ann4

JANUARY 2000 57S I L V E R M A N A N D D R A C U P

Artificial Neural Networks and Long-Range Precipitation Prediction in California

DAVID SILVERMAN AND JOHN A. DRACUP

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

(Manuscript received 18 August 1998, in final form 5 March 1999)

ABSTRACT

Artificial neural networks (ANNs), which are modeled on the operating behavior of the brain, are tolerant ofsome imprecision and are especially useful for classification and function approximation/mapping problems, towhich hard and fast rules cannot be applied easily. Using ANNs, this study maps a 1-yr monthly (JanuaryDecember) time series of the 700-hPa teleconnection indices and ENSO indicators onto the water year (OctoberSeptember) total precipitation of Californias seven climatic zones, with different lag times between the inputsand outputs. It was found that the pattern of rainfall predicted by the ANN model matched closely the observedrainfall with a 1-yr time lag for most California climate zones and for most years. This research shows thepossibility of making long-range predictions using ANNs and large-scale climatological parameters. This researchalso extends the use of neural networks to determine important parameters in long-range precipitation predictionby comparing results gained using all the inputs with results from leaving an individual index out of the networktraining. This comparison gives insight into the physical meteorological factors that influence Californias rainfall.

1. Introduction

Although California includes seven distinct climaticzones (Fig. 1) in which duration and intensity of pre-cipitation vary markedly, all the zones have a well-defined wet season (NovemberMarch) separated by along dry season. Activity in the El NinoSouthern Os-cillation (ENSO) in the east Pacific and the 700-mbheight anomaly over North America has been shown tobe related to various phenomena in specific regions ofCalifornia (Kahya and Dracup 1993; Redmond andKoch 1991; Ropelewski and Halpert 1989, 1987, 1986;Barnston and Livezey 1987; Wallace and Gutzler 1981).Because these activities appear to influence Californiaprecipitation, they continue to be studied, for by notingtheir regional and global patterns of climate variability[National Drought Mitigation Center (NDMC 1998)],scientists may be able to use their recurring patterns ofchanges in the height anomaly and ENSO as tools forlong-range climate predictions.

The 700-mb circulation is a major force in the globalclimate and is a good measure of atmospheric circulation(speed and direction of the winds at about 3 km abovesea level). Patterns in the 700-mb height anomaly mayallow for regional precipitation predictions a year or

Corresponding author address: Dr. John A. Dracup, Civil and En-vironmental Engineering Department, University of California, LosAngeles, 5732 Boelter Hall, Los Angeles, CA 90095-1593.E-mail: [email protected]

more in advance based on the state of the system. Theteleconnection indices for the 700-mb height are derivedfrom a principal component analysis and as such rep-resent the major 700-mb pressure patterns.

The relationship between future California precipi-tation and both ENSO and the 700-mb height anomalyis most likely nonlinear and not easily determined byordinary statistical methods. Current methods have beenunable to detect the patterns or governing modes nec-essary for long-range precipitation prediction (Navoneand Ceccatto 1994; Venkatesan et al. 1997). Such fail-ures may have their source in the noise or fuzzinessinherent in the data, the overwhelming amount of data,in the nonlinear relationships involved, or in the limi-tations of current methods. Clearly, new methods thatcan analyze complex systems and their relationshipsneed to be explored. Artificial neural networks (ANNs)may be powerful enough to identify such relationships.

This study is the beginning of a larger study withintertwined goals. The first goal is to verify the hy-pothesis that 700-mb circulation patterns are a drivingforce of regional precipitation in California. The secondis that neural networks are able to determine patternsin the overwhelming amount of data. The third is toshow that a trained neural network contains knowledgeabout the modeled process that can be extracted.

2. Artificial neural networks (ANNs)a. Background

ANNs are based on biological models of the brainand the manner in which it recognizes patterns and

58 VOLUME 39J O U R N A L O F A P P L I E D M E T E O R O L O G Y

FIG. 1. Californias seven climate zones.

FIG. 2. The ANN feed forwardback propagation network is com-posed of an input layer of neurons, one or more hidden layers, andan output layer. Each layer comprises multiple units connected com-pletely with the next layer, with an independent weight attached toeach connection.

learns from example. The human brain contains morethan a billion neurons with trillions of interconnectionsworking simultaneously, enabling it immediately to pickan individual out of a crowd or to distinguish one voiceout of a babble of voices and background noisestasksthat are difficult or even impossible for the most pow-erful supercomputers. Its construct also allows the brainto learn quickly from experience. An ANN comprisesinterconnected simple processing units that work in par-allel, much as do the neuron networks of the brain, andwhich can discern patterns from input that is ill-defined,chaotic, and noisy. For an excellent laymans discussionon artificial neural networks, see Hinton (1992).

