Downscaling large-scale circulation to local winter rainfall in north-eastern Mexico

INTERNATIONAL JOURNAL OF CLIMATOLOGY, VOL. 17, 1069±1082 (1997)

DOWNSCALING LARGE-SCALE CIRCULATION TO LOCAL WINTERRAINFALL IN NORTH-EASTERN MEXICO

TEREZA CAVAZOS*

Department of Geography, The Pennsylvania State University, University Park, PA 16802, USA

Received 5 July 1996Revised 25 February 1997

Accepted 6 March 1997

ABSTRACT

The large-scale atmospheric controls on winter rainfall variability for north-eastern Mexico and south-eastern Texas arediagnosed based on 8 years (1985±1993) of daily data from the Goddard Space Flight Center four-dimensional dataassimilation scheme. Downscaling techniques based on arti®cial neural nets are used to derive transfer functions from thelarge-scale circulation to local precipitation. Daily rainfall amounts are predicted from synoptic sea-level pressure, 500 hPaheights, and the 1000±500 hPa thickness, and summed over the cool season (NDJF). The monthly rainfall totals are alsopredicted independently from other indices of the large-scale circulation, such as 1000±500 hPa thickness, the Paci®c/NorthAmerican (PNA) pattern, and a standardized Southern Oscillation Index (SOI) derived from the Tahiti minus Darwin sea-levelpressure difference.

Time-lagged component scores from a rotated principal component analysis of sea-level pressure, 500 hPa heights, and1000±500 hPa thickness serve as input to a neural net that produces time-series of daily rainfall amounts for 20 grid-points inthe study area. The correlation between the observed and predicted rainfall is greater than 0�7 in the coastal plains of the Gulfof Mexico and less than 0�7 over the Sierra Madre and the Gulf, suggesting an increase in the importance of local rainfallprocesses in the last two regions. The analysis shows a systematic relationship between the performance of the net andphysiography, which is con®rmed by the consistency of the patterns of spatial correlation, mean absolute error, and root-mean-square error at different time-scales.

The net captures the phase and amplitude of most of the rainfall events, re¯ecting the in¯uence of the large-scalecirculation. However, interannual ¯uctuations in rainfall associated with persistent El NinÄo conditions are partly bypassed bythe net, suggesting that more information is needed to predict extreme events. The PNA pattern does not seem to be associatedwith local rainfall in north-eastern Mexico and south-eastern Texas during the period analysed. # 1997 by the RoyalMeteorological Society. Int. J. Climatol., 17: 1069±1082 (1997)

(No. of Figures: 9 No. of Tables: 2 No. of References: 47)

KEY WORDS: Downscaling; neural nets; winter rainfall; El NinÄo; north-eastern Mexico; southern Texas

INTRODUCTION

One of the most important sources of winter climate variability in the subtropics is associated with the incursion

of cold-air outbreaks from higher latitudes. In particular, frontal penetrations into the Gulf of Mexico precede

cold surges from the Rocky Mountains (Tilley, 1990; Mecikalski and Tilley, 1992; Colle and Mass, 1995) that are

associated with polar anticyclones from north-western Canada (Dallavalle and Bosart, 1975). In eastern Mexico,

the anticyclonic circulation following the passage of cold-air incursions is known as Nortes, and it has a marked

impact on the weather and climate. Of special importance for agriculture are the light rains, low temperatures,

and the damaging frosts generated by the Nortes during the cool season (NDJF). There is also considerable

evidence that the low/warm phase of the Southern Oscillation (El NinÄo events) in¯uences the North American

winter circulation in the mid-latitude and subtropical sectors (Horel and Wallace, 1981; Wallace and Gutzler,

CCC 0899-8418/97/101069-14 $17.50

# 1997 by the Royal Meteorological Society

*Correspondence to: Tereza Cavazos, 333 Walker Bldg., Department of Geography, The Pennsylvania State University, University Park, PA16892, USA, Tel. (814) 861-5881. E-mail: [email protected] grant sponsor:Fulbright-Conacyt and UANL-Mexico.

1981; Shukla and Wallace, 1983) by enhancing a strong ridge over north-western Canada and a strong subtropical

westerly jet across Mexico and the Gulf of Mexico (Kiladis and Diaz, 1989). Accordingly, most El NinÄo winters

have been documented as wet (Ropelewski and Halpert, 1986, 1987, 1989; Rogers, 1988; Kiladis and Diaz, 1989;

Cavazos and Hastenrath, 1990) over north-eastern Mexico and the southern USA from Texas to Florida. These

and other studies (e.g. MosinÄo, 1963; Klaus, 1973) suggest that the winter climate of north-eastern Mexico

depends on the large-scale circulation.

The objective of this study is to diagnose the large-scale atmospheric controls on the local winter rainfall of

north-eastern Mexico and the southernmost portion of Texas. Large-scale circulation at the Earth's surface and at

the 500 hPa height level are considered in this analysis for the entire geographical window shown in Figure 1. It

is well known that rainfall is also dependent on local processes, so that a complete speci®cation of winter

precipitation is unlikely. This may be particularly true in the present case, where the regional-scale study area

(smaller window in Figure 1) includes the Gulf of Mexico and the Sierra Madre Oriental, the latter having

altitudes exceeding 2000 m in some parts. However, downscaling techniques based on non-linear arti®cial neural

networks have been applied successfully to derive transfer functions empirically from the large-scale ¯ow

(1000 km) to the regional precipitation, with a spatial scale that ranges from a few kilometres to several hundred

kilometres (e.g. Hewitson and Crane, 1992, 1994a, 1996; Hastenrath et al., 1995). Thus, neural nets are used here

to predict rainfall through transfer functions from the large-scale circulation. The predictive skill of the neural net

is then taken as a measure of the local rainfall variance that can be attributed to the large-scale circulation.

