Climate Variability and Rainfed Agriculture in Ceará Brazil

Liqiang Sun1*, Huilan Li1, M. Neil Ward1, and David F. Moncunill2

1 International Research Institute for Climate Prediction,

Columbia University, Palisades, New York 10964

2 FUNCEME, Av. Rui Barbosa, 1246, Aldeota, Fortaleza, CE

CEP 60115-221; Brazil

March 2005

Submit to the Journal of Applied Meteorology

__________________________________________ *Corresponding author email: sun@iri.columbia.edu

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ABSTRACT

The climate influence on rainfed agriculture and the crop predictability in Ceará,

Brazil were examined in this study. The historical (1952-2001) response of the yields,

prices, and total values of corns and beans to climate variability was analyzed. We

defined a crop drought index, flooding index and weather index to measure the severity

of the drought, flooding and the combination of them, respectively. Crop simulations

using linear regression in a cross-validated mode indicated that the weather index was

clearly superior to the seasonal mean rainfall, the Niño3.4 sea surface temperature (SST),

and the Atlantic SST anomaly dipole for crop simulations. Weather index explained

56.8% (35.9%), 22.2% (32.5%), and 60.3% (19.4%) of the variance in the detrended corn

(bean) yields, prices, and total values, respectively. High predictability of seasonal mean

rainfall and weather index was revealed by the evaluation of an ensemble of 10 runs with

the NCEP regional spectral model nested into the ECHAM4.5 AGCM using observed

SSTs for the period of 1971-2000. The degree to which the predictability of local climate

and weather response to SST forcing translated into crop predictability was striking.

Statistical crop predictions using weather index as the only predictor accounted for 49.5%

(35.7%), 26.3% (42.3%), and 48.6% (21.6%) of the variance of the detrended corn (bean)

yields, price, and total values, respectively. Incorporating the predictability of weather

statistics (e.g., drought index, flooding index, and weather index) into stochastic weather

generators may improve crop model performance.

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1. Introduction

The state of Ceará, situated in the semi-arid northeast Brazil, occupies an area of

146,348 km2 (Fig. 1). Recent data from the 2000 census report about 43% of the

economically active population of Ceará is employed in the agricultural sector (Chimeli

et al. 2002). About 92% of farm families do not have access to irrigated land and thus

depend entirely on rainfall (Lemos et al. 2002). Crop production is highly vulnerable to

climate variability, particularly the recurrent droughts. The loss due to devastating

droughts has been recorded since the Portuguese settlement of Brazil in the early 1500s.

The Great Drought of 1877-79 incurred a famine in which about 500,000 inhabitants

perished in Ceará (Lemos et al. 2002). Given the vulnerability of rainfed agriculture, a

better understanding of climate influence on rainfed agriculture helps on the design of

policies to reduce the climate vulnerability of the most affected populations.

Ceará experiences one rain season during the year, i.e., from February to May. During

the rain season, the Atlantic Intertropical Convergence Zone (ITCZ) attains its

southernmost position and its location nearby or over the region enhances atmospheric

instability, being responsible for the presence of most of rainy systems. Abnormal

latitudinal migrations of the ITCZ are associated with excess (southward) or deficit

(northward) rainfall (Hastenrath and Heller 1977). Previous investigations have firmly

established that sea surface temperature (SST) anomaly forcing is the primary factor

responsible for the interannual variability of rainfall in Northeast Brazil (Harzallah et al.

1996; Mechoso et al. 1990; Moron et al. 1998; Moura and Shukla 1981; Nobre and

Shukla 1996; Pezzi and Cavalcanti 2001; Ropelewski and Halpert 1996; Roucou et al.

1996; Sun et al. 2005; Uvo et al. 1998; Ward and Folland 1991). Positive (negative)

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rainfall anomalies in Northeast Brazil are usually observed when the Atlantic SSTs are

colder (warmer) than normal north of the Equator and warmer (colder) than normal south

of it. Droughts also tend to coincide with the El Niño - Southern Oscillation (ENSO)

episodes.

Large interannual fluctuations and strong spatial variations of rainfall in Ceará are

observed. Localized climate information is required for farming management. The

current atmospheric general circulation models (AGCMs) forced by observed SSTs

simulate well the large-scale circulation in northeast South America (Moron et al. 1998;

Sperber and Palmer 1996). However, they are unable to resolve the local rainfall pattern

and variability in northeast Brazil due to the coarse resolution (Nobre et al. 2001; Sun et

al. 2005). Rainfall variability at the sub-AGCM scale is substantial in Ceará and

Northeast Brazil (Sun et al. 2004). High-resolution limited-area models nested with

AGCMs can provide spatial details of rainfall. Climate simulations with regional models

over South America indicated that monthly or seasonal mean precipitation was improved

in the regional models (Mirsa et al. 2003; Nobre et al. 2001; Seth and Rojas 2003; Sun et

al. 2005; Ward and Sun 2002). Sun et al. (2004) further indicated that the regional model

has reasonable skill in producing daily rainfall statistics, such as dry and wet spells.

Seasonal climate forecasts for the Brazilian Northeast have been issuing since December

2001, using a dynamical downscaling prediction system. Forecast evaluation for the

2002-04 periods indicates that positive skill exists over most of northeast Brazil (Sun et

al. 2004).

