cases, existing ratings adequately defined the long-term condi- tion and were used in the analysis. At a majority of gages, however, this was not the case, and new rating were developed. The rating function used was of the following form: LQM = B1 + B3 (LOG(GHT - B2)), (7) where LQM = the logarithmic (base e) value of the measured discharge, and GHT = the recorded gage height corresponding to the measured discharge. The constants Bl, B2, and B3 were determined by a graphical fit of straight line segments as illustrated in figure 6. The residuals about the long-term rating for individual gages defined the total variance. A review of discharge measurements made in Puerto Rico and the U.S. Virgin Islands indicated that the average standard error of open-water measurements was about 4 percent. The measurement variance for all gages, therefore, was defined as equal to the square of the 4 percent standard error. The process variance required in the model is, thus, the variance of the residuals about the long-term rating, minus the constant measurement variance. Time-series analyses of the process variance were used to compute sample estimates of the lag-one auto- correlation coefficient; this coefficient is required to compute the variance during the time when the re- corders are functioning. STATION NUMBER 50138000 MEAN OF RESIDUALS= -0.0035 VARIANCE OF RESIDUALS= 0.0096 RATIO MEAN SQUARE TO VARIANCE= 0.0012 EXPLANATION: UTINC_______ O MEASUREMOftS DISCHARGE. IN CUBIC FEET PER SECOND The values of lag-one autocorrelation coefficient, measurement and process variances, length of season (365 days), and data from the definition of missing record probabilities (6 percent - an average of missing record for all sites used in the computations) are used jointly to define uncertainty functions for each gaging station. The uncertainty functions give the relation be- tween error variance and the number of visits (12 and 6 per year), assuming a measurement is made at each visit Statistics of the uncertainty curves are given in table 5, and examples of typical uncertainty functions are shown in figure 7. The uncertainty curve for station 50345000 is representative of stations with a large process vari- ance and that for station 50031200 represents stations with relatively small process variance. The uncertainty, in percent standard error of estimate for the number of visits per year (12), is 48 and 15 percent for stations 50345000 and 50031200, respectively, as shown in fig- ure 7. A total of 16 of the 50 stations in Puerto Rico were excluded from the analysis because the records were too short and the number of discharge measurements was insufficient to meet the assumptions of the model. These stations are marked by an asterisk in table 1 and are used as null sites in the final analysis so they will be accounted for in the cost and route computation analy- sis. Definition of Variance When Record is Missing When stage record is missing at a gaging station, the model assumes that the discharge record is either reconstructed using correlation with another gage or estimated from historical discharge for that period. STATION NUMBER 50031200 10 20 30 40 NUMBER OF VISITS AND MEASUREMENTS Figure 6.~Rating curve plotted on logarithmic axes using straight-line segments. Figure 7.~Typical uncertainty function for instantaneous discharge and number of visits for selected stations in Puerto Rico and the U.S. Virgin Islands. 19 Table 5.--Summary of the autocovariance analysis Number of Station measurements number analyzed RHO (1-day autocorrelation coefficient) Measurement Process variance variance (log base e)**2] [(log base e)**2] 50027750 50028000 50028400 50031200 50035000 50038100 50038320 50039500 50043000 50046000 50050900 50051310 50055000 50056400 50057000 50061800 50063800 50065500 50067000 50071000 50075000 50092000 50112500 50114000 50115000 50124200 50136000 50138000 50144000 50147800 50252000 50276000 50295000 50345000 28 208 34 157 256 179 67 67 26 68 64 25 59 116 336 27 181 31 65 94 63 78 50 38 66 25 57 47 51 117 21 35 23 18 0.989 0.995 0.569 0.988 0.991 0.978 0.992 0.982 0.988 0.972 0.981 0.994 0.976 0.991 0.997 0.784 0.986 0.987 0.972 0.995 0.937 0.975 0.975 0.972 0.994 0.986 0.979 0.986 0.978 0.989 0.999 0.994 0.540 0.540 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.001599 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.000302 0.00879 0.00879 0.00052 0.00164 0.01300 0.00554 0.02147 0.01417 0.02176 0.01852 0.00788 0.04398 0.00385 0.00962 0.22240 0.00275 0.00820 0.02725 0.01198 0.05174 