BACKGROUND CLIMATOLOGY

North-eastern Mexico (Figure 1) is located in a subtropical region where the Sierra Madre Oriental and the Gulf

of Mexico play an important role in the weather and climate. The circulation over north-eastern Mexico is

strongly affected by the North Paci®c and North Atlantic high pressure systems, which are displaced southward

Figure 1. Large-scale study area. Inset: regional-scale study area in north-eastern Mexico and the southernmost portion of Texas

1070 T. CAVAZOS

INT. J. CLIMATOL, VOL. 17: 1069±1082 (1997) # 1997 Royal Meteorological Society

during the boreal winter. The coastal plain adjacent to the Gulf of Mexico is generally under the in¯uence of the

trade wind inversion that is enhanced by radiational cooling of the mid-troposphere and by upper tropospheric

convergence. As a consequence, only 10 per cent of the annual precipitation falls during the cool season

extending from November through to February. Although low in amount, winter precipitation is important for the

®rst seeding-time of the year for agriculture, which is dependent largely on winter rainfall. On the other hand,

precipitation amounts may vary drastically from year to year and on decadal periods; for example, the 1985±1993

winter contribution to the annual precipitation was approximately 25 per cent.

The upper-tropospheric circulation is dominated by the Subtropical Westerly Jet, with westerlies extending

deep into the tropics during the cool season (Hastenrath, 1988, p. 107). The north-westerly winds are stronger and

penetrate farther east in winter and early spring, when they are sometimes associated with outbreaks of cold

continental air. The rainfall that occurs during the cool season takes place with the passage of cold fronts.

DiMego et al. (1976) have suggested that the trade wind inversion may actually disappear in some cases during a

pre-frontal period, thus better permitting convection. After the passage of the front, winds back with time and

with height and are accompanied by cold advection, subsidence, and increased stability. Air trajectories in the

descending cold air curve anticyclonically. This subsidence and destruction of vorticity support the development

of a low-level anticyclone over the Gulf of Mexico (DiMego et al., 1976). The resulting return ¯ow of modi®ed

polar air into the continent and to the Sierra Madre Oriental is characteristic of a Norte event. Thus, winter

precipitation along the Gulf Coast region is also strongly affected by the differential heating between land and

ocean and by topography (orographic uplift) within travelling winter storms such as cold fronts and Nortes. The

topographic effect is evident from Figure 2), where the mean winter (NDJF) total precipitation shows a variable

structure on scales of less than a few hundred kilometres; greater effects are observed in the form of a tongue

along the piedmont of the Sierra Madre Oriental. Modi®ed shallow air masses that move over the Sierra Madre

usually develop a stratiform cloud deck (Fitzjarrald, 1986) that may appear independent of the upper level

convergence. In other situations, the moist air is deeper and tropical in nature and can lead to deep convection

(Crisp and Lewis, 1992). Consequently, an analysis of the vertical structure of the atmosphere on time scales of

less than a week are fundamental to determine the in¯uence of the main large-scale controls on winter rainfall in

this region.

In a global-scale context and on longer time-scales (seasonal-interannual), El NinÄo±Southern Oscillation

(ENSO) events seem to modulate the rainfall variability of the study area. Rasmusson and Mo (1993) have

suggested a `Mexican connection' that links the wintertime ENSO circulation anomalies of the Paci®c with the

circulation anomalies over the western equatorial Atlantic. Past studies (Erickson, 1979; Douglas and Englehart,

1981; Iskenderian, 1995) have also documented cloud masses originating along the central equatorial Paci®c

during the northern winter of El NinÄo years and tracking into the Gulf of Mexico, to produce heavy rainfall over

the Gulf coast.

Figure 2. Mean total winter (NDJF) precipitation (mm) in north-eastern Mexico and south-eastern Texas for the period November 1985±February 1993. Data from the Goddard Space Flight Center four-dimensional assimilation scheme

LARGE-SCALE CIRCULATION AND LOCAL RAINFALL 1071

# 1997 Royal Meteorological Society INT. J. CLIMATOL, VOL. 17: 1069±1082 (1997)

DATA

The observational records for this study consist of 8 years (1985±1993) of daily winter (NDJF) climate data from

the Goddard Space Flight Center (GSFC) four-dimensional assimilation scheme (Schubert et al., 1993) for grid

cells on a 2� latitude by 2�5� longitude grid over northern Mexico and the southern USA (larger area in Figure 1:

22�±34�N; 110�±90�W). Winter is considered from November to February in this particular study because the

main occurrence of cold-air outbreaks and Nortes is during these months. The grid values of the sea-level

pressure (SLP), 500 hPa geopotential heights, and 1000±500 hPa thickness (derived from the 500 hPa heights

minus the 1000 hPa heights difference) for the large-scale study area were regridded to a 4�65� grid to ®t the

Goddard Institute for Space Studies (GISS) general circulation model (GCM). The thickness ®eld is based on

500-hPa heights and SLP and the conversion of the latter ®eld to 1000-hPa heights via application of the

hypsometric equation. It should be noticed that although the use of sea-level pressure adjustments over complex

terrain may lead to bogus results, the pressure pattern remains a worthwhile approximation on a monthly basis.

Data on daily precipitation were used at the original 2�762�5� GSFC grid resolution for 20 grid-points that

correspond to the regional-scale area in north-eastern Mexico and the southernmost portion of Texas (small

window in Figure 1: 22�±30�N; 102�5�±95�W). The complete daily record taken at 0000Z (5 pm local time)

contains a total of 962 winter days with no data gaps from November 1985 to February 1993.