Before embarking on the development of a climate-crop forecast system, the physical

basis for predictability needs to be established. There should be a proven relationship

4

between seasonal climate and crop data, and the system should operate on the spatial

scales for which the relationship has been demonstrated. The principle purpose of this

paper is to investigate the connection between climate variability and rainfed agriculture

in Ceará, and examine the crop potential predictability in Ceará. The data and the

evaluation methods used in this study are described in sections 2 and 3, respectively.

Relationships between climatic variables and crop data are examined, and the crop yields,

prices and total values are estimated using observed climate conditions in section 4. The

dynamical models’ ability for crop prediction is verified in section 5, and summaries are

given in section 6.

2. Data

2.1 Crops

Ideally, we should use the crop data from the rainfed agricultural region. However,

the crop data in Ceará were aggregated at the State level, leading us to use some

predominantly rainfed crops as indicators of the climate stress that this agricultural

activity is subject to. In particular we chose corn and bean following conversations with

local experts. A major fraction of the agricultural activity is under rainfed conditions in

Ceará, and corn and bean production is predominant among crops rainfed farmers

produce. Historical crop production, area planted, price, and total value statistics for the

period of 1952-2001 in Ceará are from Fundação Instituto de Pesquisa e Informação do

Ceará (IPLANCE). The mean yields for each crop were calculated from the total

productions and the areas planted.

Many non-climatic factors influence crop yield, price and total value, including

institutional and technological changes. Notable examples are the hybrid corn types

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introduced in the late 1980s in Brazil, a seed distribution plan (“Hora de Plantar”)

introduced in 1987 by the Ceará government (Chimeli and Souza-Filho 2004). “Hora de

Plantar” uses the climate information to decide the timing of distribution of seeds to small

rainfed farmers. Many non-climatic factors prevailed in different periods in our dataset.

This resulted in potentially non-linear trends for crop data.

Examination of the observations indicated that no trends in rainfall and temperature

are detectable over the period 1952-2001. We thus assume that climate influences on crop

data generally operate at a higher frequency than non-climatic influences. We applied a

low-pass spectral smoothing filter to the raw crop data to separate higher-frequency

variations and lower-frequency trends (Press et al. 1989). The trends were obtained using

the Fourier analysis. We applied a Fourier transformation to the crop data series, remove

variations above a specified frequency, and then applied the inverse Fourier

transformation to obtain the trends. Although the choice of smoothing period is

subjective, we used a 10-year smoothing based on experience with many crop datasets.

Fig. 2 presented the non-linear trends fitted to the time series of the crop data. The trends

are subtracted from the total fields to obtain the detrended crop data. Fluctuations in the

detrended crop data are illustrated in Fig. 3. Large interannual variability is observed. For

example, the average detrended data-to-the trend ratio for the corn yield is 26%. The

detrended data were further normalized by the standard deviation. Subsequent analyses

were done on the normalized detrended crop data.

Corns are usually planted in January or early February, and it takes 90-120 days for

corns to reach maturity. Beans are usually planted in February or early March. It usually

takes 60-90 days to reach maturity. To simplify our study, we used the same growing

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season every year: February, March, April, and May (FMAM) for corns, and February,

March, and April (FMA) for beans. The values of climatic variables during the crop-

growing season were used in the analyses.

2.2 SSTs

The observed monthly SST data were from the National Atmospheric Administration

(NOAA) Climate Prediction Center (CPC). Two SST indices, the Niño3.4 SST anomaly

and the tropical Atlantic SST anomaly dipole, were used in this study. The Niño3.4 SST

anomaly represented the SST anomalies averaged over the area (170oW-120oW, 5oS-

5oN), and the tropical Atlantic dipole represented the SST anomaly difference between

the area (60oW-30oW, 5oN-20oN) and the area (30oW-10oE, 0-20oS).

2.3 Observed rainfall

Since the crop data were aggregated at the State level, and the Ceará State is not a

rainfall homogeneous region, we need to choose a rainfall homogeneous region where the

rainfed crops can be treated as an indicator for the State. The Small-scale rainfed

agriculture prevails in the Sertão Central region of Ceará. Corn and bean production in

this region serves as a barometer for drought impact in Ceará. An observational network

with high station density for rainfall is available in this region (Fig. 1). The 115 stations

shown in Fig. 1 indicated the Sertão Central region. Daily rainfall correlations between

station Cococi (40.5oW, 6.41oS) and all the other stations were calculated, and the

correlation coefficients are above the 90% significance level except for 3 stations. Thus,

the Sertão Central region can be treated as a homogeneous region for daily rainfall, and

the rainfall data in this region is used in our analysis. The number of stations with

completed records in the crop growing season varies from year to year. There are around

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50 stations in 1950s, around 80 stations from early 1960s to early 1980s, and around 30

stations in 1990s. Available observations exhibit a sharp increase from 1961 to 1962, and

a graduate decrease in1980s. Monthly rainfall was calculated at the stations with

completed records during the month.