The advantages of using ANNs include the following(French et al. 1992; Raman and Sunilkumar 1995).

R A priori knowledge of the underlying process is notrequired.

R Existing complex relationships among the various as-pects of the process under investigation need not berecognized.

R Solution conditions, such as those required by stan-dard optimization or statistical models, are not preset.

R Constraints and a priori solution structures are neitherassumed nor enforced.

Disadvantages (Masters 1993) include exponential in-crease of training time with increased dataset size, un-certainty about network and training set size require-ments, and uncertainty about the relationships used bythe network to produce the networks output.

b. Structure

An ANN is composed of an input layer of neurons,one or more hidden layers, and an output layer. Eachlayer comprises multiple units connected completely

with the next layer (Fig. 2), with an independent weightattached to each connection. The number of nodes inthe output layer is equal to the number of values to bepredicted. In our network, we have one output node forthe yearly total precipitation. The number of nodes inthe hidden layer(s) is dependent on the process beingmodeled and must be determined by trial and error. Thenumber of nodes in the input layer is equal to the numberof input parameters. For our network, it is 12 monthsof the 17 teleconnection indices, or 204 input nodes.

Known values (e.g., monthly teleconnection indexvalues) are presented to the input nodes. As the inputnodes pass these values to the next level, the values aremultiplied by the weight of the connection. At the nextlevel, each processing unit (neuron) sums all of itsweighted inputs and then applies an activation functionto determine whether the neuron fires or remains dor-mant. The connection weights/neuron group, by firingor remaining dormant, determines the importance of thatparticular input to the overall prediction.

The activation function is normally the s-shaped sig-moid function of the form such as

1,

2x1 1 e

where x 5 the sum of all weighted inputs coming tothat node (Fig. 3). The function is scaled such that theasymptotes are either 0 and 1 or 21 and 1. This processis repeated for each successive layer, including the out-put layer.

During the training process, the error between thedesired output and the calculated output is propagatedback through the network (hence back propagation net-works). At the beginning of the training, all weightsare set to independent random values. The back prop-agation attempts to minimize iteratively the averagesquared error


FIG. 3. The sigmoid neuron activation function (1 1 e2x)21 (solid) and its derivative (dashed). The sigmoid function determinesthe activation level of a neuron based on the weighted inputs. Thederivative is used during network development to determine the levelof training a weight connection receives.

K12E 5 (y 2 d ) ,O k k2 k51

where E 5 error for a given training case, K 5 numberof output nodes, yk 5 calculated output, and dk 5 desiredoutput. This is done by computing the gradient for eachelement on the output layer

dk 5 dsk (yk 2 dk),

where dsk 5 the derivative of the sigmoid functionapplied at yk determined for each output node k. For thenext layer back, the gradient for the hidden layer is

K

d 5 ds d w ,Oj j k jkk51

where dsj 5 the derivative of the sigmoid function, andwjk 5 weight from hidden node j to output node k. Theweights are updated by

Dwjk 5 wjk 2 hdkyj

for the output layer and

Dwij 5 wij 2 hdjyi,

where h 5 the learning rate, for each layer back.Input sets are chosen randomly, and the weights are

adjusted by the above procedure until the error is min-imized or reduced to a predefined limit or the desirednumber of training periods, or epochs, is achieved.

3. Teleconnections

A teleconnection is a recurring and persistent rela-tionship between anomalous climatic phenomena in twodiscrete areas of the earth. Activity in one part of theearth can lead to climatic phenomena occurring in an-other part of the globe. ENSO refers to a large-scalecirculation pattern that is influenced by oceanatmo-

spheric phenomena in the eastern tropical Pacific. TheSouthern Oscillation, the atmospheric component, isgauged by the Southern Oscillation index (SOI), whichis the measure of the pressure difference between Tahitiand Darwin, Australia, and which is known to affectthe strength of the tropical Pacific trade winds. El Ninorepresents the oceanic component and is measured bythe sea surface temperature (SST) anomaly in the trop-ical Pacific Ocean.