Mean monthly indices of the large-scale circulation were also used in this study to characterize and to predict

monthly winter rainfall for the same period of analysis (32 winter months). Values of the standardized Paci®c/

North American pattern (PNA) and the Southern Oscillation Index (SOI), the latter derived from the standardized

Tahiti minus standardized Darwin sea-level pressure, were obtained via anonymous ftp from the NOAA/NWS/

NMC/Climate Analysis Center.

METHOD

Principal component analysis

The data analysis is based on rotated principal component analysis (RPCA) and non-linear arti®cial neural

network (ANN) techniques. This method is similar to that of Hewitson and Crane (1992) for southern Mexico.

However, one of the advantages of the present analysis is the use of 20 grid-points over the regional-scale study

area (Figure 1) instead of a single area-average point. An S-mode principal component analysis (PCA) was used

to identify the primary modes of variance of the SLP, 500 hPa height ®eld, and the 1000±500 hPa thickness ®eld

across the grid-points of the larger region shown in Figure 1. The primary advantage of the PCA solution is

its ability to compress the complicated variability of the original data set into a relatively few temporally

uncorrelated components (Richman, 1986). The component loadings and time series were computed from the

correlation matrix. The number of components to retain for rotation was decided by applying Rule-N of Overland

and Preisendorfer (1982). This rule calculates the point at which an eigenvector is as likely to be due to random

noise as to some real feature of the data. Four components for each of the circulation ®elds were retained for

rotation. Then the components were rotated orthogonally using the varimax method, which causes the loadings of

the RPCs to be distributed widely with a few large loadings and many close to zero. Hence the new rotated

components are more likely to be objective weather `types' in the sense that their spatial patterns more closely

resemble the observed regional anomaly ®elds (Ladd and Driscoll, 1980).

To examine the relationship between the circulation features represented by the RPC loadings and local

rainfall, time series of scores for each rotated component were obtained by multiplying the original data by the

PC score coef®cients. The score of each day on each component represents the degree to which that spatial

pattern of variance is present in that day's circulation ®eld. The local response may vary depending on the

synoptic history of particular storm tracks and air masses (Hewitson and Crane, 1996); accordingly, the

component score time series of each circulation ®eld were time lagged (from 2 to 5 days) to determine the period

that best explained the local rainfall variance. Four-day lag matrices performed best as multivariate indices of the

atmospheric circulation and therefore were used as predictors of preciptation in the neural network analysis.

1072 T. CAVAZOS


Transfer functions from an arti®cial neural net (ANN)

In recent years, the derivation of empirical transfer functions has been the topic of many studies, especially

those related to climate downscaling (e.g. Karl et al., 1990; Wigley et al., 1990; von Storch et al., 1993; Carbone

and Bramante, 1995; Hewitson and Crane, 1996;), climate prediction (e.g. Hastenrath et al., 1995), climate

change (e.g. von Storch et al., 1993; Hewitson and Crane, 1996), and downscaling applications (Hewitson and

Crane, 1994a). The empirical approach is used to derive transfer functions from the large-scale circulation to

local-scale climate using a statistical or mathematical relationship. In this study, an arti®cial neural network

(ANN) is used to derive a direct mathematical relationship between the atmospheric circulation and the local

climate variable.

The ANN technique has the ability to generalize relationships after being `trained' in a self-organizing learning

process through a procedure that minimizes the output error. Although ANNs are analogous to multiple

regression, the attractiveness of ANNs lies in their ability to, in theory, represent any arbitrary non-linear

function, and their capability to generalize a relationship from only a small subset of data (Hewitson and Crane,

1994b). the neural net used in this study is a feed-forward type of neural network that learns via back propagation

(Figure 3). The back-propagation algorithm used is the NevProp version 1.16 developed by researchers at the

University of Nevada Center for Biomedical Modeling Research, and it was obtained via anonymous ftp.

Several net con®gurations had to be constructed, on a trial-and-error basis, to ®nd the simplest design of nodes

and layers. The best results were obtained with a single hidden layer, which doubles the number of nodes of the

input layer (Figure 3). The neural net was trained using 75 per cent of the daily circulation indices, represented by

700 consecutive days, for which the desired target precipitation (O) was known; the remaining 25 per cent (238

days) was reserved as an independent data set to validate the net. The training and testing data sets were not

originally randomized because the neural net package did not have that option. Before starting the training

process, a random seed generator was used to initialize the weights, W, to small numbers. Then each input node,

xi, was connected to every hidden node through a separate weight, wi, which acts as a multiplier of the input

value, xi. This may be expressed as follows:

Netk �P

xiWi j

Figure 3. Example of a simple feed-forward arti®cial neural network (ANN) that learns via back-propagation. In this study the input vector Xrepresents daily atmospheric indices from a RPCA that are used to predict local precipitation (target)



Figure 4. Spatial winter (NDJF) patterns of rotated component (RPC) loadings in northern Mexico and the southern USA for (a) SLP,(b) 500 hPa geopotential heights, and (c) 1000±500 hPa thickness for the period November 1985±February 1993. Variance explained is inparentheses. Darker shades represent a maximum loading of 0�9, except for component 4 of SLP and thickness, which is 0�5. Interval is 0�1 in

all cases

1074 T. CAVAZOS


where Netk refers to the summation of the weighted inputs during the kth training iteration. The Net signal is

usually further processed by an activation function F to produce the node's output signal,

Pk � tan h�Netk�The output vector Pk is a simple S shaped bipolar hyperbolic tangent function of the weighted summation of the

nodes in the input and hidden layers, ranging from 71 to 1. Before training, the target vector O (the observed

precipitation) was scaled initially to 70�4/� 0�4 to ®t within the node output range of the hyperbolic tangent

error function and also to avoid its asymptotic areas. With each training iteration k, the root-mean-square error