0.00134 0.04425 0.09350 0.02026 0.09684 0.07405 0.00724 0.00912 0.00259 0.00859 0.15640 0.25700 0.03175 0.03175 20 Fontaine and others (1984, p. 24) indicate that the frac- tion of time a record must be either reconstructed or estimated can be defined by a single parameter in a probability distribution of equipment failure times. The reciprocal of the parameter represents the average time to the average of all failure times since the last service visit. The average time to failure varies from site to site depending on the type of equipment at the site, the exposure to natural elements, such as floods and vandal- ism. Data collected in Puerto Rico and in the U.S. Virgin Islands in recent years were reviewed to define the average time to failure for recording equipment and stage-sensing devices. In Puerto Rico, stream-gaging stations were examined 12 times per year, except for one station. Visits to the latter station and the four stations in the U.S. Virgin Islands were made six times per year. The average amount of missing record for stations was 6 percent. This average was computed over an 8-month (243-day) period for stations visited on a monthly basis and over a 16-month (486-day) period for stations vis- ited on a bi-monthly basis. The model defines the uncertainty as the sum of the multiples of the fraction of time each error source (rating, reconstruction, or estimation) is applicable and the variance of the error source. The variance associated with reconstruction and estimation of a discharge record is a function of the coefficient of cross correlation with the stations used in reconstruction and the coefficient of variation (Cv) of daily discharges at the station. Daily streamflows for the last 26 water years were used to define seasonally averaged coefficients of variation for each station. In addition, cross-correlation coefficients (with seasonal trends removed) were defined for various combinations with other stations. In current practice, many different sources of in- formation are used to reconstruct periods of missing record. These sources include, but are not limited to, recorded ranges in stage (for graphic recorders with clock stoppage), known discharges on adjacent days, recession analyses, observer's staff-gage readings, weather records, highwater-mark elevations, and com- parisons with nearby stations. However, most of these techniques are unique to a given station or to a specific period of missing record. Using all the information available, short periods (several days) of missing record usually can be reconstructed quite accurately. Even longer periods (more than a month) of missing record can be reconstructed with reasonable accuracy if ob- server's readings are available. If, however, none of these data are available, reconstruction of long periods of record can be subject to large errors. The present study could not reasonably quantify the uncertainty as- sociated with all the possible methods of reconstructing missing record at the individual sites. Historically, operating procedures have caused most periods of missing record to be measured in days rather than months. Given the low cross correlations and the relatively high variability of flow that usually occurs in Puerto Rico and the U.S. Virgin Islands, the model may overstate the uncertainty associated with short periods of missing record. For two stations a cross-correlation coefficient was not computed due to short or poor records, and a cross-correlation coefficient of 0.50 was arbitrarily used. For two stations cross- correlation coefficients less than 0.50 were computed and used. In reconstructing records, the cross correlation coefficient was, therefore, used as a surro- gate for the knowledge of basin response that remains unquantified in the present model. This assumption is believed to be reasonable for short periods of missing record; it may cause the uncertainty to be overstated for long periods of missing record. Uncertainty functions were defined for 34 of the 50 stations operated in the streamflow programs in Puerto Rico and the U.S. Virgin Islands. Statistics used to define those uncertainty functions are given in table 6. Discussion of Routes and Costs Although there are only 50 continuous surface- water stations in the network, a crest-stage gage (operated to record peak stages), ground-water observa- tion wells, and quality of water monitors are serviced on the same field trips. The operating budgets for these other types of stations are not included in the surface- water budget being