The term ENSO embraces the interaction of atmo-sphere and ocean. ENSO activity, as well as that of otherteleconnections such as the MaddenJulian oscillation(Lau et al. 1988), is forced by changes in the tropicalSSTs and tropical convection (Mo and Livezey 1986;Barnston and Livezey 1991), which also affect jetstream locations and intensity, storm tracks, tempera-ture, and rainfall. For example, as the water temperatureincreases off the South American coastline, more wateris released into the atmosphere in the western hemi-sphere, providing a huge increase in the source of wateravailable in the West for precipitation. By extension,tracking the SSTs in the tropical Pacific can foreshadowclimatic conditions in parts of California and the north-western United States.

The 700-mb height anomaly embraces a number ofpersistent large-scale pressure patterns that cover theglobe and reflect the dynamics of the chaotic atmo-spheric system, including large-scale changes in the at-mospheric wave and jet stream patterns. These indicesrepresent a relationship in atmospheric pressure similarto that found for the SOI. Each index is a pressureoscillation between two distant points in the earths at-mosphere. For purposes of this study, we are concernedwith all 13 700-mb level patterns that lie over the North-ern Hemisphere. Full descriptions and example pressurepattern pictures can be found through the U.S. NationalOceanic and Atmospheric Administration (NOAA) Cli-mate Analysis Center Web site http://www.cpc.ncep.noaa.gov/data/teledoc.

4. Background

Although few studies applying ANNs specifically torainfall prediction have been reported (Thirumalaiahand Deo 1998), the use of ANNs in the field of waterresources overall in the past decade has grown exten-sively. ANN results are found to be superior when com-pared with those of other models using such methodsas linear regression, persistence, or nowcasting. Themathematical process used by ANNs is well docu-mented, but the physical meaning of each step used byANNs to manipulate data to arrive at their results is notknown and is constantly being researched, nor does thecontinued development of the ANN model give us anyadditional insight into the real process being studied.Yet the research referred to below indicates that ANNshave indeed great potential as an effective modelingtool.


Venkatesan et al. (1997) compared three neural net-work models to predict river elevations for total summerand two days in advance using upstream river elevationdata and the river elevation data at the gauge in questionfor the training. The network was able to accurately (r5 0.880.98) predict river elevations at the gauge inquestion. It was found that omitting the upstream datadid not significantly decrease prediction results.

Muttiah et al. (1997) compared ANN predictions of2-yr peak stream discharges with the output from mul-tivariate linear regression models for 17 river basins inthe continental United States. Results for the ANNswere comparable with those from the regression model.

Probably the most studied application of ANNs to thefield of hydrology is that for modeling the rainfallrun-off process. All studies are similar in methodology andresults. For example, Hsu et al. (1995) developed anANN model to study the rainfallrunoff process in theLeaf River basin, Mississippi. The network was com-pared with conceptual rainfallrunoff models, such asHydrologic Engineering Center (HEC)-I and the Stan-ford Watershed Model, and to linear time series models.The ANN was found to give the best one-step aheadpredictions. The authors emphasize that the ANN hasan unknown basis in the physical properties of a wa-tershed and that, from a conceptual standpoint, the mod-eling technique may not be desirable.

Ozelkan et al. (1996) used 500-mb atmospheric cir-culation patterns to predict precipitation one month inadvance. Their study used a fuzzy rule-based model andcirculation pattern indices developed by the researchersfor the prior 12 months to predict a months precipitationin various areas of Arizona. When results were com-pared with those from a regression model, the fuzzyrule-based model gave better results than did the re-gression model. January prediction was better than July,probably because July is the monsoon season in thestudy area and local factors may control.

These studies show that artificial neural networkshave a wide range of applicability and ability in the areaof water resources and that improvement over manyaccepted models and techniques is possible.

5. Data

Data in this study are based on two types of telecon-nections: ENSO and the 700-mb height anomaly. Com-plete datasets for the indices are available from 1951 tothe present.

a. ENSO

ENSO data in this study were obtained from theNOAA Climate Analysis Center. The data on SOI aremeasured following the method developed by Rope-lewski and Jones (1987). The El Nino data included inthis study are from the Nino-112 lying in 08108S, 908

808W, and the Nino-3.4 lying in 58N58S, 17081208W.All data are available on the Internet (NOAA 1998a).

b. 700-mb height data

NOAA has identified 13 teleconnection patterns inthe Northern Hemisphere using a rotated principal com-ponent analysis of the 700-mb height data (NOAA1998b). Following is a list of the prominent telecon-nection patterns and the regions and months of effect.

Prominent patterns over the North Atlantic:

North Atlantic Oscillation pattern (NAO) exists in allmonths.

East Atlantic pattern (EA) exists from September toApril.

