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«APPENDIX G Long range prediction of river flow: a preliminary assessment WJR Alexander Note: The text in this report is an OCR copy of the original ...»

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Analytical methods for water resource development and management

APPENDIX G

Long range prediction of river flow:

a preliminary assessment

WJR Alexander

Note: The text in this report is an OCR copy of the original in my possession. I have

retained the page layout as far as possible but there may be a few remaining undetected

errors. Because of digital space constraints I have omitted the graphs on pages 32 to 47.

The graph on page 31 provides the basic information. The information on all the graphs was subsequently updated in my more recent studies.

This was the basis for my subsequent prediction models.

2 Appendix C Long range prediction model 3

DEPARTMENT OF WATER AFFAIRS

Branch of Scientific Services Technical Report No TR 80

LONG RANGE PREDICTION OF RIVER FLOW - A PRELIMINARY ASSESSMENT

by W J R A1exander June, 1978 Department of Water Affairs Private Bag X313

PRETORIA

ISBN 0 621 05252 3 4 Appendix C INDEX Page

INTRODUCTION

1. RESULTS OF STUDIES IN SOUTH AFRICA AND OVERSEAS 2

Numerical methods 2 Extrapolation methods 2 Pure analogy 2 Probability forecasts 3

2. SUBSEQUENT RESEARCH IN SOUTH AFRICA 4

3. OVERSEAS EXPERIENCE 6

4. SUMMARY OF PRESENT STATE OF KNOWLEOGE 7

5. VISUAL EXAMINATION OF SOUTH AFRICAN RUNOFF DATA 9

5.1 Moving averages 9

5.2 Mass flow presentation 10

6. AN EXAMINATIQN OF THE VAAL DAM RECORD 11

7. PRESENTATIQN OF SUNSPOT DATA 16

8. EXAMINATIQN OF OTHER FLOW RECOROS 18

9. CORRELATION BETWEEN RIVER FLOW AND SUNSPOT NUMBERS 21

10. RESULTS QF VISUAL EXAMINATIONS 26

11. CONCLUSIQNS 27 REFERENCES 28 ANNEXURE 1 30 Long range prediction model 5

INTRODUCTION

The ability to predict changes in annual river flow within the next decade would be of considerable value to those responsible for the planning construction and operation of water supply projects.

During periods of high runoff larger water allocations could be made from the country's water conservation dams, while stricter control and possible restrictions on consumption could be imposed when periods of lower runoff were imminent. Dams upstream of areas prone to flood damage could be kept at lower capacities during high runoff periods to aIlow some measure of flood absorption and thereby reduce the risk of flood damage to downstream areas.

For many decades hydrologists and water resources engineers have studied the structure of hydrological time series in an attempt to develop some predictive capability. So far their efforts have not been successful.

Since 1970 Tyson, Dyer and others have shown that annual precipitation over large areas of South Africa exhibits a quasi 20-year periodicity which is in phase with the double sunspot cycle. Tyson (1977) has found that these properties have no parallel in the literature. No physical explanation for this phenomenon has yet been found.

South Africa is currently in the fifth year of abnormally high runoff. This country-wide phenomenon has had no precedent in the past fifty years. It is of course possible that this is purely the result of a random process, but it fits in very well with the precipitation cyclicity which Tyson found in the early 1970's.

The purpose of the present assessment is to examine the records of river flow in South Africa in an attempt to ascertain whether they show a periodicity or correlation with sunspot phenomena that could be used as a predictive tool.

6 Appendix C

1. RESULTS OF STUDIES IN SOUTH AFRICA AND OVERSEAS

One of the comments in the Report of the Commission of Enquiry into Water Matters (1970) was:Efficient economic utilisation of available water supplies, and therefore decisions as to whether to impose or relax restrictions on water consumption, depend on whether rainfall during the ensuing month or season is likely to be normal, or above or below averaae. The possible value of long-rang weather forecasting to planned water utilisation is thus of deep concern."