(RMSE) is calculated by comparing the daily predicted output (Pi) with the desired target precipitation (Oi)

RMSEk � �Nÿ1P �Pi ÿ Oi�2�12

where the summation is from i� 1 to N training days (or testing days for the RMSE of the test data set). The

output error is then back-propagated through the net to determine the weights for the next training iteration in a

way that minimizes the error according to a given threshold. After each training iteration the net is validated

using the test data set, although the errors are not used to adjust the weights at this step; only data from the

training data set are used to train the net. Training continues until the RMSE of the test data set reaches a

minimum. The data sets were trained ®ve times with 250 iterations to obtain the random seed that generated the

lowest RMSE in the test data set. After that, the net was trained once again with the same random seed but this

time the net was stopped and the weights saved at the training iteration that had the lowest overall error (training

and testing). The ®nal stage of neural net training entailed experimenting with different input combinations to

select the atmospheric indices that explained the largest amount of the winter rainfall variance over the study

area. Each of the 20 grid-points of the regional-scale study area (Figure 1) were trained individually in order to

obtain the spatial and temporal diagnosis presented in the following sections.

The forecast skill of the neural set was de®ned initially by the RMSE of the training and testing data sets, as

explained above. After training, the mean absolute error (MAE) between the unscaled values of P and O was also

obtained to evaluate the performance of the net.

MAE � Nÿ1P jPi ÿ Oij

A correlation (r) analysis between predicted and observed precipitation and the coef®cient of determination (r2)

to measure variance explained were also calculated.

Figure 5. Winter (NDJF) spatial correlation patterns of observed and neural net predicted daily precipitation smoothed with a 5-day ®lter.(a) Training period, November 1985±February 1991; (b) testing period, November 1991±February 1993



RESULTS AND DISCUSSION

Principal modes of the large-scale circulation

The spatial patterns association with the four leading RPCs of SLP, 500 hPa heights and 1000±500 hPa

thickness collectively describe between 92 per cent and 94 per cent of the original data set variance. Figure 4

Figure 6. Neural net predicted (P) and observed (O) daily winter (NDJF) rainfall (mm) smoothed with a 5-day ®lter for a selected grid-point(2�62�5� area) in southern Texas (30�N, 100�W). Correlation (r)� 0�86 for the training period and r� 0�77 for the testing period

Figure 7. Same as Figure 6 but for a grid-point located to the north-east of the Sierra Madre Oriental in the state of Nuevo LeoÂn, Mexico(26�N, 100�W). r� 0�79 for the training period and r� 0�74 for the testing data set

1076 T. CAVAZOS


shows the loadings of the rotated PCs for the three circulation ®elds. More than 60 per cent of the variance

explained by the ®rst three components is observed over the Gulf of Mexico, the Central Plains of the USA, and

the Paci®c region. The distribution of variance represented by the component loading patterns match the

circulation features that generate the winter rainfall in the study area, as described before. Very interesting is that

the maximum variance explained by the ®rst mode in each of the three ®elds (SLP, 500 hPa height, and 1000±

500 hPa thickness) is observed over the coastal plains of the Gulf of Mexico and the Gulf itself. This re¯ects the

in¯uence of the North Atlantic High and the divergent branch of the subtropical westerly jet on the Atlantic side.

The ®rst RPC also highlights the importance of synoptic systems and storm tracks over the gulf region (e.g.

Table I. North±south cross-section of the neural net predicted (P) and observed (O) total winter (NDJF) precipitation (mmseason71): days, the number of days of the season; MAE, the mean absolute error (MAE) (mm day71), and r2 the percentageof variance explained. Grid-points are: Sierra Madre (SM), Nuevo LeeÂn, Mexico (NL), and southern Texas (TX). Extremewinter events of the Southern Oscillation are indicated as L (for low/warm El NinÄo) and H (for high/cold non-El NinÄo).

Training period, November 1985±February 1991; testing period, November 1991±February 1993)

100�W, 24�N: SM 100�W, 26�N: NL 100�W, 30�N: TX

Winter Days P O MAE r2 P O MAE r2 P O MAE r2

1985/86 117 142�5 137�0 1�26 43 157�7 155�9 1�09 76 146�8 113�7 0�67 901986/87 (L) 117 219�6 392�4 2�21 53 214�5 320�6 1�62 66 236�0 256�0 1�12 791987/88 118 141�0 187�6 1�65 25 109�1 158�0 1�18 30 115�2 118�9 1�01 361988/89 (H) 117 179�0 124�3 1�33 47 154�8 107�8 0�92 88 139�6 107�8 0�70 671989/90 117 175�2 180�3 1�26 58 131�7 144�8 1�05 55 166�3 106�6 0�69 881990/91 117 155�6 166�4 1�35 69 138�0 164�5 1�14 69 148�5 147�3 0�95 691991/92 (L) 118 208�1 451�7 3�23 39 210�1 322�9 2�10 59 226�2 282�8 2�11 581992/93 (L) 117 134�3 284�9 1�70 34 151�7 229�2 1�36 52 140�6 161�1 1�24 69

Average precipitation(mm season71)

169�5 240�6 158�5 200�5 164�9 161�8

Figure 8. Same as Figure 6 but for a grid-point located on the Sierra Madre Oriental (24�N, 100�W). r� 0�66 for the training period andr� 0�58 for the testing data set



convective activity and Norte events). The second component of the SLP and 500 hPa height ®elds is associated

with the synoptic systems resulting from cyclogenesis on the lee side of the Rockies. The second component of

thickness and the third component of SLP and 500 hPa heights represent the in¯uence of the North Paci®c High

and the southern branch of the subtropical jet stream. The minor variance represented by the fourth component of

SLP and thickness relates to synoptic systems over the Mexican Plateau. The synoptic forcing mechanisms over

the key regions of maximum variance, displayed in Figure 4, are assumed to plan an essential role in the winter

rainfall variability over north-eastern Mexico and south-eastern Texas. Thus, the daily relationship between each

circulation pattern and local precipitation over the study area is derived from using circulation indices,

represented by 4-day lagged component scores, as inputs for the neural networks.