analyzed; however, the investigation could not ignore the additional mileage required to in- clude these stations on field trips. These stations were, therefore, added to the 50 continuous surface-water sta- tions to define the mileage associated with practical operating routes. These added stations acted as null stations in the analyses because there were no uncer- tainty functions or annual operating costs defined for them. Routes were defined for a total of 76 stations, including the null stations as listed in table 7. Uncer- tainty functions could not be defined for 16 of the 50 continuous surface-water stations. These 16 stations were treated like null stations except that all operating costs were included in the analyses. Minimum visit constraints were defined for each of the 76 stations prior to defining the practical service routes. Minimum visits are dependent on the types of equipment and uses of the data. For example, water- quality samples generally are required on a monthly basis, so those stations where samples are collected must be visited at least once a month (or 12 times during 21 Table 6 . --Statistics of record recountruction [Cv, coefficient of variation; CROSS, Cross Correlation Coefficients] Station number 50027750 50028000 50028400 50031200 50035000 50038100 50038320 50039500 50043000 50046000 50050900 50051310 50055000 50056400 50057000 50061800 50063800 50065500 50067000 50071000 50075000 50092000 50112500 50114000 50115000 50124200 50136000 50138000 50144000 50147800 50252000 50276000 50295000 50345000 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 Cv .780 .910 .580 .220 .390 .150 .340 .150 .960 .620 .940 .880 .420 .300 .580 .470 .400 .990 .940 .330 .740 .330 .050 .010 .190 .710 .930 .070 .830 .140 .100 .100 .160 .100 CROSS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .360 .690 .680 .910 .890 .890 .830 .780 .790 .770 .740 .800 .830 .790 .820 .730 .800 .790 .690 .850 .640 .770 .780 .850 .790 .520 .680 .700 .760 .540 .500 .410 .610 .500 Stations used in record reconstruction 50038100 50144000 50028000 50035000 50031200 50035000 50039500 50038100 50055000 50038100 50055000 50050900 50057000 50057000 50055000 50063800 50061800 50061800 50071000 50063800 50065500 50050900 50114000 50112500 50114000 50115000 50138000 50136000 50147800 50144000 50276000 50252000 50252000 50276000 5C 5( 5C 5C 5C 5C 5C 5C 5C 5C 5C 5C 5C 5ti 5(j 5C 5C 5C 5C 5( 5( 5( 028400 031200 035000 (038320 )038100 (039500 '031200 '046000 '046000 '043000 (056400 1056400 1050900 )061800 )056400 )067000 1075000 063800 1063800 1065500 1056400 1051310 5^)115000 50092000 5(1)114000 50114000 50144000 50136000 50138000 5( 5( 345000 345000 50035000 50035000 50038100 50038100 50039500 50027750 50046000 50035000 50057000 50039500 50043000 50055000 50056400 50075000 50061800 50071000 50057000 50071000 50065500 50075000 50071000 50071000 50092000 50124200 50112500 50112500 50147000 50028000 50028000 22 Table 7.--Summary of the routes that may be used to visit stations in Puerto Rico and the U.S. Virgin Islands [C, crest-gage stage-discharge station; Q, water-quality monitor; U, undefined uncertainty curve for this station, null station; W, ground-water observation well] Route IS 2S 3A 4S 5A 6A 7A 8S 9S 10S US 12S 13S 14S 15S 16S 17S 18S 19S 20S 21A 22S 23A 24A 25S 26A 27S 28A 29S 30S 31S 32S 33A 34S 35S 36S 37S 38S 39S 40A 41S 42S 43S 44S 45S Stations serviced on the route-- (third to the eighth digit of station number used) 027750 035000 031200 039500 061800 U063500 067000 039500 031200 038320 046000 035000 031200 061800 U063440 065500 U063440 065500 061800 067000 U055650 056400 056400 U056900 055000 055000 U053050 U051150 U053050 056400 043000 U051150 050900 U051150 050900 051310 050900 U051150 U051180 092000 043000 043000 U106500 U106500 138000 U010600 144000 028400 W70 W135 038320 046000 W70 U063440 065500 075000 W70 035000 039500 W70 W70 039500 W70 039500 W70 U063440 U063500 U063500 067000 U063500 075000 075000 075000 071000 071000 U055650 W96 U056900 057000 U056900 057000 055000 U051180 U053050 U051180 071000 U053050 U053050 051310 051310 U051150 055000 055000 055000 055000 W6 W96 W6 W87 U106500 W87 U108000 W87 U108000 U111500 114000 115000 124200 U129900 136000 W87 W132 W141 W143 C114400 C115900 U011200 U011400 U014800 U015700 027750 028000 028400 147800 W135 23 Table 7.