East Atlantic jet pattern (EA Jet) exists from Aprilto August.

Prominent patterns over Eurasia:

East AtlanticWestern Russia pattern (EATLWRUS) exists from September to May.

Scandinavia pattern (SCAND) exists in all monthsexcept June and July.

PolarEurasia pattern (POL) exists from Decemberto February.

Asian summer pattern (ASU) exists from June to Au-gust.

Prominent patterns over North PacificNorth America:

West Pacific pattern (WP) exists in all months.East Pacific pattern (EP) exists in all months except

August and September.North Pacific pattern (NP) exists from March to July.PacificNorth American pattern (PNA) exists in all

months except June and July.TropicalNorthern Hemisphere pattern (TNH) exists

from November to January.Pacific transition pattern (PT) exists from May to Au-

gust.

The East AtlanticWestern Russia pattern and theScandinavia pattern are referred to by Barnston and Liv-ezey (1987) as the Eurasia-2 and Eurasia-1 patterns,respectively. The data run from 1950 to the present. Theindex values are available at http://www.cpc.ncep.noaa.gov/data/teledoc.

6. Methodology

This study is unique with regard to the input dataused, so no other model results are available with whichto compare accuracy or improvement. Model results canonly be compared with the observed values. There aretoo many inputs and not a sufficiently long dataset fora linear regression model.

Even though the network produces predictions, an-other goal is to determine which of the teleconnections


FIG. 4. Prediction periods used in the development of the neural networks. The inputdata are monthly index values for the calendar year. The predicted output is the totalprecipitation for the water year, OctSep.

are the most important in each zone for precipitationprediction and which interactions, if any, among theteleconnections are dominant. Because of this secondgoal, some aspects of the network training differ fromtraditional network training to enhance the ability toextract useful information from the trained network. Allthe recognized Northern Hemisphere teleconnection in-dices are included in the study to see if the network isable to discern useless information from important pa-rameters.

a. Development of a predictive neural network

The first step is to justify the use of neural networksand the teleconnection indices for precipitation predic-tion. The networks consist of an input layer with nodesfor each monthly value of the teleconnection indices, ahidden layer, and an output layer of a single node forthe predicted (OctoberSeptember) precipitation. Thelag-0 network is trained using the monthly data fora given year (JanuaryDecember) to predict the follow-ing water year (OctoberSeptember) precipitation; forexample, the input of JanuaryDecember 1990 predictsthe precipitation for October 1990September 1991.The lag-1 network is trained to predict the next wateryear precipitation; that is, input of JanuaryDecember1990 predicts the precipitation for October 1991Sep-tember 1992 (Fig. 4).

The general procedure for network development is tochoose a subset of the data containing the majority ofthe cases, train a network, and test against the remainingcases (Masters 1993). The first networks were trainedusing data for 19511987 and tested against 19881996.The number of hidden nodes were varied to determinethe best network structure. An ANN is trained until theroot-mean-square error is below a small error tolerance,in this case 0.0001 in. of rainfall. Because of its im-portance to Californias water supply, we chose Zone 3(Fig. 1) as a test case. The number of hidden nodes wasvaried from 2, 4, 8, 12, 16, and then 20. Each increasein the number of hidden nodes showed a slight increasein predictive ability. After 12 nodes, the rate of increasedecreased. Increasing from 20 to 50 nodes showed onlyslight improvement, so 12 nodes were chosen as thenetwork size for the rest of the study. After training,the network for each zonelag combination was run withthe complete dataset and the predictions for each yearwere recorded and compared with observed values.

b. Development of the networks for data extraction

In this study, again two separate neural networks foreach zone are trained using different lag times to predictthe total water year precipitation. The network archi-tecture and prediction periods are the same as before.The purpose of this networks development is to containas much information as possible determined from as fewexamples as possible.

The first step before training is to determine whichdataset will be used for developing the ANN. Normally,many examples of the process being modeled are avail-able, so a subset of the available examples is taken atrandom for training, with the hope that examples of allimportant patterns are included. With only 45 yr of com-plete data for the inputs, however, using a randomlyselected training set does not guarantee that all or evenmost patterns will be presented during the training pe-riod. To determine that the training set is fully compre-hensive without adding too much personal bias to thetraining (Masters 1993), small subsets of 5 yr of con-secutive data (195155, 195660, 196165, etc.) areused to train a series of networks. We again chose cli-mate Zone 3 (Fig. 1) for developing the 5-yr subsetmodels. The years successfully predicted by each mini-network are recorded. The process is repeated to ensurethat the ANN is finding patterns in the data and notgiving random results. The results show that the first 15yr (195155, 195660, and 196165) of data predictedall of the remaining years except for some years thatwere never predicted correctly by any subset. The train-ing set was set to these 15 yr (195165) plus the anom-alous yr (1974, 1975, 1980, 1981, 1984, 1985, 1992,1993) that were never predicted correctly. Twenty-threeyears of data were used to train the network to predict45 yr of precipitation. Other combinations of the 5-yrtraining sets could also predict all years correctly, butthe set chosen used the smallest number of years.