Daily neural net results

A training combination that included the circulation indices from the SLP, 500 hPa geopotential heights, and

1000±500 hPa thickness ®elds produced the best predictions of daily winter (NDJF) rainfall over the whole study

area. Figure 5 shows the spatial correlation patterns between observed and predicted winter rainfall for the

training (November 1985±February 1991) and testing (November 1991±February 1993) periods. The neural net

performs best along the coastal plains of the Gulf of Mexico, explaining more than 56 per cent (r� 0�75) of the

rainfall variance during the training period (Figure 5(a)) and a maximum of 49 per cent (r� 0�7) during the

testing period (Figure 5(b)). Separate net analyses using the same circulation indices individually suggest that

500 hPa height and the thickness ®elds have an overall stronger in¯uence on local rainfall than does sea-level

pressure. This result implies that during the period analysed the mid-tropospheric circulation controls were

signi®cantly more important. Although the 500 hPa height ®eld helps to determine the upper air synoptic forcing

Figure 9. Spatial winter (NDJF) patterns of (a) root mean square error (RMSE) and (b) mean absolute error (MAE) between predicted andobserved precipitation (mm) from a daily neural net analysis for the period November 1985±February 1993.

Table II. Meridional cross-section (100�W longitude) of average daily measures from a neural net analysis for the winter(NDJF) period of November 1985±February 1993 (938 days). Pm and Om are the mean predicted and mean observed dailyprecipitation (mm), respectively. The percentage difference is (Pm7Om)/Om. MAE is the mean absolute error and RMSE isthe root mean square error. A negative percentage difference indicates the predicted precipitation is underestimated. Grid-

points as in Table I

Grid Pm Om Difference MAE RMSE r2

TX 1�40 1�38 (� ) 1�5 1�06 2�06 67�2NL 1�35 1�70 (7) 20�6 1�31 2�36 59�3SM 1�44 2�05 (7) 29�8 1�75 3�16 38�4

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mechanisms, such as meridional and zonal wind ¯ows, the thickness ®eld conveys important information about

the thermal structure of the vertical layer, especially during frontal events. These two ®elds may re¯ect the

strength and location of the subtropical westerly jet over the study area through the change of height and

temperature in the vertical layer.

The contribution of the large-scale circulation to the rainfall variance is further disclosed in Figures 6±8

through the daily performance of the neural net for three grid-points along the 100�W longitude: at 30�N on the

coastal plains of southern Texas, at 26�N on the piedmont of the Sierra Madre in the state of Neuvo LeoÂn, and at

24�N over the complex terrain of the Sierra Madre Oriental. Each grid covers an area of 2�5� longitude by 2�

latitude, with the grid-point in the centre. The skill of the net in this north±south cross-section displays some

similarities: (i) overall the prediction is better during the training period; (ii) the neural net captures the phase of

many of the large precipitation events; and (iii) the net tends to overestimate small events and underestimate large

rainfall events.

The net is successful at reproducing the phase and, to some degree, the amplitude of large precipitation events

during the training period by explaining 74 per cent (r� 0�86) of the rainfall variance in southern Texas (Figure

6(a)) and 62 per cent (r� 0�79) in Nuevo LeoÂn, Mexico (Figure 7(a)). In the complex terrain of the Sierra Madre

Oriental, where rainfall is the largest for the region, the net is less effective at reproducing these events (Figure 8).

During the testing period (Figures 6(b), 7(b), and 8(b)), the net is still able to identify extreme events, but the

amplitude of the predicted rainfall is not consistent with the observed precipitation. This is also noticed in Table

I, which shows that the largest underestimation of precipitation (and the largest MAEs) along the north±south

cross-section is for the anomalously wet winters of the test data set. The presence of strong El NinÄo events (e.g.

1991±1993) may be one reason why the skill of the net and the correlation between the observed and predicted

rainfall (Figure 5) are so much lower for the test data set, although the net is still relatively skilful in capturing a

great deal of the rainfall variance over the coastal plains.

The skill of the net decreases from the coastal plains of Texas to the Sierra Madre Oriental. This is re¯ected in

the spatial patterns of the correlation that follow the piedmont of the Sierra Madre (Figure 5(a)), where the

variance explained decreases with altitude. The variance explained also decreases over the Gulf of Mexico. This

suggests an increase in the importance of local processes in these regions (e.g. orographic lifting over the Sierra

Madre and convection over the Gulf). The analysis reveals a systematic relationship between the performance of

the neural net and physiography, which is con®rmed by generally high consistency among the spatial patterns of

correlation (Figure 5) and MAE and RMSE (Figure 9) in intraseasonal and interannual time-scales). Table II

shows the measures of performance of the daily neural net analysis for the meridional cross-section. The best

results are observed again in the coastal plains of Texas (TX), where the percentage difference ratio between the

mean of the neural net predicted (Pm) and the observed (Om) precipitation is close to zero. However, the measures

of performance (MAE and RMSE) indicate that on a daily basis the residual precipitation is different from zero,

suggesting the presence of extreme values, especially to the south of the cross-section (e.g. NL and SM in Tables

I and II), where the errors are much in¯ated.