2.4 Rainfall hindcasts

A global model and a regional model were used to generate the rainfall hindcasts. The

ECHAM4.5 Atmospheric General Circulation Model (AGCM) was developed at Max

Plank Institute of Meteorology (MPI) in Germany. This AGCM was configured at

triangular 42 (T42) spectral truncation, giving a spatial resolution of about 2.8o latitude-

longitude, with 19 vertical layers extending from the surface to 10 hPa. The mass flux

scheme of Tiedtke (1989) for deep, shallow, and midlevel convections is used with the

modified closure schemes for penetrative convection and the formation of organized

entrainment and detrainment (Nordeng 1995). The model includes prognostic clouds and

prognostic cloud water, and uses the radiation scheme of Eickerling (1989). The land

surface parameterizations include a snow cover model, a catchment-based soil

moisture/runoff treatment, and vegetative effects. Gravity wave drag associated with

orographic gravity waves is simulated after Miller et al. (1989). Description of the

numerics and the physical parameterizations are available from Roeckner et al. (1996).

The Regional Spectral Model (RSM) version 97 was developed at the National

Centers for Environmental Prediction (NCEP) (Juang and Kanamitsu 1994; Juang et al.

1997). The RSM uses the terrain following sigma coordinates in the vertical with 19

layers. A simplified Arakawa-Schubert scheme is used for deep convection (Pan and Wu

1995). Shallow convection following Tiedtke (1984) is invoked only in the absence of

8

deep convection. The solar and terrestrial radiation follows Chou (1992) and

Harshvardhan et al. (1987), respectively. An orographic statistics-based wave-breaking

mechanism (Kim and Arakawa 1995) is applied to the gravity wave drag scheme.

Boundary layer physics employs a nonlocal diffusion scheme developed by Hong and

Pan (1996). The fluxes in the surface layer are based on Monin-Obukhov similarity

theory. The model also includes a two-layer soil model of Pan and Mahrt (1987) and Pan

(1990).

The RSM horizontal resolution is 60 km, and the domain encompasses most of Brazil

and the entire tropical Atlantic Ocean. The main topographical features are resolved by

the RSM. For example, the small ranges of Serra Ibiapaba and Chapada do Araripe in

Ceará can be identified, and these topographic features cannot be resolved in ECHAM4.5

AGCM at T42 resolution. This configuration was also used by past studies (Sun et al.

2004 & 2005).

An ensemble of 10 integrations with the ECHAM4.5 AGCM using observed SSTs

has been done for the period of 1971-2000. The RSM ensemble members were generated

by initializing and forcing at 6-hour intervals with each ensemble member of the AGCM.

The RSM integrations were for the period of January-May, 1971-2000. The first month

(i.e., January) of the integrations was discarded because of possible spinup effects of the

regional model. Daily and monthly rainfall was calculated for each ensemble run.

3. Statistical analyses

Correlations between various climate variables and crop data were used to identify

the climate variables that affect crop production. Regressions from the climate variables

were used to predict the crop yield, price and total value. The crop predictions were

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evaluated using three goodness-of-fit measures: the coefficient of determination (r2), the

index of agreement (d), and the mean absolute error (MAE).

The coefficient of determination (r2) is the square of the correlation coefficient. It

describes the proportion of the total variance in the observed crop data explained by the

climate variables. It ranges from 0 to 1, where the higher values indicate better agreement

between the observed and predicted data. One of the problems with r2 is that its values

are highly sensitive to outliers (Lagates and McCabe 1999).

The index of agreement (d) is calculated using

�

�

=

=

−+−

−−= N

iii

N

iii

OOOP

OPd

1

2

1

2

|)||(|

)(0.1 (1)

where N is the number of years, Oi and Pi are the observation and prediction for year i,

respectively. O is the mean of the observations. The index of agreement measures the

degree to which the observed data are approached by the predicted data. The index of

agreement varies between 0 and 1, where 0 indicates no agreement between the predicted

and observed data, and 1 indicates perfect agreement. The index of agreement overcomes

the insensitivity of the coefficient of determination to differences in the observed and

predicted means and variances (Lagates and McCabe 1999).

The mean absolute error is calculated using

||1

1i

N

ii OP

NMEA −= �

=

(2)

MEA represents overall error. It is less sensitive than Root-mean-squared error (RMSE)

to errors in large predicted departments from the mean, and is therefore considered a

more robust measure of accuracy (Hansen et al. 2004).

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Rainfall hindcasts are generated by the nested model ensemble runs. We estimated

the rainfall potential predictability using a variance ratio (�) defined by Powell (1998),

2

2

TOT

SST

σσρ = (3)

where 2SSTσ is the variance due to SST forcing and 2

TOTσ is the total variance. The

unbiased estimates of 2SSTσ and 2

TOTσ follow Rowell et al. (1995). The variance ratio

describes the proportion of the total variance in the model hindcasts can be explained by

the SST forcing. It ranges from 0 to 1, where the higher values indicate smaller

unpredictable internal variance, and more robust response of the nested model, thus

higher predictability.

4. Linking climate variability and crop simulation

Correlations between corn and bean yields and between yields and prices or total

values during the 50-year period were calculated. The correlation between corn and bean

yields is 0.87. This suggests that the responses of corns and beans to climate variability

are similar. The correlation between yields and prices of the corn (bean) is –0.66 (-0.69).

Apparently, crop prices are largely influenced by the local supply and demand forces.

The total value of corns (beans) is also highly correlated to the yield of corns (beans),

with correlation of 0.83 (0.53) between them. To simplify our analysis, we focus on the

climate impact on the corn yield, and find out the connection between climate and corn

yield variability. Similar analysis on associations between climate and five other crop

variables (i.e., corn price, corn value, bean yield, price and value) were also performed,

and results were summarized at the end of this section.