--Summary of the routes that may be used to visit stations In Puerto Rico and the U.S. Virgin Islands Continued Route 46S 47S 48S 49A 50A 51A 52A 53S 54A 55S 56S 57S 58A 59S 60S 61A 62A 63B 64B 65B 66B 67B 68B 69B 70B 71B 72B 73B 74B 75B 76B 77B 78B 79S SOS 81S 82S 83S 84S 85S 86S 87S 88A Stations U051150 U051150 U108000 U010600 W70 U010600 W135 U108000 W143 252000 027750 039500 038320 035000 031200 U055650 043000 U106500 U106500 138000 U010600 144000 U011400 028000 031200 038320 039500 043000 046000 055000 063800 071000 092000 U106500 114000 115000 138000 144000 U010600 U011200 U011400 U014800 U015700 027750 028000 028400 031200 035000 serviced on the route-- (third to the eighth digit of station number used) U051180 051310 U051180 055000 W6 W87 W96 U011200 U014800 U015700 027750 028400 147800 W135 U011200 U014800 U015700 027750 028400 144000 147800 W70 U111500 124200 U129900 136000 W87 W132 W141 C114400 C115900 276000 295000 345000 028400 046000 039500 039500 039500 056400 U106500 U108000 U108000 U111500 114000 115000 124200 U129900 136000 U011200 U011400 U014800 U015700 027750 028000 028400 147800 Q011400 Q028000 Q031200 Q038320 Q039500 Q043000 Q046000 Q055000 Q063800 Q071000 Q092000 Q106500 Q114000 Q115000 Q138000 Q144000 Table 7 .-- Summary of the routes that may be used to visit stations in Puerto Rico and the U.S. Virgin Islands--Continued Route 89A 90S 91S 92A 93S 94S 95S 96S 97S 98S 99S 100S 101S 102S 103S 104S 105S 106S 107S 108S 109S 110S HIS 112A 113S 114S 115S 116A 117S 118S 119S 120S 121S 122S 123S 124S 125S 126S 127S 128S Stations serviced on the route-- (third to the eighth digit of station number used) 038100 038320 039500 043000 046000 050900 U051150 U051180 051310 U053050 055000 U055650 056400 U056900 057000 061800 U063440 U063500 063800 065500 067000 071000 075000 092000 U106500 U108000 U111500 112500 114000 115000 124200 U129900 136000 138000 144000 147800 252000 276000 295000 345000 25 the water year). It is estimated that visits to each gage are required about every other month, just to maintain the equipment. Therefore, unless a more stringent re- quirement exists, a minimum of six visits during the 12-month period are specified for all gages, except for the water-quality sampling sites. Practical routes to service the 76 stations were determined after consultation with personnel respon- sible for maintaining the stations and with consideration of the uncertainty functions and minimum visit require- ments. A total of 128 routes were selected to service all the stream gages in Puerto Rico and in the U.S. Virgin Islands. These routes included all possible combina- tions that describe the current operating practice, alternatives that were under consideration as future pos- sibilities, routes that visited certain key stations, and combinations that grouped proximate gages where the levels of uncertainty indicated more frequent visits might be useful. The costs associated with the practical routes are divided into three categories. Those categories are fixed costs, visit costs, and route costs and are defined in the following paragraphs. Overhead is, of course, added to the total of these costs. Fixed costs typically include charges for equip- ment rental, batteries, electricity, data processing and storage, maintenance, and miscellaneous supplies, in addition to supervisory charges and the costs of comput- ing the record. Average values for Puerto Rico and the U.S. Virgin Islands generally were applied to individual stations. However, costs of record computation and su- pervision form a large percentage of the cost at each gaging station and can vary widely. These, as well as unusual equipment costs, were determined on a station- by-station basis from past experience. Visit costs are those associated with paying the hydrographer for the time actually spent at a station making a discharge measurement. These costs vary from station to station, depending on the difficulty of the measurement and the size of the channel. Average visit times were estimated for each station based on historical operations. This time was then multiplied by the aver- age hourly salary of the hydrographers in Puerto Rico and the U.S. Virgin Islands to determine total visit costs. Route costs include vehicle use, time spent servic- ing equipment, cost of the hydrographer's time while in transit, and any travel expenses. The fixed costs were computed on an annual basis, but the visit and route costs are only applied when a trip is made. Results The "Traveling Hydrographer Program" uses the uncertainty functions along with the appropriate cost data, route definitions, and minimum visit constraints to optimize the operation of the stream-gaging program. The objective function in the optimization process is the sum of the variances