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When a couple on Rodman Street in Northwest Washington opened their D.C. water bill envelope a few weeks ago, they were startled to discover that they apparently owed the city $2,403.51. Their last bill had been only $53.00.

After calls to the office of Third Ward City Council Member Polly Shackleton and to the D.C. Department of Environmental Services, which oversees the city's anti-quate dand error-prone water billing process, the couple was able to have their meter read again and their bill was adjusted to $132.

The problem was that the original reading of the couple's water meter had been recorded at 4,200. When city meter readers went back and reread the meter it was only 1,468.

The obviously out-of-line reading had apparently not been double-checked by a meter reade rsupervison. The resulting astronomical bill had slipped undetected past the eyes of one of the $8,000-a-year auditors whose job it is to make sure that strangely disproportinate bills are not sent out without first being re-examined.

"That was just pure error on out part," said Edward Scott, chief of the city's water revenue division. "You've got a manual system, your auditors are human beings and they let things slip through. That's as simple an answer as I can give."

Many city residents have been baffled by the latest round of city water bills, many of which show charges three, four and five times higher then homeowners are used to getting.

City water officials believe much of the complaining that ras tied up the telephones in their dingy third-floor office at 499 Pennsylvania Ave. NW is the result of people not understanding that the new bills include a 40 per cent rate increase and cover a period twice as long as usual.

Nevertheless, DES officials acknowledge that the water billing system is fraught with room for error from the unsupervised meter-readers and the sometimes careless auditors. Moreover, officials say, the delicately balanced system is also incapable of absorbing such a seemingly simple thing as installment payments.

"When you've got a system that's this much dependent on people, something could always happen that could throw us into problems," said John Ingram, associate director of the environmental services department.

One place where the errors can being is in the very first step, the meter reading. The city tries to read meters twice each year for residential customers and four times annually for commercial water users.

A 12-person crew with two supervisors is responsible for those readings. It sounds like a simple process, just picking up a leather-bound book of meter cards, going out to the proper area of the city, and recording the position of four dials on the face of one of half a dozen different styled meters. But city water officials say it is not all that easy.

Grass, rosebushes, floral pits and shrubberry often impede access to the meters. If there has been heavy rain, the underground pit in which the meter is located could be flooded and the dials thus invisible. In severe Washington winters, like last year, frozen ground, ice or snow may prevent meter readings for as long as a month.

About 95,000 of the 104,000 residetial meters in the city are outside. The remainder are indoors and sometimes cannot be read because no one is at home to let the reader in.

Ideally, most of the city's water billing would be based on real rather than estimated readings. "My gut feeling is that the majority of our readings are actual readings," Scott said.

When pressed on the checks of the present system, however, Scott acknowledged that supervisors who are supposed to routinely spot-check readings are sometimes deployed as readers themselves. When asked how frequently the weekly spot-check schedule is adhered to, he responded, "Not too often.

It is possible for a reader to go through his entire book of 100 or 200 meter cards and estimate the readings based on previous readings recorded, Scott said. When asked if there were any statistics on how frequently such "curbstone readings" occurred, Scott said there were not.

Without an actual meter reading the city must estimate the usage based on past billings. Because water use varies by as much as 15 per cent between summer and winter months, an estimate can be made only on a similar six-month calendar period. In order to find such a similar period, an estimator may have to go back as far as 1971 or 1972, when perhaps a different family with different water use habits occupied the home.

Once the reading has been recorded, it is keypuched on a computer tape two separate times and cross-checked to make sure it is accurate. From there the tape is taken to the city's computer center in the municipal building. There, bills and ledger stickers are run off and returned to the water department before being mailed out.

City water officials cannot say precisely how many of the 132,000 bills sent to residential and commercial customers since June have been inaccurate. "My general feeling," Ingram said, "is that it's less than 5 per cent.The question of meter misreading is a small percentage."

About 1,300 bills have been sent because, based on routine audits, city officials believe those bills are inaccurate. In the case of another 13,000 bills, the proper amount of arrears due has not been entered on the original bill because that information is not in the computer, Ingram said. The mailing of those bills has also been delayed.

Some residents have complained to their representatives on the City Council that nearly a month has passed before they hear from the water department. Scott said that is because if the department chooses to answer incoming calls it does not have time to return earlier calls. If it answers the previous calls, he said, people complain they cannot get through to protest their bill.

Many of the problems that have cropped up with that latest mailing of water bills are, in Scott's opinion, related to factors beyond the department's control. Foremost among these, he said, is the recent rate increase and extended billing period, which many of the city's water customers do not understand.

In an attempt to catch up with past backlogs the city decided in May to bill for a 10- to 11-month period, instead of the normal six. Thus, Scott said, assuming normal usage, a customer's latest bill would have been Complicating this even more was city adopted higher water and sewer use rates. Before that time, cutomers paid $8.75 for the first 3,600 cubic feet of water used and 30 cents for each additional 100 cubic feet. The sewer charge was equal to 90 per cent of the water charge.

As of July 1, 1976, the water rate became a flat 39.4 cents per 100 cubic feet and the sewer rate was set at 44.8 cents per 100 cubic feet.

Under the old rates, a customer using, for example, 11,900 cubic feet during the billing period would have paid $31.60 for water and $28.44 for sewer, a total of $60.04. With the new rates in effect, that same customer would pay $46.89 for water and nd $53.31 for sewer, for a totaotataotl of $100.20 - $40.16, or 67 per cent, more. (Percentage increases vary according to the amount of water consumed).

What also confused customers, Scott said, was a change from the advanced minimum allowance system to the present pay-as-you-go, flat-rate system. Under the old system a standard fee of $16.63 was charged for the first 3600 cubic feet of water and sewer and was paid in advance.

If a customer used less than that, he would get no refund nor any credit, but would merely have to pay another $16.63 minimum at the beginning of the next billing period. If more than the 3600 cubic foot minimum were used the excess was billed at the 30-cent rate.

Under the new system, there is no minimum fee and customers pay only for what they use. Someone using less than 3,600 cubic feet would pay only for that and, theoretically, should have a smaller bill.

On the other hand, since sewer charges are no longer figured at 90 per cent of the water charge and sewer rates are the higher of the two, sewer charges under the new system are usuallly higher than water charges.

Few water users realize how much water is wasted by leaks and how much it costs, Scott said.

Based on current water rates, a dripping faucet would add $5 to a six-month water bill, a running faucet would cost $20 more and a leaking toilet could add nearly $30 to the bill.

For many city residents the final frustration of the city's current system has been its inability to take partial payments for the unusually high bills. The City Council passed legislation that would have allowed an optional partial payment plan, but Mayor Walter E. Washington rejected such a scheme on grounds that the water department was not equipped to handle installment payments.

Water officials contend that they are just now getting control over a habitually fault-ridden manual system and trying to convert it to an automated system.

A premature injection of a new element into that process - namely, partial payments - could upset the process and throw the water billings back into confusion, officials say.