Several possible methods for long-range weather forecasting were considered in the report:Numerical methods These involve the application of pure hydrodynamic principles to the modelling of weather systems.

Extrapolation methods (a) Movement of anomalies. This assumes that positive and negative departures from the mean condition will occur in an apparently regular manner with respect to time.

(b) Extrapolation in time of predominant waves and periodicities.

Predominant waves and periodicities in the historical record are identified and extrapolated into the future.

Pure analogy Current weather conditions are correlated with typical patterns in the past, and it is assumed that current weather conditions will follow a similar sequence.

Long range prediction model 7

Probability forecasts These are based on statistical correlations between different climatic regions (eg. summer and winter rainfall areas in South Africa) or between different continents on the assumption that general atmospheric anomalies exist on a world-wide scale.





Forecasts based on climatological probabilities, singularities and persistence tendencies are related to meteorological conditions which exhibit the tendency to persist longer than might be expected as a matter of chance.

In the report it is stated that some of South Africa's most severe and prolonged droughts of the nineteenth and twentieth centuries have coincided with troughs of minimum sunspot activity, and that the sun therefore appears to be either directly or indirectly responsible for abnormal weather.

The Commission of Enquiry strongly recommended that a purposeful attack on the problems associated with long-range weather forecasting be made:Long-range weather forecasts, even though approximate, can be of tremendous benefit in the management of water resources. Even were it possible to forecast that next year will be wetter or drier than usual, with perhaps some indication of the probable degree of departure from the mean, this would greatly aid the taking of decisions that might be of vital importance to the country's economy."

8 Appendix C

2. SUBSEQUENT RESEARCH IN SOUTH AFRICA

At the Convention on Water for the Future held in Pretoria in 1970, Tyson (1970) presented the first of what was to be a series of papers related to long-range weather forecasting in South Africa. These papers were under the individual or joint authorship of Tyson, Dyer, Mametse, Abbott and Gillooly.

Tyson, Dyer and Mametse (1975) drew attention to the quasi-periodic oscillations in precipitation over South Africa. The predominant oscillations are a 20-year fluctuation in the summer rainfall region of South Africa, and fluctuations of smaller periodicities in the other rainfall regions.

Abbott and Dyer (1976) used the same analytical procedure on river runoff data from ten South African rivers and concluded that runoff and rainfall exhibit the same oscillatory character which has a wavelength of approximately 20 years in the summer rainfall region of the country.

Dyer (1976) showed that there was a periodicity and phase similarity between the double sunspot series and regional rainfall series over the north-eastern half of South Africa, and from this he proposed a tentative precipitation prediction model for the region. He predicted a continuation of above average precipitation for the late 1970's and early 1980's followed by below average rainfall for the rest of the 1980's.

Dyer and Tyson (1977) fitted a trigonometrical regression model to a regionally averaged annual precipitation time series for the period 1910-72 and by extrapolation suggested that the summer rainfall region of South Africa will experience above normal rainfall during the periods 1972-81 and 1991-2000, while the period 1981-90 will be drier than normal.

Long range prediction model 9

Tyson (1977) reviewed the enigma of climatic change and stated that recent changes in South African rainfall exhibit a degree of organisation in both time and space that to date finds no parallel in the literature. He recommended that efforts should be made to find explanations for the observations and to place predictions of future changes in South African climate on a stronger basis than the mere extrapolation of past events into the future.

10 Appendix C

3. OVERSEAS EXPERIENCE

For nearly a century water resources engineers and hydrologists have studied the structure of time series of river flows, as well as their possible correlation with sunspot activity. One of the more recent investigations is that by Rodrigues-Iturbe and Yevjevich (1968).

These authors examined the runoff from 16 major rivers of the world with average length of record of 94 years. In addition, 174 precipitation records with an average length of 79 years from the continental region of western North America were examined. The authors concluded that there was no statistical evidence of significant correlation between precipitation or runoff series and sunspot numbers.