of the errors of instantaneous dis- charge (in percent) for the entire gaging station network. The current practices were simulated to define the total uncertainty associated with present practice. This was done by restricting the specific routes and number of visits to each stream gage to those now being used. This was done only to compute the standard errors of present practice; no optimization was done. The restric- tions were then released and the model was allowed to define optimal visit schedules for the current budget. The optimization procedure was repeated for other pos- sible budgets. The results for both the present operation and the optimal solutions are shown in figure 8 and presented in table 8. The analysis was repeated for each budget under the assumption that no stage record was lost. Those results, labeled "Without missing record" in figure 8, show the average standard errors of estimate for instan- taneous discharge attainable if perfectly reliable systems were available to measure and record stage for the pre- sent and other budgets. It also shows the error (or accuracy) that occurs when the gages are operating property, which is about 94 percent of the time. Assumptions made in the model need to be kept in mind when interpreting these results. Residuals about the ratings for 34 of the 50 stations in the surface-water networc were judged to follow the first-order Mark- ovian process assumed in the model. The remaining 16 Current practice With missing record Without missing record 300 350 400 450 500 BUDGET. IN THOUSANDS OF DOLLARS Figure $.~Average standard error per gaging station as a function of budget. 26 Table 8.- -Selected results of K-CERA analysis given In standard error of Instantaneous discharge. In percent; equivalent Oausslan Spread, In brackets; and number of visits per year to site. In parentheses Budget , Station number Average per station 50027750 50028000 50028400 50031200 50035000 50038100 50038320 50039500 50043000 50046000 Current operations 310 296 20.6 12.8 [5.3] (12) 16.9 [5.7] (12) 11.5 [5.5] (12) 12.9 [3.9] (12) 17.5 [9.1] (12) 15.3 [9.2] (12) 20.8 [11.0] (12) 21.3 [13.3] (12) 31.8 [13.6] (12) 30.6 [19.0] (12) 21.1 17.9 [7.6] (6) 16.9 [5.7] (12) 15.2 [6.0] (6) 15.6 [4.9] (8) 21.2 [11.5] (8) 15.3 [9.2] (12) 22.7 [12.2] (10) 19.8 [12.2] (14) 27.7 [11.5] (16) 26.7 [16.4] (16) 300 20.3 17.9 [7.6] (6) 16.9 [5.7] (12) 15.2 [6.0] (6) 14.8 [4.6] (9) 20.1 [10.7] (9) 15.3 [9.2] (12) 21.7 [11.5] (ID 18.6 [11.4] (16) 26.9 [11.2] (17) 25.3 [15.4] (18) in thousands of 1984 dollars 310 18.8 16.6 [7.0] (7) 16.9 [5.7] (12) 14.3 [5.9] (7) 13.4 [4.1] (11) 18.3 [9.5] (11) 15.3 [9.2] (12) 18.7 [9.7] (15) 16.7 [10.1] (20) 23.2 [9.4] (23) 22.0 [13.3] (24) 320 18.1 15.6 [6.5] (8) 18.4 [6.4] (10) 13.6 [5.8] (8) 12.4 [3.8] (13) 17.5 [9.1] (12) 15.3 [9.2] (12) 18.1 [9.4] (16) 15.6 [9.3] (23) 22.3 [9.0] (25) 21.2 [12.7] (26) 340 16.2 14.0 [5.8] (10) 15.7 [5.3] (14) 12.4 [5.6] (10) 10.6 [3.2] (18) 14.8 [7.5] (17) 13.4 [7.9] (16) 15.2 [7.7] (23) 13>5 [8.0] (31) 19.2 [7.6] (34) 17.6 [10.4] (38) 350 15.6 12.8 [5.3] (12) 15.2 [5.0] (15) 11.5 [5.5] (12) 10.3 [3.1] (19) 14.1 [7.1] (19) 13.0 [7.7] (17) 14.6 [7.3] (25) 12.9 [7.7] (34) 18.7 [7.5] (36) 16.7 [9.9] (42) 400 13.6 10.8 [4.4] (17) 12.4 [4.0] (23) 10.1 [5.3] (17) 8.4 [2.5] (29) 11.7 [5.8] (28) 10.4 [6.0] (27) 12.4 [6.2] (35) 11.0 [6.4] (47) 15.4 [6.2] (53) 14.1 [8.3] (59) 450 12.4 9.5 [3.9] (22) 11.0 [3.6] (29) 9.2 [9.2] (22) 7.5 [2.2] (37) 10.8 [5.4] (33) 9.6 [5.6] (32) 10.8 [5.4] (46) 10.1 [5.9] (56) 13.8 [5.5] (67) 12.7 [7.4] (74) 500 11.3 8.6 [3.5] (27) 10.1 [3.3] (35) 8.5 [5.1] (27) 7.1 [2.1] (41) 9.9 [4.9] (39) 8.5 [4.9] (41) 10.3 [5.1] (51) 9.1 [5.3] (70) 12.6 [5.1] (80) 11.7 [6.8] (87) 27 Table 8. --Selected results of K-CERA analysis given in standard error of Instantaneous discharge, in percent equivalent Gauss!an Spread, In brackets; and number of visits per year to site, In parentheses Continued Budget , in Station number 50050900 50051310 50055000 50056400 50057000 50061800 50063800 50065500 50067000 50071000 50075000 50092000 Current operations 310 296 18.0 [10.2] (12) 17.8 [13.4] (12) 20.7 [8.1] (12) 20.8 [7.9] (12) 29.2 [20.9] (12) 26.9 [12.2] (12) 23.4 [12.4] (12) 20.5 [15.6] (12) 21.9 [14.9] (12) 20.9 [13.2] (12) 15.2 [6.8] (12) 32.4 [27.2] (12) 20.6 [11.9] (9) 19.4 [14.8] (10) 21.6 [8.4] (11) 21.6 [8.3] (ID 25.4 [17.8] (16) 26.1 [12.0] (13) 20.5 [10.7] (8) 21.4 [16.3] (11) 22.8 [15.6] (11) 21.8 [13.9] (11) 18.2 [7.9] (8) 32.4 [27.2] (12) 300 18.8 [10.7] (11) 18.5 [14.0] (11) 20.7 [8.1] (12) 20.8 [7.9] (12) 