Again, we varied the number of hidden nodes to de-termine the best network structure with the new trainingset. Again, using Zone 3 as a test case, the number ofhidden nodes was varied from 2, 4, 8, 12, 16, and then20. Each increase in the number of hidden nodes showeda slight increase in predictive ability. Twelve nodes werechosen as the network size for the study. After training,the network for each zonelag combination was run withthe complete dataset and the predictions for each yearwere recorded and compared with observed values. In


TABLE 1. Individual training years for each lag and zone. The Xs represent years to be included in the training set.

Year

Lag 0

1 2 3 4 5 6 7

Lag 1

1 2 3 4 5 6 7

1951 X X X X X X1952 X X X X X X X1953 X X X X X X1954 X X X X X X X1955 X X X X X X1956 X X X X X X X X X X1957 X X X X X X X X X X1958 X X X X X X X1959 X X X X X X X X1960 X X X X X X X X X1961 X X X X X X1962 X X X X X X X1963 X X X X X1964 X X X X1965 X X X X X X X X X X1966 X X1967 X X X X X X1968 X X X1969 X X1970 X X1971 X X X X X X X X X1972 X X X X X X X X1973 X X X X X X X X X1974 X X X X X X X X X1975 X X X X X X X X X X1976 X X X X X X X X X X1977 X X X X X X X X1978 X X X X X X X1979 X X X X X X1980 X X X X X X X X X X X1981 X X X X X X X X X X X X X1982 X X X X X X X X X X X X1983 X X X X X X X X X X1984 X X X X X X X X X X X X X1985 X X X X X X X X X X X X X1986 X X X X X X X X X X X X1987 X X X X X X X X X X1988 X X X X X X X X X X X1989 X X X X X X X X X X1990 X X X X X X X X X X19911992 X1993 X

this case, the correlation value is a proxy for the amountof information contained in the network, so the valueis the correlation between the observed and predictedvalues for all years.

ANNs were also trained for each climate zone, omit-ting one variable at a time (i.e., using each combinationof 16 of the 17 inputs). In addition to leaving out onevariable, networks were also trained by, first, leavingout all ENSO indicators (SOI, Nino-112, and Nino-3.4)and, second, by using only ENSO indicators.

Training by the standard back propagation method iscomputationally slow, and the lack of time was pre-venting an exploration of different combinations of in-puts. By modifying the network training method to usethe conjugate gradient method (Masters 1993), trainingtime for the 14 cases decreased by 95%. With this in-creased performance, it was possible to determine a dif-

ferent training set using the 5-yr subset method de-scribed earlier for each zone and lag. Taking these in-dividualized training sets, networks were again trainedfor each zone and lag. The individualized training setsare shown in Table 1.

7. Results and discussion

a. Development of a predictive neural network

The correlations between the observed and predictedprecipitation for the verification cases for the 12-nodenetwork were 0.66, 0.73, 0.55, 0.39, 0.68, 0.61, and0.42 for the seven zones, respectively, for lag 1. Theresults for lag 0 were 20.07, 0.16, 0.17, 0.11, 0.6, 0.73,and 0.84. The lag-1 results show that the network canextract information necessary for prediction from the


TABLE 2. Correlation between observed and predicted precipitationwith the training set determined using Zone 3, lag 1 as the basis.

Lag

Zone

1 2 3 4 5 6 7

01

0.590.85

0.630.83

0.650.85

0.640.78

0.550.80

0.640.64

0.630.60

TABLE 3. Correlation between observed and predicted precipitation with the listed variable removed from the training set.

