Artificial Neural Network Forecasts of California's Precipitation

contributed by David Silverman and John A. Dracup

Civil and Environmental Engineering Department, University of California, Los Angeles, California

Forecasts are made for each of California's seven climatic zones on a sliding, bi-monthly (Oct/Nov, Nov/Dec, etc.) basis. Inputs to the artificial neural network (ANN) are a one-year (Jan-Dec) monthly time series of the southern oscillation index (SOI), El Niño1+2, El Niño3.4, and the fourteen northern hemisphere 700 mb pressure anomaly teleconnection indices. Forecasts are made for the following water year (i.e., Jan-Dec 1998 inputs forecast Oct 1999-Sept 2000 bi-monthly cumulative precipitation).

The El Niño-Southern Oscillation (ENSO) in the tropical east Pacific and the 700 mb height anomaly over North America has been shown to be related to various phenomena in specific regions of California (Kahya and Dracup, 1993; Redmond and Koch, 1991; Ropelewski and Halpert, 1989, 1987, 1986; Barnston and Livezey, 1987; Wallace and Gutzler, 1981). By noting the regional and global patterns of variability in these activities (NDMC 1995), scientists may be able to use these recurring patterns of changes in the height anomaly and ENSO as tools for long range climate predictions.

The 700 mb pressure is a measure of the global atmospheric circulation (speed and direction of the winds, about 3 km above sea level) and is an indicator of the global climate. Recurring temporal patterns in the 700 mb height anomaly may allow for regional precipitation predictions a year or more in advance based on the state of the system. A rotated principal component analysis of the 700 mb pressure field gives 14 significant modes in the northern hemisphere. Each mode represents recurring and persistent concurrent regions of high pressure and low pressure zones over two distinct areas of the globe. These modes of related high/low pressure zones are termed "teleconnections". The principal component analysis for each month gives the relative strength of each mode for that month. These indices of mode strength, in a sense, summarize the strength and direction of the atmospheric circulation allowing the incorporation of the whole northern hemisphere circulation into the model by using a few variables.

The interaction of both ENSO and the 700 mb height anomaly that affects the precipitation in California is not easily determined by ordinary statistical methods. Current methods have been unable to detect the patterns or interactions necessary for long-range precipitation prediction (Navone and Ceccatto, 1994; Venkatesan et al., 1997). Such failures may have their source in the noise or fuzziness inherent in the data, in the overwhelming amount of data for each case but with relatively few cases to analyze, in possible nonlinear relationships involved, or in the limitations of current methods. The properties of ANNs may overcome these problems.

Artificial Neural Networks

Artificial neural networks (ANNs) are based on biological models of the brain and the manner in which it recognizes patterns and learns from example. The human brain contains more than a billion neurons with trillions of interconnections working simultaneously, enabling it immediately to pick an individual out of a crowd or to distinguish one voice out of a babble of voices and background noises - tasks that are difficult or even impossible for the most powerful supercomputers. Its construct also allows the brain to learn quickly from experience. An ANN comprises interconnected simple processing units that work in parallel, much as do the neuron networks of the brain, and which can discern patterns from input that is ill-defined, chaotic, and noisy. For an excellent layman's discussion on artificial neural networks, see Hinton (1992). A more technical discussion can be found in Masters (1993) or Fausett (1994).

Training an ANN for this problem requires careful consideration of the training set because the ANNs learn by example and there are relatively few years of complete data for examples. A method of choosing a training set without adding bias to the training when a limited amount of cases are available was used previously by the authors (Silverman, 1999; Silverman and Dracup, 2000). One of the shortcomings of ANNs is that a trained neural network is a "black box," i.e. there is no direct way of determining how the inputs and outputs are related. The authors primary goal is "opening" the black box (Silverman and Dracup, in press) to determine the important factors in the forecasts which will lead to a better understanding of the relationship between these teleconnections and precipitation.

Methodology

The methodology applied here is an extension of earlier work (Silverman, 1999, Silverman and Dracup, 2000) used to forecast the cumulative water year precipitation for each climate zone. Artificial neural networks were trained with an optimized training set for each climatic zone. Forecasts from the earlier work are shown in Table 1. The accuracy of the original work for the time period 1951-1997 is shown in Table 2.

The same training sets developed for the complete water year forecasts were used for training for the bi-monthly forecasts. The predictive score represented by a correlation between the observed and predicted precipitation for each bi-month since 1952 is shown in Table 1. The bi-monthly predictions for the October 1999 and 2000 water years are shown in Tables 3 and 4, respectively. The correlation between the forecast and observed values for 1952-1998 are shown in Table 5.

Conclusion

Using ANN's as a forecast tool has promise. The results show that forecasts better than climatology or random chance are possible with long lead times. The yearly cumulative forecasts have a higher success rate than the bi-monthly forecasts. Most of the difference can be attributed to the effort in optimizing the training set for the yearly predictions. Future work will optimize the training set for each month and zone, creating a series of ANNs with specific knowledge about a zone and time frame. Using techniques of data extraction (Silverman and Dracup, in press), these ANNs should provide insight into the interaction between large scale climatological parameters and precipitation.

References:

Barnston, A., and E.J. Livezey, 1987: Classification, seasonality, and persistence of low-frequency atmospheric circulation patterns. Monthly Weather Review, 115, 1082-1126.

Fausett, L. (1994): Fundamentals of Neural Networks, Prentice-Hall, Inc., 461pp

Hinton, G.E., 1992: How neural networks learn from experience. Sci. Amer., 9, 144-151.

Kahya, E., and J. A. Dracup, 1993: U.S. streamflow patterns in relation to the El Niño/Southern Oscillation. Water Resources Research, 29:8, 2491-2503.

Masters, T., 1993: Practical Neural Network Recipes in C++, Academic Press, 493pp.