Yevjevich (1972) was even more emphatic when it came to other periodicities

"One of the earliest deterministic methods used in hydrology was the application of the concept of almost-periodic series to various hydrologic sequences in search for their hidden periodicities. The hydrologic literature is full of these attempts to find cycles beyond the presence of the known astronomical cycles. Often, series that were statistically undistinguishable from stationary stochastic processes were decomposed into a limited number of hidden non-commensurate periodicities. However, their extrapolation as the prediction of future events represented one of the most spectacular failures of past hydrologic investigations."

–  –  –

4. SUMMARY OF PRESENT STATE OF KNOWLEDGE

Overseas investfgators have been unable to develop long-range prediction methods for river flow nor find significant correlations between river flow and sunspot cycles (Yevjevich 1972). Despite a fairly extensive literature survey I have not found any reference to the use of long-range forecasting methods in water resource management.

Based on trigonometrical regression studies, the South African authors (Dyer and Tyson

1972) have predicted that the present above normal rainfall conditions will change to drier than normal conditions early in the 1980s.

Dyer (1977) showed that there was a periodicity and phase similarity between the double sunspot series and regional rainfall over most of the summer rainfall region in South Africa.

No physical explanations have yet been found In South Africa or elsewhere either for regular periodic changes in rainfall or for the relationship between rainfall and sunspot activity that can provide a basis for long-range predictions.

All the authors quoted above used cross-spectral analysis as the main analytical tool (Rodriguez-Iturbe 1976 and Dyer 1976). This is a mathematical curve-fitting procedure which assumes that the phenomenon has the following characteristics:Positive and negative departures from a stable, mean condition.

2. The departures have fixed periodicity and amplitude.

3. The departures are symmetrical about the mean.

4. The departures are sinusoidal tn shape and can therefore be described mathematically by trigonometrical functions.

12 Appendix C

It is important to note that none of the authors have stated or implied that the physical processes are such that the phenomena should meet all or any of these assumptions. The authors were looking for a mathematical expression that fitted the data – not a mathematical expression which described the phenomenon.

Abbott and Dyer (1976) made no adjustments to their flow data to account for its nonsymmetrical properties whereas Rodriguez-Iturbe and Yevjevich (1968) followed the conventional hydrological practice of using the logarithms of the data rather than the untransformed data in their analyses to overcome this difficulty.

–  –  –

5. VISUAL EXAMINATION OF SOUTH AFRICAN RUNOFF DATA

In the present exercise it was decided to rely on visual examination of the data rather than mathematical treatment. This avoids having to make a priori assumptions about the nature of the time series. The subjectivity associated with visual examination is no greater than that associated with the subjective choice of mathematical curve fitting functions.

A visual examination of the annual flow series of South African rivers shows no obvious quasi-regular fluctuations. This is because of the large variance of the flow of rivers – particularly those in semi-arid regions.

There are two methods that could be used to enhance any periodicity that may be present.

One is the use of moving averages which has the effect of suppressing the variation and so smoothing the data. The second is the use of mass flow techniques.

5.1 Moving averages Instead of using individual annual values, the mean of a selected number of values is determined and plotted at the central point. For example, if a 5-term moving average is used, then the value obtained for the tenth year of a sequence would be the average of the five years 8, 9, 10, 11, 12. All five years are given equal weight.

This method can be improved by giving more weight to the central year and progressively less weight to the other years being averaged. This can be achieved by using a binomial smoothing function. The relative weights given to a sequence using a 5-term binomial smoothing function would be 1 - 4 - 6 - 4 - 1 respectively. The value of the tenth year of a sequence would be six-sixteenths of the value for year ten, plus 14 Appendix C four-sixteenths of the values for years 9 and 11, plus one-sixteenth of the values for years 8 and 12.

Abbott and Dyer (1976) used a 5-term binomial smoothing function in their analyses.



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