Extra Long-rang Daily Forecast

Calculate of Meteorological Calendar

Zhang Shichao

Meteorological Bureau of Shaanxi province

CHINA

Numerical weather forecast has been advance greatly by application of computer, but it only limits for forecast of short-range weather situation, because the meteorological factors (such as precipitation) were forecasted according to weather situation, the forecast accuracy is little lower. For weather forecast of long-range above 15-day, it perhaps may be said: there is not a method that is recognized generally and reliable, the forecast accuracy is lower and lower. For instance, the forecast accuracy which the predict for temperature and rainfall of next month is higher or lower, less or more than historical average is 67٪ and 52٪ in USA, 58٪ and 54٪ in Soviet Union, 66٪and 58٪ in Japan respectively. There is not make daily forecast for exceed toa month except Japan in the world. At 1970's,there is existed a method of extra long-range daily forecast in China. It is called meteorological calendar, that it lists some dates of enable rainfall. It was said the meteorological calendar is welcome, but it disapeares now. I think that the reason is it's accuracy to be the lowest and make it to be difficulty. I have developed a software of computer, it only uses records of some meteorological factors of a single observation station and may make up daily forecast of the meteorological factors in next 15 months. This method has a lot of steady accuracies and can use not only daily rainfall and temperature forecast, but also daily hail and seism forecast.

My major is not meteorology. I have begun to study meteorological forecast since 1968. Since 1976 I have made meteorological calendar by the abacus and the slide rule, wroten a paper (its title is¡°Essential Periodical Analysis¡±). There are many methods of periodical analysis in statistical forecast, I think that a method of harmonious analysis is more scientific, but it has more defects to apply on the time series which has infinite length, such as the data length to be not longer, the numbers of period to be not more than four and five. My method overcomes above defects at certainly degree. There are many things that layman is no fetter and makes a breakthrough in scientific history. Do I find a new way? Although the model has many layers, the initial field is closer and the step is shorter, the numerical weather forecast can not forecast longer. This means controlling atmosphere move should need to find other new ideas. Therefore the research should carry out from other directions, study the periodicity and discover periods. Atmosphere may be considered a super system (black box) that involves all of influential factories. If there is any law in such a system (especially in the time series), it is only periodicity. Virtually, metre, relation and similarity has all belong to periodicity. The astronomy is first to discover some periods and may predict solar and lunar eclipse, then to form the theory of solar system, and final to appear Newton's mechanism. In beginning, the physics sense was not pursued.

The appraisal method for extra long-range daily forecast of mine is described below. (1).The SMALLEST ERROR be called that is a mean square deviation of the smallest difference which is between real daily rainfall and predict values of before and after a day (total 3 days), and is between predict values and real rainfall of before and after a day (total 3 days). The smallest error is compared with standard deviation (S.D.) of real daily rainfall series. (2).The SLIDE ERROR be called that is a mean square deviation of difference which is between slide values in 3 days of real rainfall and predict value at same day. Slide error is compared with standard deviation (S.D.) of slide real rainfall series. If all of predict values equal averages of real daily rainfall in corresponding months, the errors equal to corresponding the standard deviation. Because the averages do not know, it is obliged to use the history averages of special months. As a result, the errors is bigger than corresponding the standard deviation.

For rainfall series, I still compute two accuracies. (1).ACCURACY OF RAIN DAY: there is a real rainfall amount at least in before and after a day (total 3 days) if predict value bigger than 0.0, and there is a predict value is bigger than 0.0 at least in before and after three predict values if real daily rainfall is bigger than 0.0, otherwise it is inaccurate. (2).ACCURACY OF FINE OR RAIN: the appraisal method is similar to above, and addes that there is a day not rainfall amount at least in before and after a day (total 3 days) if a predict value equals 0.0, and there is a 0.0 at least in before and after a day (total 3 days) of predict series if a real daily rainfall doesn't bigger than 0.0, otherwise it is inaccurate. Because the probability (R) of daily rainfall is bigger than 0.0 and smaller than 0.5 (at Xian R=0.325) in general region, the predict of daily rainfall by climatic probability always equal to 0.0. According to above, the accuracy of rain day equals to 0.0, the accuracy of fine or rain is little bigger than (1 - R), and not more than (1 - R/2). If a predict daily rainfall always equals to the history average precipitation, the accuracy of rain day is little bigger than [2R/(1 + R)] and not more than [4R/(1 + R)], the accuracy of fine or rain is little bigger than R and not more than 2R.