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Highest corn yield will be obtained only where environmental conditions are

favorable at all stages of growth. Unfavorable conditions in early growth stages may limit

the size of the leaves (i.e., the photosynthetic factory). In later stages, unfavorable

conditions may reduce the number of silks produced, result in poor pollination of the

ovules and restrict the number of kernels that develop; or growth may stop prematurely

and restrict the size of the kernels produced. In this study, values of climate variables

averaged over the whole growing period were used due to the limited climate

predictability.

The SST anomalies over the tropical Pacific and the Atlantic Oceans play an

important role in modulating climate conditions over Ceará. The corn yield is

significantly correlated to the Niño3.4 SST anomalies and the tropical Atlantic SST

anomaly dipole (Fig. 4a&b). Positive (negative) values of the Niño3.4 SST anomaly or

the tropical Atlantic dipole generally lead to low (high) corn yield. The Niño3.4 SST

anomaly and the tropical Atlantic dipole account for 27.7% and 18.8% of the corn yield

variance, respectively. The yield also exhibits large variance with a given value of the

Niño3.4 SST anomaly or the tropical Atlantic dipole. This result indicates that the two

SST indices do contribute to the yield variance, but the uncertainty of the yield is also

large when only the two SST indices are used.

SSTs are the remote forcing for the local climate in the Sertão Central region.

Examination of local climate conditions is required. Previous studies indicated rainfall

and surface temperature are the major driving climate variables that directly affect corn

yields (Hodges et al. 1987; Hu and Buyanovsky 2003; Liu et al. 1989; Riha et al. 1996;

Runge 1968; Smith 1914). The Sertão Central region is situated in the deep tropics with

12

warm temperature and abundant solar radiation. Examination of the CRU05 data with

0.5o resolution (New 2000) for the period of 1952-1995 shows that the mean surface

temperature and diurnal temperature range in the Sertão Central region during February-

May are 25.5oC and 9.3oC, respectively. The standard deviation of both surface

temperature and diurnal temperature range is less than 1oC. The small interannual

variations of temperature have essentially no impact on the corn yield.

Rainfall has been considered to be the main limiting resource for crop growth in

semi-arid tropical regions (Barron et al. 2003; Hansen and Indeje 2004; Magalhães and

Glantz 1992). We found that the corn yields are generally associated with the seasonal

mean rainfall anomalies (Fig. 4c). Strong negative rainfall anomalies often lead to low

yield, and high yield is often associated with small rainfall anomalies. Extremely positive

rainfall anomalies can also cause damages on the yield. Seasonal mean rainfall can only

account for 16.9% of the yield variance. We also found that the corn yield is not related

to the seasonal mean rainfall anomalies when the normalized seasonal rainfall anomalies

range from -1 and 0.

Previous studies have demonstrated that rainfall variance at daily time scales can

affect the crop yields as well (Mearns et al. 1996; Monteith 1991; Riha et al. 1996). Over

the Sertão Central region, the soil has low water capacity, and the soil can lose most of

the rain water quickly (in order of days) because of the shallow soil layer and large

evapotranspiration rate. The average depth of soil layer is 0.5 m, and the annual potential

evapotranspiration is about 3 times of the annual rainfall amount. Crop water demand

thus highly depends on rainfall partitioning. Dry spells that occasionally interrupt the rain

season can adversely affect the corn yield. Our experience is that the period length of a

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dry spell, for grain cultivation in the Sertão Central region generally ranges between 3

and 15 days. Crop water stress due to a soil water deficit is often associated with dry

spells, particularly with dry spells longer than 10 days. We defined a long dry spell as 10

or more consecutive days with daily rainfall less than 2 mm. We calculated the number of

long dry spells at every rainfall station. Normalized anomalies of long dry spell numbers,

averaged over all available stations in the Sertão Central region, are correlated to the corn

yield (Fig. 4d). Correlation of 0.47 is above the 99% significance level. Higher (lower)

long dry spell numbers usually lead to lower (higher) corn yields, except for very low dry

spell numbers, which lead to negative yield anomalies. The dry spell variance can

account for 22.4% of the yield variance.

Both frequency and duration of dry spells can affect corn yields. To assess the impact

of dry spells on corn yield more accurately, we defined a crop drought index to measure

the severity of drought conditions:

WLDn

iiindex ×=�

=1

(4)

Where Li is the length of the ith dry spell, and

���

≥<

=10 510 1

i

i

Lif

LifW

A dry spell is defined as 3 or more consecutively days with daily rainfall less than 2 mm.

A strong weight is given to long dry spells because of severe damage to crop yield in this

region.

We calculated the observed drought index at every rainfall station. Normalized

anomalies of drought index averaged over all stations in Sertão Central region are

correlated to the corn yield (Fig. 4e). Higher correlation than that with long dry spell

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numbers is obtained. The yield exhibits small variance with a given value of the drought

index. However, very low drought index is associated with lower yield instead of higher

yield. We found that very low drought index is usually associated with excessive rainfall.

As shown in Fig. 4c, large rainfall anomalies adversely affect the yield.

