# Missing Temperature and Precipitation Data

Nearly all climate observations in the U.S. are made by volunteers who are part of the NWS Cooperative Station Network. Events such as sickness, vacation, or equipment failure can create missing daily data values. Since missing data values do affect climate statistics, guidelines have been established to accommodate missing data and still provide representative statistics.

## Missing Temperature Algorithm for Calculating Averages

To create representative averages and totals, the WETS program scans each month for missing temperature and precipitation values using the following logic:

To be included in a temperature analysis, a month must contain at least 21 maximum and minimum temperature values. Because temperature is a continuous function, previous research has shown that representative averages can be calculated using 21 or more temperature values for a particular month (Duchon, 1981).

## Missing Precipitation Algorithm for Calculating Averages

To be included in a precipitation analysis, a month must contain at least 25 observed daily precipitation values. (Zero is considered a valid observation and not treated as missing.) Since precipitation occurs as distinct events rather than continuously, and significant amounts can occur in a single day, a more stringent criterion for missing days has been imposed than for temperature.

One exception to the 25 day rule is the calculation of average monthly snowfall. Since snowfall is observed less frequently than liquid precipitation (rain) and larger sample sizes ensure more stable estimates, no months are excluded from the calculation unless an entire month's snowfall dataset is reported as missing.

## Zero Monthly Precipitation Totals

Monthly precipitation totals of zero present a problem when one uses the logarithmic transformations to calculate the exceedence probabilities as shown in the WETS Table. The logarithm of zero is undefined and cannot be included in the exceedence probability calculation.

Zero monthly precipitation totals are a seasonal characteristic of the western and southwestern United States. They are most often observed in the summer.

The WETS program adjusts for this situation by using a mixed distribution, binomial and two parameter gamma, to calculate representative probabilities (Kite, 1977). Given a dataset containing zero monthly precipitation, the first step is to fit the probability distribution to those events greater than zero. The next step is to multiply the resulting probabilities by the ratio of the number of events equal to zero to the total number of events in the sample. This will result in the required probability of exceedence.

If, for example, 16 months out of 24 valid sample years reported zero precipitation valid years (probability of non- occurrence equal to 67 percent), a 30 percent probability value could not be calculated and would be shown as a zero in the table. This logic applies to all probabilities calculated by the WETS table.