When I compute two kinds of the accuracy, the forecast time may before or after stride a day in time. This is serious for extra long-range forecast, because the short-range forecast may after stride 12 hours. Because forecast can after or before stride a day, if predict always a rain day by a fine day, it's accurate seems to equal to 100٪ in any case of rain or fine. In fact, this is true if the appraise is only for real rainfall series. Thus above methods must appraisal for predict series too. As long as there is a subseries of three days of sustained rain or of sustained fine in real rainfall series, a error will be appear. The result of my forecasting is obtained by accumulate for more hundreds of periods, it can predict of sustained rain or of sustained fine, has both sum of rainfall and numbers of rain day conformed to real and can't be speculate. So this method of appraise is stringent and rational.

For daily mean temperature series, similar to daily rain series, two forecast accuracies are computed: (1).ACCURACY OF DETEMPERATURE: if a real daily average of temperature is lower than preceding exceed to 1˚C, then there is a day's predict value in before and after a day in predict series is lower than preceding exceed to 1˚C ; if a day's predict value is lower than preceding exceed to 1˚C , then there is a day's daily temperature in before and after a day of real series is lower than preceding exceed to 1˚C, otherwise is inaccurate. It is neglected that the detemperature is less than 1˚C . (2).ACCURACY OF RAISING TEMPERATURE: The method of appraisal is same above, as long as raising temperature instead of detemperature. If above two errors (slide err. And the smallest err.) were pursued to be smaller and the accuracy were not used, the history data would be longer and the numbers of selected period were not need more, this time, the curve of predict is smoother and the predict don't include fluctuation of daily temperature with cold air.

The rainfall forecast have been taken 14 times with my method, the each predict encloses daily rainfall of 450 days (15 months), the appraised result with above showed bellow table 1:

Table 1

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average the highest the lowest

slid S.D. 2.90 3.8 2.0

slide err. 3.25 4.0 2.5

series S.D. 4.90 6.4 3.4

the smallest err. 3.31 4.0 2.6

accuracy of rain day 64.38 70.6 58.9

accuracy of fine or rain 83.97 88.0 81.1

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The forecasts are obtained by accumulating and inferencing of the 150 - 160 periods which were gotten by analysis of 15000 days (about 41 years) data in before forecast day. All of accuracies are true and not fitting. Please attention, the differences of the highest and of the lowest among 14 times are about 10٪. In other words, the forecast effects are stable. Particular, two standard deviation(S.D.) have bigger fluctuation (the difference of the highest and of the lowest is 1.8 and 3.0 respectively), but two predict errors are smaller (1.5 and 1.4 respectively).

Good forecast of daily temperature may be obtained by using short preceding data (1500 days) and selectting few periods (90). The result of appraise for 12 times forecasts has a same stable. The two predict errors are smaller than daily rainfall forecast and both have same characteristic, the smallest error is lower than standard deviation and the slide error is little bigger than slide standard deviation. All of results showed below table 2.

Table 2

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average the highest the lowest

slide S.D. 2.39 2.6 2.1

slide err. 3.08 3.4 2.7

series S.D. 3.50 3.8 3.1

the smallest err. 2.50 2.7 2.2

accuracy of detemperature 66.45 74.3 60.5

accuracy of raising tem. 71.59 77.6 68.4

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The results of above two accuracies are appraised for all 15 months. For examinning the period of validity, I have studied the accuracy variation as inference to be farther and appraised according to the forecast of each month. I have the distance of two forecasts been not exact one year, but been 300 days, the months of fewer and more rainfall been staggered, the statistician of monthly accuracy been not the season influence, The table 3 showed that the forecast accuracy is not dropping. Except the accuracy of fine or rain, the other monthly statistic value don’t include the smaller.

Table 3

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month 1 2 3 4 5 6

accuracy of rain day 56.7 62.1 45.9 62.7 58.0 60.1

accuracy of fine or rain 81.2 86.6 81.4 88.0 81.6 83.2

accuracy of detemperature 65.7 67.9 55.0 63.8 71.2 74.9

accuracy of raising tem. 72.9 70.1 72.3 66.9 68.7 69.2

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7 8 9 10 11 12 13 14 15

64.1 61.0 57.7 51.9 55.6 63.7 54.6 57.9 53.3

87.2 83.7 84.2 85.5 79.1 86.2 83.3 86.9 81.8

71.3 63.4 61.2 65.4 58.2 69.0 66.6 58.6 64.8

69.6 71.4 67.2 70.3 65.1 74.0 68.9 63.3 70.1

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