Long wet spells can also reduce the corn yield in the Sertão Central region. Due to the

shallow soil layer, flooding conditions associated with wet spells often wash away corn

plants, resulting in low plant density. To assess the impact of wet spells on corn yield, we

defined a crop flooding index to measure the severity of the flooding conditions:

WLFn

iiindex ×=�

=1

(5)

Where Li is the length of the ith wet spell, and

���

≥<

=10 510 1

i

i

Lif

LifW

A wet spell is defined as 3 or more consecutively days with daily rainfall more than 10

mm. A strong weight is given to wet spells lasting at least 10 days because of severe

damage to crop yield.

We calculated the observed crop flooding index at every rainfall station. Normalized

anomalies of flooding index, averaged over all available stations in the Sertão Central

region, are correlated to the corn yield (Fig. 4f). The flooding index is not significantly

correlated to the corn yield. This may be due to the recurrent drought episodes and low

frequency of wet spell occurrence in this region. The mean flooding index is 3.3.

Nevertheless, we can extract some useful information from Fig. 4f. Moderate positive

anomalies of the flooding index favor higher yields, and strong positive anomalies of the

flooding index adversely affect the yield.

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To combine the impact of drought and flooding conditions on the corn yield, we

defined a crop weather index,

��

��

�

≤≤≤−>≤+>

=5.10 0 5.1 0 0

indexindexindexindex

indexindexindexindex

indexindex

index

FandDifFD

FandDifFD

DifD

W (6)

The crop weather index is highly correlated to the corn yield, and can account for

60.6% of the yield variance (Fig. 4g). Examination of the relationship between the

seasonal mean rainfall and the weather index indicated that, i) the weather index is

closely associated with the seasonal mean rainfall only when the weather index is

extremely high or low (i.e., the weather index is at least one standard deviation higher or

lower than the average), and ii) the weather index is essentially not correlated to the

seasonal mean rainfall when the weather index variance is less than one standard

deviation. Thus, the weather index can not be derived from the seasonal mean rainfall,

and can be treated as an independent variable except for the years with extreme

anomalies.

The detrended corn yield is significantly correlated with the Niño3.4 SST anomaly,

the tropical Atlantic dipole, the seasonal mean rainfall, and the weather index. We used

each of the four climatic variables to simulate the corn yield by linear regression. One of

the assumptions for ordinary least squares linear regression is the normality of

distribution. Diagnostics of the data indicated no significant departures from normality

for all the variables except for the seasonal mean rainfall. Observed seasonal mean

rainfall showed a positive skewness. To correct the departure from normality, we applied

a Box and Cox (1964) transformation to the seasonal mean rainfall. The procedure finds

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the optimal transformation to normality within the family of power transformation

(Hansen et al. 2004):

��

���

≠−=

=0 ,

10 ,ln

' λλ

λλRR

R (7)

by selecting the value of � that maximizes the log-likelihood function,

�=

−−+−−=N

iR R

NN

SN

L1

2' ln

1)1(ln

21 λ (8)

where R and R´ are the seasonal rainfall and transformed seasonal rainfall, respectively.

2'RS is the variance of R´. The value of � is 0.22 for the observed seasonal mean rainfall.

Cross-validated least-squares linear regression was applied to the corn yield

simulation using the Niño3.4 SST anomaly, the tropical Atlantic dipole, the transformed

seasonal mean rainfall, and the weather index. Leave-one-out cross-validation ensured

that observations from the forecast period did not directly influence forecasts, while

allowing us to make efficient use of limited data (Hansen and Indeje 2004). For each year

i, we solved the model by linear regression using the observed corn yields and the

climatic variable(s) from all the years except for the year i, then calculated the simulated

yield from the fitted slope and intercept and the observed climatic variable(s) for the year

i. Fig. 5 presented the comparison between the simulated yields and the observations. The

yield simulation with the weather index tends to agree most closely with the observations.

It is superior to the simulations with the other three predictors during the 50 year period.

The performance statistics for the corn yield simulations are summarized in Table 1. Of

the four predictors, the weather index ranks first in all three goodness-of-fit measures.

The simulated yield with the weather index correlates best with the observations (r=0.75),

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it can account for 56.8% of the observed yield variance. It agrees most closely with the

observations (d=0.85), and it has the least mount of error. The Niño3.4 SST ranked

second in all three performance statistics, followed by the seasonal mean rainfall. The

Atlantic dipole is the least effective predictor for the corn yield. The yield simulations

with the two SST indices can serve as a baseline scenario. There is no improvement with

the predictor “seasonal mean rainfall” compared to the SST indices.

Linear regressions with predictors of the transformed seasonal mean rainfall and

weather index in a cross-validated mode in the same manner for corn price and value,

bean yield, price and value have been performed as well, and the performance statistics

are summarized in Table 2. Since bean values are not significantly correlated to the

seasonal mean rainfall, simulated bean values are obtained with the predictor “weather

index” only. All simulations are reasonably well compared with observations. The

simulations using the weather index are systematically better than those with the seasonal

mean rainfall in all three goodness-of-fit measures, and the significant improvement is

found for crop yields and values. The yield and value simulations are systematically

better for corns than beans. These may be related to the difference in the length of

growing period. The longer growing period of corns increases the opportunities for corns

to be affected by climate factors. The price simulations are better for beans than corns.

This may be related to the larger interannual variability of the bean price.