Navone, H.D., and H.A. Ceccatto, 1994: Predicting Indian monsoon rainfall: a neural network approach. Climate Dynamics, 10:6-7, 305-312.

NDMC/National Drought Mitigation Center, cited January 15, 1998, Predicting drought. [Available online, from http://enso.unl.edu.ndmc/enigma/predict.htm].

Redmond, K. T., and R W. Koch, 1991: Surface climate and streamflow variability in the western United States and their relationship to large-scale circulation indices. Water Resources Research, 27:9, 2381-2399.

Ropelewski, C.F., and M.S. Halpert, 1989: Precipitation patterns associated with the high index phase of the Southern Oscillation. Journal of Climate, 2, 268-284.

Ropelewski, C.F., and M.S. Halpert, 1987: Global and regional scale precipitation patterns associated with the El Niño/Southern Oscillation. Monthly Weather Review, 115,1606-1626.

Ropelewski, C.F., and M.S. Halpert, 1986: North American precipitation and temperature patterns associated with the El Niño/Southern Oscillation (ENSO). Monthly Weather Review, 114, 2352-2362.

Silverman, D. (1999) Neural Network Analysis of Long Range Precipitation Forecasts, Ph.D dissertation, University of California, Los Angeles, UMI, 99pp

Silverman, D. and Dracup, J. (2000) Artificial Neural Networks and Long Range Precipitation Prediction in California, Journal of Applied Meteorology, 31:1 pp.57-66

Silverman, D. and Dracup, J. (in press): "Data mining in the trained backpropagation network," edited book on Artificial Neural Networks in Hydrology, Water Science and Technology book series (Prof. V.P. Singh), published by Kluwer

Venkatesan, C., S.D. Raskar, S.S. Tambe, B.D. Kulkarni, and R.N. Keshavamurty, 1997: Prediction of all India summer monsoon rainfall using error-back-propagation neural networks. Meteorology and Atmospheric Physics, 62:225-240.

Wallace, J.M., and D. S. Gutzier, 1981: Teleconnections in the potential height field during the Northern Hemisphere winter, Monthly Weather Review, 109, 784-812.

Table 1 Cumulative precipitation forecasts in inches for water years 1998-99, 1999-2000, and 2000-01. Numbers in parenthesis are observed values.

YEAR

Table 2 Forecast percent correct with forecast error less than 5%, 10%, and 15%.

ZONES

Table 3 Forecasts for the 1999-2000 water year made in February, 1999.

CALIFORNIA CLIMATE ZONE

1 2 3 4 5 6 7

Oct/Nov	7.4	2.6	2.9	1.8	1.1	0.6	0.5
Nov/Dec	3.6	0.2	0	2.5	0.3	1.1	0.6
Dec/Jan	3.5	1.4	0	3.1	1.8	1.1	0.7
Jan/Feb	8.9	20.8	12.3	4.9	3.9	1.6	1.2
Feb/Mar	15.6	23.5	15.6	8.9	12.1	6.8	1.9
Mar/Apr	8.4	10.3	3.2	5.2	4.8	3.8	1.1
Apr/May	3.1	3.0	1.3	1.0	0.3	1.2	0.4
May/Jun	3.3	0.4	0.5	0.7	0.1	0.3	0.3
Jun/Jul	1.3	0.1	0.5	0.1	0.1	0.1	0.3
Jul/Aug	0.4	0	0	0	0.2	0.4	0.9
Aug/Sep	1.2	1.7	1.4	0.5	0.9	1.1	1.5

Table 4 Forecasts for the 2000-2001 water year made in March, 2000.

CALIFORNIA CLIMATE ZONE

1 2 3 4 5 6 7

Oct/Nov	5.4	10.6	6.0	2.8	4.3	1.9	0.6
Nov/Dec	2.6	8.1	4.4	2.7	4.5	3.8	0.9
Dec/Jan	4.7	9.5	5.0	4.7	5.9	1.8	1.7
Jan/Feb	14.9	13.6	7.4	7.8	6.5	1.6	2.3
Feb/Mar	17.4	15.7	8.5	9.2	8.8	5.0	1.8
Mar/Apr	9.2	11.1	6.3	6.8	7.2	7.6	2.0
Apr/May	3.8	6.6	3.5	2.3	3.6	3.0	0.7
May/Jun	2.6	2.4	2.0	0.8	1.5	0.6	0.3
Jun/Jul	0.8	0.9	1.5	0.1	0.3	0.1	0.2
Jul/Aug	1.1	0.4	0.8	0.2	0.6	0.7	1.3
Aug/Sep	1.8	1.3	1.7	0.8	0.4	2.2	0.9

Table 5 Correlations between the observed and forecast precipitation.

CALIFORNIA CLIMATE ZONE

1 2 3 4 5 6 7

Oct/Nov	0.61	0.69	0.66	0.61	0.60	0.48	0.73
Nov/Dec	0.67	0.75	0.80	0.46	0.67	0.62	0.67
Dec/Jan	0.75	0.75	0.81	0.38	0.62	0.76	0.49
Jan/Feb	0.67	0.41	0.38	0.52	0.25	0.77	0.69
Feb/Mar	0.59	0.42	0.43	0.66	0.48	0.67	0.77
Mar/Apr	0.61	0.70	0.71	0.70	0.66	0.62	0.81
Apr/May	0.53	0.57	0.64	0.70	0.72	0.66	0.62
May/Jun	0.53	0.57	0.59	0.40	0.43	0.53	0.49
Jun/Jul	0.53	0.64	0.56	0.64	0.42	0.54	0.28
Jul/Aug	0.60	0.54	0.60	0.72	0.40	0.71	0.27
Aug/Sep	0.72	0.58	0.57	0.67	0.60	0.70	0.41