Zone Lag

Performance correlation with variable left out of training

NONE SOI N12 N34 NAO EA EAJ WP EP NP PNA EAW SCA TNH POL PT SZ ASU

11223

01010

0.590.850.630.830.65

0.60.80.60.80.7

0.60.90.60.80.7

0.60.90.60.80.7

0.60.90.70.90.7

0.60.80.60.80.6

0.60.80.60.80.7

0.60.80.60.80.6

0.60.90.60.80.6

0.60.90.60.80.7

0.60.90.60.80.7

0.60.80.70.80.7

0.60.90.70.80.7

0.60.90.60.80.6

0.60.90.60.80.7

0.60.90.70.80.7

0.60.90.60.80.6

0.60.90.70.80.7

34455

10101

0.850.640.780.550.80

0.80.60.80.60.8

0.80.60.80.60.8

0.80.60.70.60.8

0.90.70.80.60.8

0.90.60.70.50.8

0.80.60.80.60.8

0.80.60.70.60.8

0.80.60.80.50.8

0.80.60.80.60.8

0.80.60.80.60.8

0.80.70.80.60.8

0.90.70.80.60.8

0.90.70.80.60.8

0.80.60.70.60.8

0.90.70.80.60.8

0.80.70.70.60.8

0.80.70.80.60.8

6677

0101

0.640.640.630.60

0.60.60.60.6

0.70.60.60.6

0.60.60.60.5

0.70.60.60.6

0.60.50.60.5

0.60.60.60.6

0.70.60.60.5

0.60.70.60.6

0.60.60.60.6

0.60.60.60.6

0.70.70.60.6

0.60.60.60.6

0.60.60.60.6

0.60.60.60.6

0.70.70.60.6

0.60.60.60.6

0.60.70.60.6

indices and that a long-range predictive model is pos-sible. The lag-0 results show that the 700-mb atmo-spheric circulation is not, in general, a dominant factorin shorter-term prediction. This difference between theresults for the different lag periods was expected. The700-mb circulation on a global scale brings weather toa region. As the prediction period shortens, local con-ditions begin to dominate and, if strong enough, overridethe weather patterns brought in by the 700-mb circu-lation.

b. Development of the networks for data extraction

The ANNs were easily able to learn the new trainingset and gave consistent results over the three trainingattempts. Table 2 shows the correlation between the bestnetwork predictions of the three developed for each zoneand the observed precipitation for each zone for thedifferent lag times. Example graphs of the results arein Fig. 4. The high lag-1 prediction correlations againshow the ability of ANNs to produce good, long-rangepredictions. All zones except Zone 7 predict as well orbetter with lag 1 versus lag 0, although some zones wereabout equally good at short- and long-term prediction.Zone 7 is the desert area of California and gives a bettershort-term prediction, showing that the desert climatesystem has a more variable system that is easily changedby local changes in the atmosphere, while the otherzones are more persistent.

The improved lag-0 predictions using the new train-ing set show that for some years the 700-mb circulationis still a dominant force in the short term, but there are

other important parameters that have not been identified.The change in the results show that in the short term itis common for local conditions to overcome the short-term 700-mb conditions. The years used in producingthe refined training set must therefore contain some im-portant information about Californias precipitation thatbecomes muddied when most years are included in train-ing because the unidentified parameters that affect theshort-term prediction are not included in the training.

When the networks were trained for each climate zoneby omitting one variable, the correlations for these net-works were usually close to the full input networks (Ta-ble 3). The average absolute change in correlations byleaving out a variable during training was 0.023; theaverage change was 0.009. Table 4 shows those omittedvariables that caused a change in correlations of one(***) or two (XXX) standard deviations from the totalcorrelation change distribution. The changes in corre-lation do not appear to be random. Looking at the EPpattern, every zone except Zone 1 had more than onestandard deviation change in error for lag 0, but no effecton the lag 1. Leaving out most variables affected onlyone of the lag periods, showing that the ANN was find-ing distinct influences of the indices for different zonesand lags.

It also appeared that Nino-112 has no relationship tothe California climate, which was expected because ofNino-112s very small area.

The correlations for the ANNs trained by leaving outall ENSO indicators or by including only ENSO indi-cators (Table 5) show that these variables alone are notenough for a complete prediction. The correlations alsoshow that lag 1 is influenced more than lag 0 by ENSO,indicating the acknowledged time lag between the onsetof El Nino and its influence in California.

Looking at Fig. 5, we see that prediction phase (theupdown motion) follows the observed pattern in mostcases, but the magnitude is not predicted as well. Thenetwork usually predicts when there will be an increaseor decrease in rainfall totals, but does not always predict


TABLE 4. Correlation between observed and predicted precipitation with the listed variable removed from the training set; *** representschanges in correlation between one and two standard deviations, and XXX represents changes in correlation of more than two standarddeviations.