5. Crop predictability

5.1 Dynamical model validation

There are 13 RSM grids over the Sertão Central region. Seasonal mean rainfall,

drought, flooding and weather indices were calculated on model grids for each of the 10

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integrations, and averaged over the 13 grids in the Sertão Central region. Fig. 6 illustrated

the FMAM ensemble mean anomalies versus observations. For the seasonal mean

rainfall, the model simulated the observed anomalies well, particularly the extremely

anomalies. The model showed relatively large biases in 5 years (i.e., 1971, 1992, 1997,

1999, and 2000). These are all near average rainfall years in the observations. The model

biases seem to be random: three years with positive biases, and two years with negative

biases. The model hindcasts for drought index tend to agree with the observations as well.

It is interesting to note that the model reproduced the observed drought index anomalies

well in 1971 and 1999, which the model had large biases of seasonal mean rainfall

anomalies. In 1972, 1981, 1988 and 1994, the model showed relatively large biases of

drought index, but the model simulated the observed seasonal rainfall anomalies well.

The model hindcasts for flooding index is highly correlated to the observations. The

model also produced the interannual variations stronger than the observations. The model

generally captured the observed interannual variability of the weather index. The model

biases of the weather index are mostly associated with the biases of drought index.

Model performance statistics for both FMAM and MAM period are summarized in

Table 3. The large values of the variance ratio for all the four variables indicated the SST

forcing has a statistically significant, and therefore predictable, influence on interannual

variability. The model hindcasts show significantly agreement with the observations, and

account for a large portion of the observed variance for all the four variables during both

FMAM and MAM periods. The seasonal mean rainfall showed the highest predictability

among the four variables, and the seasonal mean rainfall hindcasts agreed most closely

with the observations, and accounted most of the observed variance during the 30-year

19

period. It is striking that the model is able to capture the interannual variability of weather

index as well. This may significantly contribute to the crop prediction.

5.2 Crop prediction

We applied the Box and Cox (1964) transformation to the seasonal mean rainfall

hindcasts in the same manner for the observed seasonal rainfall. The value of � is 0.39.

Cross-validated least-squares linear regression is applied to the corn yield prediction

using the transformed seasonal mean rainfall and the weather index hindcasts. The

predicted corn yields using seasonal mean rainfall or weather index are significantly

correlated to the observations at the 95% significant level. The yield predictions with the

weather index are statistically better than those with seasonal rainfall. They correlate with

the observations higher (0.70), account much larger portion of the observed yield

variance (49.5%), agree more closely with the observations (0.82), and have smaller

errors (Table 4). Only a small shortfall from the corn simulation skill (Table 1) is found

for corn prediction.

Linear regressions with predictors of the transformed seasonal rainfall and weather

index hindcasts in a cross-validated mode in the same manner for corn price and value,

bean yield, price and value have been performed as well, and the performance statistics

are summarized in Table 4. Since bean values are not significantly correlated to the

seasonal mean rainfall, predicted bean values are obtained with the predictor “weather

index” only. Predictions are reasonably well for crop yield and values. The predictions

using the weather index are significantly better than those with the seasonal mean rainfall

in all three goodness-of-fit measures. The yield and value predictions are systematically

better for corns than beans. This result is consistent with the simulations.

20

The model predicted crop prices poorly. The predicted prices showed very small

variance from year to year, and practically useless (not shown). This is primarily due to

the weak seasonal mean rainfall anomalies and poor predictions of the weather index

during most of the 1970s. We excluded the 1970s, and regenerate price predictions using

linear regression in a cross-validated mode for the 1980s and 1990s. The prediction

performance is generally well (Table 4). This may indicate that crop prices are very

sensitive to the quality of climate predictions, and accurate climate prediction is

prerequisite for the price prediction.

6. Summary

The relationship between climate variability and rainfed agriculture in Ceará was

studied. Corns and beans are the predominant rainfed crops in Ceará. We defined a crop

drought index, flooding index and weather index, using daily rainfall time series during

the crop growing season, to measure the severity of drought, flooding, and the

combination of them. We found that the yields, prices and total values of the two crops

are significantly affected by the Niño3.4 SST anomaly, the tropical Atlantic dipole, the

seasonal mean rainfall, and the crop weather index. High (low) yields and total values

and low (high) prices of both crops are generally associated with negative (positive)

values of the Niño3.4 SST anomaly, the tropical Atlantic dipole, the crop weather index,

and positive (negative) seasonal mean rainfall anomalies. A power transformation on

seasonal mean rainfall has been performed to correct any departments from normality.

Crop simulations were obtained by linear regressions in a cross-validated mode using

observed climatic variables. The crop weather index is superior to the other three climatic

variables for crop simulations, as indicated by all three goodness-of-fit measures. The

21

skill difference in crop simulations using the seasonal mean rainfall or the two SST

indices is relatively small. The simulation skill for yields and values is higher for corns

than beans, and price simulation skill is higher for beans than corns.

To examine the climate predictability in Ceará, an ensemble of 10 runs with the

NCEP RSM at horizontal resolution of 60 km, nested with the ECHAM4.5 AGCM using

observed SSTs for the period of 1971-2000 has been done. High potential predictability

was revealed by the large values of variance ratio for the seasonal mean rainfall, the

drought index, flooding index and weather index. The Model hindcasts for the four

variables agree closely with the observations, account for a significant portion of the

observed variance, and have relatively small errors. We can conclude that the nested

model is skillful for prediction of seasonal mean rainfall, and weather statistics during the

season as well.