On average, the neural net tends to underestimate precipitation as indicated by the negative percentage

difference (Table II) in the centre and south of the cross-section. However, on daily and seasonal bases,

underestimation is enhanced during El NinÄo winters (L in Table I), when precipitation is larger, while

overestimation arises during dry winters (e.g. non-El NinÄo winters: H in Table I). This may be due to several

factors: (I) the presence of external forcings during extreme events, (ii) the lack of randomization of the input

vector to the neural net, and (iii) the tendency of the neural net to generalize relationships based on the training

patterns. Thus, accuracy could be improved by introducing new input variables to account for extreme events and

by randomizing the data before neural net training.

Monthly teleconnections

The results from the daily neural net analysis reveal that the large-scale circulation exerts a signi®cant control

on the winter rainfall variance. However, the inability of the net to completely explain the rainfall variability

during strong ENSO (e.g. L and H in Table I) winters shows the vulnerability of the study area to extreme events

and suggests that other large-scale forcings not considered in this study were also involved in precipitation



processes. Thus, frequent ENSO conditions during the period 1985±1993 suggest the need to support the daily

®ndings with an analysis of larger scale teleconnection patterns.

Mecikalski and Tilley (1992) have shown that cold surges that pentrate to the Gulf of Mexico tend to be

associated with strong height gradients and low geopotential heights at the 500 hPa level over the subtropics and

strong riding over western Canada. Some authors (Wallace and Gutzler, 1981; Yarnal and Diaz, 1986; Kiladis

and Diaz, 1989; Wallace et al., 1990) have related this kind of cold winter response to the positive phase of the

PNA pattern, which also is partially related to forcing by El NinÄo warm events (Horel and Wallace, 1981).

Accordingly, these studies suggest a teleconnection between El NinÄo events, the PNA index, and rainfall activity

in north-eastern Mexico and south-eastern Texas. Thus, monthly analyses were also assessed for the same study

period (1985±1993) using 1000±500 hPa thickness scores from a rotated PCA, the SOI and the PNA index as

input vectors for the neural net.

The monthly results indicate that the PNA index does not seem to play a role in the local rainfall variance, at

least for the 1985±1993 period. The results also show that the SOI and the thickness scores explain more than 70

per cent of the rainfall variance in the grid-points that are close to the piedmont of the Sierra Madre Oriental. As

with the daily analysis, the correlation between neural net predicted and observed precipitation also decreases

with altitude. Very distinctive, however, is the decrease of the correlation pattern away from the Sierra toward the

coastal plains of the Gulf of Mexico. Cavazos (1994) found similar correlation patterns between the SOI and

January±February rainfall in the state of Nuevo Leon, Mexico for the period 1940±1988. These results indicate

that the thickness and the SOI alone have a strong association with the rainfall variance on the windward side of

the Sierra Madre, where rainfall is especially enhanced (reduced) during El NinÄo (non-El NinÄo) events. However,

wetter than normal conditions were observed during El NinÄo winters not only on the piedmont of the Sierra but

also in the coastal plains, as can be seen in Table I. The El NinÄo-related anomalies in the study region are further

substantiated by Kousky (1987, 1993) who has reported that negative height anomalies and negative anomalies of

outgoing longwave radiation (OLR) (indicating enhanced convection) prevailed in the northern Gulf of Mexico

during the winter of 1986±1987 and all over Mexico and the Gulf of Mexico during the mature phase of the

1991±1992 ENSO. Bell and Basist (1994) have also documented that negative OLR anomalies were observed in

northern Mexico and the southern USA during most of the winter of 1992±1993. These conditions favoured

above normal precipitation in the study area. On the contrary, the other ®ve winters of the analysis have been

documented as having positive or near-normal height and OLR anomalies (e.g. Halpert, 1988; Arkin, 1989;

Janowiak, 1990; Chelliah, 1993; Bell and Basist, 1994), which contributed to drier than normal conditions over

the region. Accordingly, daily and monthly neural net results suggest that for a region with an orographic

structure, such as north-eastern Mexico, and for a time series that comprises several events, such as ENSO, the

incorporation of other dynamic circulation ®elds (e.g. 700 hPa heights, OLR, moisture at different levels, etc.)

into the analysis may help to increase the contribution of extreme events to the rainfall variance.

SUMMARY AND CONCLUSIONS

Results from a rotated principal component analysis show that the most important sources of winter variance of

the large-scale circulation patterns (SLP, 500 hPa heights, and 1000±500 hPa thickness) over the study area are

found over the Gulf of Mexico region and the Rocky Mountains. Forcing mechanisms over these two regions are

known to have a strong in¯uence on the weather and climate of north-eastern Mexico and south-eastern Texas.

Therefore, a downscaling approach based on non-linear arti®cial neural networks was used to derive transfer

functions from the daily circulation patterns to local precipitation during 1985±1993. The daily results show that

the neural net is skilful in capturing a great deal of the precipitation variance over the coastal plains. However, the

prediction skill decreases from the coastal plains towards the Sierra Madre Oriental and over the Gulf of Mexico,

where local processes also appear to have a partial control in the rainfall variability. The high consistency of the

errors at different time-scales suggest that inaccuracies over the Sierra Madre Oriental could also result from the

sea-level pressure transformations, as indicated in the Data section. Therefore, the use of alternative predictor

variables (e.g. thickness above the 850 hPa level and moisture at different levels) may help to decrease the errors

over complex terrain.

1080 T. CAVAZOS


Overall, the net is successful at reproducing the phase and, to some degree, the amplitude of large precipitation

events during the training period. The average variance of rainfall explained during the training period was larger

(56 per cent) than that of the testing set (42 per cent), possibly due to the presence of a strong and extended El

NinÄo event (1993±1993) during the latter period, which was characterized by wetter than normal conditions. This

implies that the neural net may need more information to predict extreme events, as explained in the last section.