24.0 [16.7] (18) 25.3 [11.9] (14) 19.4 [10.1] (9) 20.5 [15.6] (12) 21.1 [14.4] (13) 20.9 [13.2] (12) 17.3 [7.6] (9) 30.2 [25.1] (14) thousands of 1984 dollars 310 16.8 [9.4] (14) 16.5 [12.2] (14) 18.1 [7.0] (16) 18.1 [6.7] (16) 21.8 [15.0] (22) 22.8 [11-4] (18) 16.8 [8.7] (12) 17.4 [12.8] (17) 18.6 [12.6] 17) 18.2 [11.3] (16) 15.2 [6.8] ( 12) 26.1 [21.4] (19) 320 340 15.7 13.5 [8.8] [7.4] (16) (22) 16.5 13.3 [12.2] [9.6] (14) 17.6 [6.8] (17) (22) 14.6 [5.5] (25) 17.6 14.9 [6.5] [5.5] (17) (24) 20.4 17.4 [14.0] [11.8] (25) 22.4 [11.3] (19) 16.8 [8.7] (12) (35) 18.9 [10.4] (29) 13.8 [7.1] (18) 17.4 14.1 [12.8] [10.2] (17) (26) 18.6 15.5 [12.6] [10.3] (17) 18.2 [11.3] (16) 15.2 [6.8] (12) 25.5; [20.8] (20) (25) 15.3 [9.3] (23) 12.7 [5.9] (18) 21.3 [17.1] (29) 350 12.7 [6.9] (25) 13.0 [9.4] (23) 14.0 [5.3] (27) 14.0 [5.1] (27) 16.5 [11.1] (39) 18.1 [10.2] (32) 13.2 [6.7] (20) 13.4 [9.7] (29) 14.7 [9.7] (28) 14.7 [8.9] (25) 12.1 [5.6] (20) 20.2 [16.2] (32) 400 10.8 [5.8] (35) 11.4 [8.2] (30) 11.6 [4.4] (40) 12.0 [4.4] (37) 14.0 [9.4] (55) 15.3 [9.1] (48) 11.0 [5.6] (29) 11.6 [8.3] (39) 12.0 [7.9] (42) 12.0 [7.2] (38) 10.2 [4.8] (29) 17.1 [13.5] (45) 450 9.7 [5.3] (43) 10.2 [7.3] (38) 10.5 [4.0] (49) 10.6 [3.8] (48) 12.2 [8.2] (73) 13.6 [8.3] (63) 10.0 [5.0] (35) 10.8 [7.7] (45) 11.2 [7.2] (49) 10.9 [6.6] (47) 8.9 [4.3] (38) 15.2 [12.0] (57) 500 8.9 [4.8] (52) 9.3 [6.6] (46) 9.6 [3.6] (59) 9.7 [3.5] (57) 11.4 [7.7] (84) 12.6 [7.9] (74) 9.4 [4.7] (40) 9.9 [7.0] (54) 10.2 [6.6] (59) 9.9 [5.9] (56) 8.3 [4.0] (44) 14.7 [11.6] (61) 28 Table 8. --Selected results of K-CERA analysis given in standard error of instantaneous discharge, in percent equivalent Oaussian Spread, in brackets; and number of visits per year to site, in parentheses Continued Budget, in thousands of 1984 dollars Station number 50112500 50114000 50115000 50124200 50136000 50138000 50144000 50147800 50252000 50276000 50295000 50345000 Current operations 310 296 40.1 [39.1] (12) 21.9 [19.2] (12) 25.3 [19.7] (12) 28.5 [26.2] (12) 19.1 [10.3] (12) 20.6 [9.5] (12) 14.5 [6.4] (12) 24.6 [8.2] (12) 26.7 [14.4] (6) 27.9 [14.7] (6) 46.7 [44.0] (6) 47.1 [44.1] (6) 300 310 36.2 34.0 30.0 [35.0] [32.8] [28.6] (15) 25.9 [23.1] (8) 29.0 [23.2] (9) 31.1 [28.9] (10) 26.1 [14.7] (6) 24.9 [11.9] (8) 15.8 [7.0] (10) 28.2 [9.8] (9) 26.7 [14.4] (6) 25.9 [13.4] (7) 46.7 [44.0] (6) 47.1 [44.1] (6) (17) 25.9 [23.1] (8) 26.4 [20.6] (ID 29.7 [27.5] (ID 24.4 [13.6] (7) 24.9 [11.9] (8) 15.8 [7.0] (10) 26.9 [9.2] (10) 24.8 [13.2] (7) 25.9 [13.4] (7) 46.7 [44.0] (6) 47.1 [44.1] (6) (22) 22.8 [20.0] (11) 24.3 [18.8] (13) 26.4 [24.2] (14) 23.0 [12.7] (8) 23.6 [11.2] (9) 15.8 [7.0] (10) 24.6 [8.2] (12) 24.8 [13.2] (7) 24.3 [12.4] (8) 46.7 [44.0] (6) 47.1 [44.1] (6) 320 29.3 [28.0] (23) 19.8 [17.2] (15) 22.7 [17.4] (15) 25.6 [23.3] (15) 17.2 [9.1] (15) 18.5 [8.4] (15) 17.6 [7.8] (8) 23.7 [7.9] (13) 23.3 [12.3] (8) 23.0 [11.8] (9) 46.0 [43.6] (7) 46.4 [43.7] (7) 340 24.4 [23.1] (33) 18.2 [15.7] (18) 19.8 [14.8] (20) 21.6 [19.4] (21) 18.4 [9.9] (13) 19.1 [8.8] (14) 15.1 [6.7] (11) 19.7 [6.4] (19) 20.0 [10.4] (11) 20.8 [10.4] (11) 45.5 [43.3] (8) 45.3 [43.1] (9) 350 23.4 [22.0] (36) 17.4 [14.8] (20) 18.8 [14.1] (22) 20.7 [18.5] (23) 17.8 [9.5] (14) 18.5 [8.4] (15) 14.0 [6.1] (13) 18.8 [6.1] (21) 19.1 [9.9] (12) 19.2 [9.6] (13) 45.0 [43.1] (9) 44.5 [42.7] (11) 400 19.2 [18.0] (53) 14.5 [12.2] (29) 15.5 [11.4] (33) 16.8 [14.8] (35) 14.6 [7.7] (21) 15.0 [6.7] (23) 11.6 [5.1] (19) 15.8 [5.0] (30) 15.7 [8.1] (18) 15.9 [7.9] (19) 43.0 [41.8] (16) 42.0 [41.0] (22) 450 17.2 [16.0] (66) 13.0 [10.9] (36) 13.9 [10.2] (41) 15.2 [13.3] (43) 13.0 [6.7] (27) 13.7 [6.1] (28) 10.6 [4.6] (23) 14.1 [4.5] (38) 14.0 [7.2] (23) 14.5 [7.1] (23) 41.1 [40.4] (27) 37.9 [37.4] (34) 500 15.8 [14.7] (78) 11.7 [9.7] (45) 12.8 [9.3] (49) 14.4 [12.5] (48) 12.1 [6.2] (31) 12.4 [5.5] (34) 9.8 [4.2] (27) 13.0 [4.1] (45) 13.0 [6.7] (27) 13.6 [6.7] (26) 37.1 [36.7] (59) 33.4 [33.0] (95) 29 stations were retained in the analysis. This was done in the belief that, while the absolute values of standard error may be incorrect, the values had relative signifi- cance. The current operating policy has resulted in an average standard error of estimate of streamflow of about 20.6 percent. This policy is based on a budget of $310,000 to operate the 50-station stream-gaging pro- gram. This program provides for 12 measurements per year for most stations, except for five stations which are measured six times per year. Four of the latter are in the U.S. Virgin Islands. For periods with missing record, the optimum