Zone Lag

Performance correlation error with variable left out of training

NONE SOI N12 N34 NAO EA EAJ WP EP NP PNA EAW SCA TNH POL PT SZ ASU

1 0 0.59 *** *** *** *** *** ***1 1 0.85 ***2 0 0.63 *** *** *** ***2 1 0.83 *** *** ***3 0 0.65 *** *** XXX ***3 1 0.85 *** *** XXX ***4 0 0.64 *** *** XXX4 1 0.78 *** XXX XXX *** XXX *** *** ***5 0 0.55 *** *** *** *** *** *** XXX XXX *** *** *** ***5 1 0.80 *** *** *** *** *** ***6 0 0.64 *** *** *** XXX XXX ***6 1 0.64 XXX *** XXX *** XXX *** *** *** ***7 0 0.63 XXX XXX XXX *** *** *** ***7 1 0.60 *** XXX *** XXX *** XXX *** *** *** *** *** *** ***

TABLE 5. Correlation between observed and predicted precipitationwith ENSO variables removed from the training set and with onlyENSO variables used for training.

Lag 1 2 3 4 5 6 7

No ENSO01

0.620.80

0.620.74

0.670.73

0.620.70

0.570.20

0.560.56

0.580.47

Only ENSO01

0.120.55

0.150.59

0.320.63

0.160.49

0.130.48

0.100.24

0.140.32

the magnitude of increase or decrease. Zone 6, lag 1shows this clearly. This indicates that the amount ofmoisture available for precipitation is not being pre-dicted correctly. In this study, the only indicator of mois-ture available for precipitation is the tropical Pacific SST(El Nino). Also, since the lag-1 predictions are madebefore an El Nino is fully developed, the true magnitudeand, therefore, the effect, of the El Nino event cannotbe accurately predicted. Including other sources, suchas North Pacific SST, and measures of moisture, suchas the Palmer Drought Severity Index, might increasethe accuracy. The lag-1 prediction for Zone 6 for theperiod October 1997September 1998 is 24.9 in. orabout 10 in. above the average. The prediction thatwould have been available January 1997 and made priorto the development of the 199798 El Nino, one of thelargest on record, would have predicted much greaterthan average rainfall. The actual amount received was34.4 in., an amount even greater than the prediction.The 199798 El Nino was a great source of atmosphericwater, and although the ANN indirectly predicted theEl Nino, it underpredicted its effects.

Another point that must be considered is the effectof the choice of the training set. The analysis thus faruses the networks trained on the training set developedfor Zone 3, lag 1. If the important patterns for predictionfor the other zones are not represented in that trainingset, then results may be poor. Using an optimized train-

ing set for each zone and lag improves the overall per-formance (Table 6). Except for Zone 7, no significantimprovements in lag-1 predictions were observed,showing that long-range prediction patterns are fairlyhomogeneous and leading us to believe that a simplerelationship between the indices and precipitation exists.The significant lag-1 increase in Zone 7 indicates thatit has a climate quite different from those of the othersix zones and therefore may need to be handled indi-vidually.

Lag-0 prediction improvements show that very dif-ferent patterns are necessary for long- and short-rangepredictions. The training set developed for Zone 3, lag1 is sufficient for Zones 16, lag 1. Further research willbe needed to ascertain if a single training set can be usedfor all the zones with lag 0 except, perhaps, Zone 7.

When considering the overall performance of theANN models, we find that those with the larger numberof hidden nodes predict better. A larger number of hid-den nodes enable the ANN to separate more patterns,although the difference between patterns becomes lessand less distinct as the number of nodes increases. Atthe limit, the network could specialize and match onlythe exact patterns presented. The difficulty lies in bal-ancing over- and undergeneralization to give an accurateprediction.

8. Conclusions

The results show the successful application of ANNsto long-range prediction of precipitation. The results sofar indicate the following.

1) The ANN model results show agreement with theaccepted views on the significant influence of ENSO.

2) The ANN model results agree that Nino-112 has noeffect on California precipitation.

3) The ANN model results agree that a lag relationshipexists between ENSO and its effects.


FIG. 5. Example prediction results.

TABLE 6. Correlation between observed and predicted precipitationwith the training set determined for each zone and lag independently.

Lag

Zone:

1 2 3 4 5 6 7

01

0.820.86

0.740.74

0.750.87

0.740.76

0.760.77

0.870.71

0.890.81

4) The ANN model results indicate which zones areaffected by which indices.

5) The ANN model results indicate the different effectsof different lags.

6) The ANN model results predict phases well.