Crop predictions for the period of 1971-2000 were obtained by linear regressions in a

cross-validated mode using the climate hindcasts of transformed seasonal mean rainfall

and weather index. For crop yield and value prediction, the prediction skill with the

transformed seasonal rainfall as the predictor is reasonably good. The prediction skill

with the weather index as the predictor is much higher, as indicated by all the three

goodness-of-fit measures. We also found the skill is higher for corn prediction than bean

prediction. To predict crop price, accurate climate prediction during the training period is

required.

Crop models often use stochastic weather generators to generate daily rainfall

information based on monthly or seasonal mean rainfall. The use of generated sequences

of daily rainfall generally results in under-prediction of variability (Wilks 1999). We

22

have demonstrated that the weather index is not related to the seasonal mean rainfall in

Ceará except for extremely anomaly cases, and the dynamical models can capture well

the interannual variability of weather index. More realistic daily rainfall sequences can be

obtained if the weather statistics (e.g., drought index, flooding index, and weather index)

can be incorporated in the weather generators, and thus improve the crop model

performance as well.

Acknowledgments. The authors acknowledge the enlightening discussion with J. W.

Hansen.

23

REFERENCES

Barron, J., J. Rockström, F. Gichuki, and N. Hatibu, 2003: Dry spell analysis and maize

yields for two semi-arid locations in east Africa. Agric. For. Meteor.,117, 23-37.

Box, G. E. P., and D. R. Cox, 1964: An analysis of transformations. J. R. Stat. Soc., B26,

211-243.

Chimeli, A. B., C. Z. Mutter, and C. Ropelewski, 2002: Climate Fluctuations,

demography and development: Insights and opportunities for northeast Brazil.

Journal of International Affairs, 56, 213-234.

�, and F. A. Souza Filho, 2004: Climatic shocks and contingency planning: Evidence of

Opportunities from Ceará, Brazil. In preparation.

Chou, M.-D., 1992: A solar radiation model for use in climate studies. J. Atmos. Sci., 49,

762-772.

Eickerling, H. (1989): Parameterisierung des infraoten Strahlungstransport fur

Kohlendioxide, Wasserdampf und Ozon in einem breitbandigen Strahlungstransport

model. PhD thesis, Univ. Koln (in Germany).

Hansen, J. W., and M. Indeje, 2004: Linking dynamic seasonal climate forecasts with

crop simulation for maize yield prediction in semi-arid Kenya. Agric. For. Meteor.,

125, 143-157.

�, A. Potgieter, and M. K. Tippett, 2004: Using a general circulation model

to forecast regional wheat yields in northeast Australia. Agric. For. Meteor., 127,

77-92.

Harshvardhan, R. Davies, D. A. Randall, and T. G. Corsetti, 1987: A fast radiation

24

parameterization for atmospheric circulation model. J. Geophys. Res., 92(D1),

1009-1016.

Harzallah, A., J.O.R. Aragao, and R. Sadourny, 1996: Interannual rainfall variability in

north-east Brazil: Observation and model simulation. Int. J. Climatol., 16, 861-

878.

Hastenrath, S. and L. Heller 1977: Dynamics of climatic hazards in northeast Brazil. Q. J

.R. Meteor. Soc., 103, 77-92.

Hodges, T., D. Botner, C. Sakamoto, and J. H. Haug, 1987: Using the CERES-Maize

model to estimate production for the U.S. cornbelt. Agric. For. Meteorol., 40, 293-

303.

Hong, S.-Y, and H.-L. Pan 1996: Nonlocal boundary layer vertical diffusion in a

medium-range forecast model. Mon Wea. Rev., 124, 2322-2339.

Hu, Q., and G. Buyanovsky, 2003: Climate effects on corn yield in Missouri. J. Appl.

Meteor., 42, 1626-1635.

Juang, H.-M.H. and M. Kanamitsu, 1994: The NMC nested regional spectral model.

Mon. Wea. Rev., 122, 3-26.

�, S.-Y. Hong, and M. Kanamitsu, 1997: The NCEP regional spectral Model: An

update. Bull. Amer. Meteor. Soc., 78, 2125-2143.

Kim, Y.-J., and A. Arakawa, 1995: Improvement of orographic gravity wave

25

parameterization using a mesoscale gravity wave model. J. Atmos. Sci., 52, 1875-

1902.

Legates, D. R., and G. J. McCabe, 1999: Evaluating the use of “goodness-of-fit”

measures in hydrologic and hydroclimatic model validation. Water resour. Res.,

35(1), 233-241.

Lemos, M. C., T. J. Finan, R. W. Fox, D. R. Nelson, and J. Tucker, 2002: The use of

seasonal climate forecasting in policymaking: Lessons from northeast Brazil. Clim.

Change, 55, 479-507.

Liu, W. T. H., D. M. Botner, and C. M. Sakamoto, 1989: Application of CERES-Maize

model to yield prediction of a Brazilian maize hybrid. Agric. For. Meteorol., 45,

299-312.

Magalhães, A. R., and M. H. Glantz, 1992: Socioeconomic impacts of climate variations

and policy responses in Brazil. Fundação Grupo Esquel Brasil, 166pp.