standard error of estimate of streamflow is about 18.8 percent. Under optimum conditions, stream-gaging sites are visited and measured 6 to 25 times per year. These include 28 sites which are measured less than 11 times, and 10 sites measured more than 15 times per year. For periods without missing record, the standard error of estimate of streamflow is about 12.5 percent. For optimum operation, from 6 to 35 stations are visited per year. These include 27 sites measured six times and four sites measured 25,26,27, and 35 times per year. Of the sites measured six times per year, 16 sites are ones for which uncertainty functions could not be defined. The logistics of either of these later operations, with or without missing record, is impractical in terms of equip- ment and manpower. For periods of missing record, an increase in the operating budget of 12.9 percent (from $310,000 to $350,000 of 1984 dollars) results in a standard error of estimate of about 15.6 percent. The measurements per site ranges from 9 to 42 times per year with 24 sites measured less than 15 times per year, and 17 sites meas- ured 21 or more times per year. The 17 sites are measured 21, 23, 25, 26, 27, 28, 32, 34, 36, 39, and 42 times per year. The 16 null sites are measured nine times per year. A more practical visit schedule would range from about 18 to 20 times per year or slightly less than a measurement every 3 weeks. This would result in a standard error of estimate of about 17 percent. The maximum budget analyzed was $500,000. The analyses using this budget resulted in an optimum average standard error of estimate of about 11.3 percent. For the present operational budget of $310,000, the effects of missing records adds about 6 percent to the average standard error. With a budget of $350,000, sta- tions would be visited more frequently, and the reduced number of missing records would decrease the average standard errors by about 3 percentage points. Also, improvements in equipment can have an additional positive effect on uncertainties of instantaneous dis- charges. Summary of Third Phase of Analysis The following are conclusions from this phase of the analyses: 1. The travel routes and measurement frequencies now in use could be modified in order to decrease the curren: 20.6 percent per station average standard error by 1.9 percent, given the present budget of $310,000 1984 dollars. But with present manpower and equip- ment, only a 1 percent decrease in standard estimate of error is practical based on a compromise modification of present and computed measurement visit frequencies. 2. If the present operating budget were increased by abdut 12.9 percent (to $350,000), the average stand- ard error of data would decrease to about 17 percent from t(he present figure of about 20.6 percent. These figure^ are obtained using the computed optimum K- CERA station visits as a guide to achieve a practical routing of about 18 to 20 measurements per year for most stations in Puerto Rico and 12 measurements per year at most stations in the U.S. Virgin Islands. 3. Methods for decreasing the probabilities of missing record need to be explored. Missing record presently increases the average standard error by about 6 percentage points or about 30 percent of the present standard error of estimate. The methods of decreasing missing record might include increased measurements per year at each site, improved instrumentation and in- creasetl use of local observers and satellite relay of data. SUMMARY Currently, there are 50 continuous-record stream- flow sites being operated in Puerto Rico and the U.S. Virgirt Islands at a cost of $310,000 per year. Data from most stations have multiple uses and all of the stations are recommended for continuation. Two stations (50063440 and 50063500) are used primarily for research and short-term investigations. However, these stations are located in critical tropical hydro ogic areas where more data is needed and where additional data may prove useful well beyond the dura- tion of the research projects. Thus, it would be desirable to continue these stations as index or bench mark sta- tions and to establish other similar stations on the main island of Puerto Rico, as well as on Vieques, Culebra, and the U.S. Virgin Islands. The greatest need is for stations located in 1- to 15- square mile drainage basins located far from populated areas. Hydrologic informa- tion such as streamflow, quality of water, sediment 30 discharge, and precipitation are needed at stations such as these. Flow routing and correlation