Although the phase of the precipitation was well pre-dicted, the magnitude was only sometimes predicted.This may be because the magnitude of water sources

such as El Nino had not been fully developed. Data onother water sinks and sources beside those from thetropical Pacific may need to be incorporated. In general,teleconnections are good indicators of precipitation. Thelarger number of hidden nodes in the ANN does givebetter results, but training time must then be increasedand accuracy is decreased.

REFERENCES

Barnston, A., and E. J. Livezey, 1987: Classification, seasonality, andpersistence of low-frequency atmospheric circulation patterns.Mon. Wea. Rev., 115, 10821126., and , 1991: Statistical prediction of JanuaryFebruarymean Northern Hemisphere lower-tropospheric climate from the11-year solar cycle and the Southern Oscillation for west andeast QBO phases. J. Climate, 4, 249262.

French, M. N., W. F. Krajewski, and R. R. Cuykendall, 1992: Rainfall


forecasting in space and time using a neural network. J. Hydrol.,137, 131.

Hinton, G. E., 1992: How neural networks learn from experience.Sci. Amer., (9), 144151.

Hsu, K., H. V. Gupta, and S. Sorooshian, 1995: Artificial neuralnetwork modeling of the rainfallrunoff process. Water Resour.Res., 31, 25172530.

Kahya, E., and J. A. Dracup, 1993: U.S. streamflow patterns in re-lation to the El NinoSouthern Oscillation. Water Resour. Res.,29, 24912503.

Lau, N.-C., I. M. Held, and J. D. Neelin, 1988: The MaddenJulianoscillation in an idealized general circulation model. J. Atmos.Sci., 45, 38103832.

Masters, T., 1993: Practical Neural Network Recipes in C11. Ac-ademic Press, 493 pp.

Mo, K. C., and R. E. Livezey, 1986: Tropicalextratropical geopo-tential height teleconnections during the Northern Hemispherewinter. Mon. Wea. Rev., 114, 24882515.

Muttiah, R. S., R. Srinivasan, and P. M. Allen, 1997: Prediction oftwo-year peak stream discharges using neural networks. J. Amer.Water Resour. Assoc., 33, 625650.

Navone, H. D., and H. A. Ceccatto, 1994: Predicting Indian monsoonrainfall: A neural network approach. Climate Dyn., 10, 305312.

NDMC, cited 1998: Predicting drought. [Available online at http://enso.unl.edu/ndmc/enigma/predict.htm.]

NOAA, cited 1998a: CPC-data: Current monthly atmospheric andSST index values. [Available online at http://www.cpc.ncep.noaa.gov/data/indices/.], cited 1998b: Teleconnection pattern calculations. [Availableonline at http://www.cpc.ncep.noaa.gov/data/teledoc/telepat-calc.html.]

Ozelkan, E. C., F. Ni, and L. Duckstein, 1996: Relationship betweenmonthly atmospheric circulation patterns and precipitation:Fuzzy logic and regression approaches. Water Resour. Res., 32,20972103.

Raman, H., and N. Sunilkumar, 1995: Multivariate modeling of waterresources time series using artificial neural networks. Hydrol.Sci. J., 40, 145163.

Redmond, K. T., and R. W. Koch, 1991: Surface climate and stream-flow variability in the western United States and their relation-ship to large-scale circulation indices. Water Resour. Res., 27,23812399.

Ropelewski, C. F., and M. S. Halpert, 1986: North American precip-itation and temperature patterns associated with the El NinoSouthern Oscillation (ENSO). Mon. Wea. Rev., 114, 23522362., and , 1987: Global and regional scale precipitation patternsassociated with the El Nino/Southern Oscillation. Mon. Wea.Rev., 115, 16061626., and P. D. Jones, 1987: An extension of the TahitiDarwinSouthern Oscillation index. Mon. Wea. Rev., 115, 21612165., and M. S. Halpert, 1989: Precipitation patterns associated withthe high index phase of the Southern Oscillation. J. Climate, 2,268284.

Thirumalaiah, K., and M. C. Deo, 1998: River stage forecasting usingartificial neural networks. J. Hydrol., 3, 2631.

Venkatesan, C., S. D. Raskar, S. S. Tambe, B. D. Kulkarni, and R.N. Keshavamurty, 1997: Prediction of all India summer monsoonrainfall using error-back-propagation neural networks. Meteor.Atmos. Phys., 62, 225240.

Wallace, J. M., and D. S. Gutzler, 1981: Teleconnections in the po-tential height field during the Northern Hemisphere winter. Mon.Wea. Rev., 109, 784812.

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