However, it is also possible that the inaccuracy during the testing period is due to the lack of randomization of the

input vectors to the neural net. The net tends to generalize relationships based on the range of the training

patterns. Thus, the presence of a few anomalous (large) rainfall events during the testing period could have been

in part bypassed by the net. Both daily and monthly analyses indicate that ENSO events partially modulate the

winter rainfall variance of the study area, supporting the concept of a Mexican connection (Rasmusson and Mo,

1993) that links the wintertime ENSO circulation anomalies of the Paci®c with the circulation over the Gulf of

Mexico. The monthly results also reveal that the PNA index does not seem to play a role in the local rainfall

variance during 1985±1993. This lack of an obvious PNA association may be because the PNA pattern can also

occur in the absence of anomalous external forcings (e.g. ENSO-related SST forcings) (Hoerling et al., 1995).

However, the monthly teleconnection results remain inconclusive owing to the short length of the period analysed

(32 winter months). Contrasting with the monthly teleconnections are the daily analysis and the seasonal results

shown in Table I, which evidence the great potential of the neural net technique in climate downscaling, even in

areas with complex terrain and during periods of extreme weather events. The simplicity of the arti®cial neural

networks (as compared with more complex limited area models, for example) and its adequate identi®cation of

rainfall events according to large-scale controls offer a new approach for climate diagnostic studies and climate

change assessments.

Future research will extend the framework of this study to gain a better understanding of the possible

relationship between ENSO and the Norte events and will attempt to assess their relative contributions to the

rainfall and minimum temperature variabilities in the study area. This diagnostic analysis will be used as the basis

for future work on climate variability and climate change analysis for further operational applications to the

agricultural sector in north-eastern Mexico.

ACKNOWLEDGEMENTS

I wish to thank R. Crane, A. Carleton, and B. Hewitson for examining earlier versions of the manuscript and

offering very helpful comments and suggestions. The comments of an anonymous referee are also gratefully

acknowledged. I am especially grateful to B. Hewitson for letting me use his wonderful `hcc' software, which

made my life easier. This research was supported by Fulbright-Conacyt and UANL-Mexico scholarship.

REFERENCES

Arkin, P. A. 1989. `Seasonal climate summary. The global climate for December 1988±February 1989: cold episode in the Tropical Paci®ccontinues', J. Climate, 2, 737±757.

Bell, G. D. and Basist, A. M. 1994. `Seasonal climate summary. The global climate of December 1992±February 1993. Part I: warm ENSOconditions continue in the tropical Paci®c; California drought abates', J. Climate, 7, 1581±1605.

Carbone, G. J. and Bramante, P. D. 1985. `Translating monthly temperature from regional to local scale in the southeastern United States',Climate Res., 5, 229±242.

Cavazos, T. 1994. `The in¯uence of the Southern Oscillation on the winter climate of Nuevo Leon state, Mexico', GeofõÂs. Int., 33, 295±302.

Cavazos, T. and Hastenrath, S. 1990. `Convection and rainfall over Mexico and their modulation by the Southern Oscillation', Int. J.Climatol., 10, 377±386.

Chelliah, M. 1993. `Seasonal climate summary. The global climate for December 1990±February 1991: strong temperature and precipitationcontrasts over North America and Eurasia; mixed ENSO conditions in the tropics', J. Climate, 6, 1392±1412.

Crisp, Ch. A. and Lewis, J. M. 1992. `Return ¯ow in the Gulf of Mexico. Part I: a classi®catory approach with a global historical perspective',J. Appl. Meteorol., 31, 868±880.

Colle, B. A. and Mass, C. F. 1995. `The structure and evolution of cold surges east of the Rocky Mountains', Mon. Wea. Rev., 123, 2577±2609.

Dallavalle, J. P. and Bosart, L. F. 1975. À synoptic investigation of anticyclogenesis accompanying North American polar air outbreaks',Mon. Wea. Rev., 103(11), 941±957.

DiMego, G. J., Bosart, L. F. and Endersen, G. W. 1976. Àn examination of the frequency and mean conditions surrounding frontal incursionsinto the Gulf of Mexico and Caribbean Sea', Mon. Wea. Rev., 104, 709±718.



Douglas, A. V. and Englehart, P. J. 1981. Òn a statistical relationship between autumn rainfall in the central equatorial Paci®c and subsequentwinter precipitation in Florida', Mon. Wea. Rev., 109, 2377±2382.

Erickson, C. O. 1979. `The large scale upper-tropospheric circulation associated with unusually heavy rainfall over the southern United States,Spring, 1979', Proceedings of the Fourth Annual Climate Diagnostics Workshop, Maddison, NOAA, pp. 108±110 (NTIS PB-201130).

Fitzjarrald, D. R. 1986. `Slope winds in Veracruz', J. Appl. Meteorol., 25, 133±144.Halpert, M. S. 1988. `Seasonal climate summary. The global climate for December 1987±February 1988; a return towards normal in the

Topical Paci®c', J. Climate, 1, 627±652.Hastenrath, S. 1988. Climate and Circulation of the Tropics, Reidel, Dordrech, 455 pp.Hastenrath, S., Greischar, L. and Heerden, J. V. 1995. `Prediction of the summer rainfall over South Africa', J. Climate, 8, 1511±1518.Hewitson, B. C. and Crane, R. G. 1992. `Large-scale atmospheric controls on local precipitation in Tropical Mexico', Geophys. Res. Lett., 19,

1835±1838.Hewitson, B. D. and Crane, R. G. (eds). 1994a. Neural Nets: Applications in Geography, Kluwer Acadamic Publishers, Dordrecht, 194 pp.Hewitson, B. D. and Crane, R. G. 1994b. `Looks and uses', In Hewitson, B. D. and Crane, R. G. (eds), Neural nets: Applications in

Geography, Kluwer Academic Publishers, Dordrecht, 194 pp.Hewitson, B. C. and Crane R. G. 1996. `Climate downscaling: techniques and applications', Climate Res., 7, 85±95.Hoerling, M. P., Ting, M. and Kumar, A. 1995. `Zonal ¯ow-stationary wave relationship during El NinÄo: Implications for seasonal

forecasting', J. Climate, 8, 1838±1852.Horel, J. D. and Wallace, J. M. 1981. `Planetary-scale atmospheric phenomena associated with El NinÄo-Southern Oscillation', Mon. Wea.