and regression analy- ses were found to be unacceptable for estimating discharge. There were no sites at which flow routing could be attempted. Only four sites were identified at which correlation and regression analyses might have possibilities, and only at two sites were fair measure- ments of regression accuracy obtained. At these two sites, the best results were obtained by grouping the data into dry (November through May) and rainy (May through November) seasons where the simulated flow is within 15 percent of the measured discharge a signifi- cant percent of the time. The current policy for operating the 50-station pro- gram requires a budget of $310,000 per year. The travel routes and measurement frequencies now in use can be modified to decrease the present 20.6 percent standard error of estimate by 1.9 percent, while maintaining the present budget. However, the number of discharge measurement visits required to obtain the 1.9 percent increase in accuracy is not practical with existing per- sonnel and equipment. Discharge measurement site visits might be modified to decrease the standard error of estimate by about one percent, using present person- nel and equipment. A budget increase of 12.9 percent (to $350,000 1984 dollars) and a modification of the measurements schedule at continuous stream-gaging sites (to 18 to 20 times per year) could result in a reduction of about 17.5 percent in the standard estimate of error (from 20.6 to about 17 percent). Future studies of the stream-gaging program need to examine ways to decrease the probabilities of missing record and reduce the standard error of estimate with moderate increases in personnel and funding. Analyses similar to this one would be beneficial if repeated ap- proximately every 10 to 15 years. 31 SELECTED REFERENCES Benson, M.A., and Carter, R.W., 1973, A national study of the streamflow data collection program: U.S. Geological Survey Water-Supply Paper 2028,44 p. Carter, R.W., and Benson, M.A., 1970, Concepts for the design of streamflow data programs: U.S. Geological Survey Open-File Report, 33 p. Curtis, R.E., Jr., Guzman-Rios, Sen6n, Diaz,P.L., 1985, Water Resources Data for Puerto Rico and the U.S. Virgin Islands, Water Year 1984: U.S. Geological Survey Water-Data Report PR 84-1, 374 p. Draper, N.R., and Smith, H., 1966, Applied regression analysis (second ed.): New York, John Wiley and Sons, Inc., 709 p. Ezekiel, E., Fox, K.A. 1930, Methods of correlation and regression analysis (third ed.): New York, John Wiley and Sons, Inc., 548 p. Fontaine, R.A., Moss, M.E., Smith, J.S., and Thomas, W.O., Jr., 1984, Cost-effectiveness of the stream-gaging program in Maine: U.S. Geological Survey Water-Supply Paper 2244,39 p. Gelb, A., ed., 1974, Applied optimal estimation: Cambridge, Massachusetts, The Massachusetts Institute of Technology Press, 374 p. Gilroy, E.J., and Moss, M.E., 1981, Cost-effective stream-gaging strategies for the lower Colorado River Basin: U.S. Geological Survey Open-File Report 81-1019,38 p. Hale, T.W., Stokes, W.R., in, Price, M., and Pearman, J.L., 1985, Cost-effectiveness of the stream-gaging program in Georgia: U.S. Geological Survey Water-Resources Investigations Report 84-4109, 144 p. Hirsch|, R.M., 1982, A comparison of four streamflow record extension techniques: Water Resources Research, v. 18, no. 4, p. 1081-1088. Hutchison, N.E., 1975, WATSTORE User's guide, volume 1: U.S. Geological Survey Open-File Report 75-426,315 p. Kleinbaum, D.G., and Kupper, L.L., 1978, Applied regression analysis and other multivariable methods: North Scituate, Massachusetts, Duxbury Press, 556 p. L6pez, M.A., and Fields, F.K., 1970, A proposed streamflow-data program for Puerto Rico: U.S. Geological Survey Open-File Report, 39 p. L6pez, M.A., Colon-Dieppa, Eloy, and Cobb, E.D., 1979, Floods in Puerto Rico, magnitude and frequency: U.S. Geological Survey Water-Resources Investigations Report 78-141, 66 p. McKinley, P.W., 1985, Surface-water data network for Piierto Rico: U.S. Geological Survey Water-Resources Investigations Report 83-4055, 14 p. Moss, M.E., and Gilroy, E.J., 1980, Cost-effective stream-gaging strategies for the Lower Colorado River Basin: U.S. Geological Survey Open-File Report 80-1048, 111 p. Riggs, H.C., 1973, Regional analysis of streamflow characteristics: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chapter B 3,15 p. Thomas, D.M., and Benson, M.A., 1970, Generalization of streamflow characteristics from drainage-basin characteristics: U.S. Geological Survey Water-Supply Paper 1975,55 p. 32