Rev., 109, 813±829.Iskenderian, H. 1995. Tropical cloud plumes and the interannual variability of precipitation over the southeastern United States and Mexico,

PhD dissertation, State University of New York, Albany, 147 pp.Janowiak, J. E. 1990. `Seasonal climate summary. The global climate of December 1989±February 1990; extreme temperature variations in

North America, persistent warmth in Europe and Asia, and the return of ENSO-like conditions in the western Paci®c', J. Climate, 3, 685±709.

Karl, T. R., Wang, W., Schlesinger, M. E., Knight, R. W. and Portman, D. 1990. À method of relating general circulation model simulatedclimate to the observed local climate. Part I: seasonal statistics', J. Climate, 3, 1053±1079.

Kiladis, G. M. and Diaz, H. 1989. `Global climatic anomalies associated with extremes in the Southern Oscillation', J. Climate, 2, 1069±1090.Klaus, D. 1973. `Las invasiones de aire frIÂo en los tropicos a sotavento de las MontanÄas Rocallosas', Geo®s. Int., 13(2), 99±143.Kousky, V. E. 1987. `Seasonal climate summary. The global climate for December 1986±February 1987: El NinÄo returns to the Tropical

Paci®c', Mon. Wea. Rev., 115, 2822±2838.Kousky, V. E. 1993. `Seasonal climate summary. The global climate of December 1991±February 1992: mature phase warm (ENSO) episode

conditions develop', J. Climate, 6, 1639±1655.Ladd, J. W. and Driscoll, D. W. 1980. À comparison of objective and subjective means of weather typing: an example from Western Texas',

J. Appl. Meteorol, 19, 691±704.Mecikalski, J. and Tilley, J. 1992. `Cold surges along the Front Range of the Rocky Mountains: development of a classi®cation scheme',

Meteorol. Atmos. Phys., 48, 249±271.MosinÄo, P. A. 1963. `Surface weather and upper-air ¯ow patterns in Mexico', Geo®s. Int., 4(4), 117±168.Overland, J. E. and Preisedorfer, R. W. 1982. À signi®cance test for principal components applied to cyclone meteorology', Mon. Wea. Rev.,

100, 1±4.Richman, M. B. 1986. `Review article: rotation of principal components', J. Climatol., 6, 293±335.Rasmusson, E. M. and Mo, K. 1993. `Linkages between 200 mb tropical and extratropical circulation anomalies during the 1986±1989 ENSO

cycle', J. Climate, 6, 595±616.Rogers, J. C. 1988. `Precipitation variability over the Caribbean and tropical Americas associated with the Southern Oscillation', J. Climate, 1,

172±182.Ropelewski, C. and Halpert, M. S. 1986. `North American precipitation and temperature patterns associated with El NinÄo/Southern Oscillation

(ENSO)', Mon. Wea. Rev., 114, 2352±2362.Ropelewski, C. F. and Halpert, M. S. 1987. `Global and regional scale precipitation patterns associated with the El NinÄo/Southern Oscillation',

Mon. Wea. Rev., 115, 1606±1626.Ropelewski, C. F. and Halpert, M. S. 1989. `Precipitation patterns associated with the high index phase of the Southern Oscillation',

J. Climate, 2, 268±284.Schubert, S. D., Rood, R. B. and Pfaendtner, J. 1993. Àn assimilated set for earth science applications', Bull. Am. Meterorol. Soc., 74, 2331±

2342.Shukla, J. and Wallace, J. M. 1983. `Numerical simulation of the atmospheric response to equatorial Paci®c sea surface temperature

anomalies', J. Atmos. Sci., 40, 1613±1630.Rilley, J. S. 1990. On the application of edge wave theory to terrain-bounded cold surges: a numerical study, PhD thesis, The Pennsylvania

State University, University Park, PA, and NCAR, Boulder, Co, 353 pp.Von Storch, H., Zorita, E. and Cubasch, U. 1993. `Downscaling of global climate change to regional scales: an application to Iberian rainfall in

wintertime', J. Climate, 6, 1161±1171.Wallace, J. M. and Gutzler, D. S. 1981. `Teleconnections in the geopotential height ®eld during Northern Hemisphere winter', Mon. Wea.

Rev., 109, 784±812.Wallace, J. M., Smith, C. and Jiang, Q. 1990. `Spatial patterns of atmosphere±ocean interaction in the Northern winter', J. Climate, 3, 990±

998.Wigley, T. M. L., Jones, P. D., Briffa, K. R. and Smith, G. 1990. Òbtaining sub-grid-scale information from coarse-resolution general

circulation model output', J. Geophys. Res., 95(D2), 1943±1953.Yarnal, B. and Diaz, H. F. 1986. `Relationships between extremes of the Southern Oscillation and the winter climate of the Anglo-American

Paci®c Coast', J. Climatol., 6, 197±219.

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Documents

Downscaling large-scale circulation to local winter rainfall in north-eastern Mexico