Mearns, L. O., C. Roseenzweig, and R. Goldberg, 1996: The effect of changes in daily

and interannual climatic variability on CERES-wheat: A sensitivity study. Clim.

Change, 32, 257-292.

Mechoso, C. R., S. W. Lyons, and J. A. Spahr, 1990: The impact of sea surface

temperature anomalies on the rainfall over northeast Brazil. J. Climate, 3, 812-816.

Miller, M. J., T. N. Palmer, and R. Swinbank, 1989: Parameterization and influence of

sub-grid scale orography in general circulation and numerical weather prediction

models. Meteor. Atmos. Phys., 40, 84-109.

Misra, V., P. A. Dirmeyer, and B. P. Kirtman, 2003: Dynamic downscaling of seasonal

simulations over South America. J. Climate, 16, 103-117.

26

Monteith, J. L., 1991: Weather and water in the Sudano-Sahelian zone. In: Sivakumar, M.

V. K. Wallace, J. S. Rénard, C. Giroux (Eds), Soil Water Balance in the Sudano-

Sahelian Zone. Proceedings of the International Workshop, Niamey, Niger, Febuary

1991. IAHS Publication No. 199, IAHS Press, Institute of Hydrology, Wallingford,

UK, pp. 11-30.

Moron, V., A. Navarra, M. N., Ward, and E. Roeckner, 1998: Skill and reproducibility of

seasonal rainfall patterns in the tropics in ECHAM-4GCM simulations with

prescribed SST. Clim. Dyn., 4(2), 83-100.

Moura, A. D., and J. Shukla, 1981: On the dynamics of droughts in northeast Brazil:

Observations, theory and numerical experiments with a general circulation model.

J. Atmos. Sci., 38, 2653-2675.

New, M. G., M. Hulme, and P. D. Jones, 2000. Representing twentieth century space-

time climate variability. Part II: Development of a 1901-1996 monthly terrestrial

climate fields. J. Climate, 13, 2217-2238.

Nobre, P., A. D. Moura, and L. Sun, 2001: Dynamical downscaling of seasonal climate

prediction over Nordeste Brazil with ECHAM3 and NCEP’s regional spectral

models at IRI. Bull. Amer. Meteor. Soc., 82, 2787-2796.

�, and J. Shukla, 1996: Variations of sea surface temperature, wind stress, and rainfall

over the tropical Atlantic and South America. J. Climate, 9, 2464-2479.

Nordeng, T. E., 1995: Extended versions of the convective parameterization scheme at

ECMWF and their impact on the mean and transient activity of the model in the

tropics. ECMWF Research Dept. Tech. Memo., 206, European Center for Medium-

Range Weather Forecasts, Reading, United Kingdom, 41pp.

27

Pan, H.-L. 1990: A simple parameterization scheme of evapotranspiration over land for

the NMC medium-range forecast model. Mon. Wea. Rev., 118, 2500-2512.

�, and L. Mahrt, 1987: Interaction between soil hydrology and boundary layer

development, Boundary Layer Meteorol., 38, 198-202.

�, and W.-S. Wu, 1995: Implementing a mass flux convective parameterization

package for the NMC medium-range forecast model. NMC office note 409, 40pp.

(Available from NOAA/NCEP/EMC, 5200 Auth Road, Camp Springs, MD 20746)

Pezzi, L. P., and I. F. A. Cavalcanti, 2001: The relative importance of ENSO and

tropical Atlantic sea surface temperature anomalies for seasonal precipitation over

South America: a numerical study. Clim. Dyn., 17, 205-212.

Press, W. H., B. P. Flannery, S. A. Teukolsky, and T. Vetterling, 1989: Numerical

recipes: The Art of Scientific Computing. Cambridge University Press, 702pp.

Riha, S. J., D. S. Wilks, and P. Simoens, 1996: Impact of temperature and precipitation

variability on crop model predictions. Clim. Change, 32, 293-311.

Roeckner, E., K. Arpe, L. Bengtsson, M. Christoph, M. Claussen, L. Dumenil, M. Esch,

M. Giorgetta, U. Schlese, and U. Schulzweida, 1996: The atmospheric general

circulation model ECHAM-4: Model description and simulation of present-day

climate. Technical Report 218, Max-Planck Institute for Meteorology, Hamburg,

Germany, 90pp.

Ropelewski, C. F., and M. S. Halpert, 1996: Quantifying Southern Oscillation-

precipitation relationships. J. Climate, 9, 1043-1059.

Roucou, P., J.O.R. Aragao, A. Harzallah, B. Fontaine, and S. Janicot, 1996: Vertical

motion changes related to north-east Brazil rainfall variability: A GCM

28

simulation. Int. J. Climatol., 16, 879-891.

Rowell, D. P., 1998: Assessing potential seasonal predictability with an ensemble of

multidecadal GCM simulations. J. Climate, 11, 109-120.

�, C. K. Folland, K. Maskell, and M. N. Ward, 1995: Variability of summer rainfall over

tropical North Africa (1906-92): Observations and modeling. Quart. J. Roy. Meteor.

Soc., 121, 669-704.

Runge, E. C., 1968: Effect of rainfall and temperature interaction during the growing

season on corn yield. Agon. J., 60, 503-507.

Seth, A., and M. Rojas, 2003: Simulation and sensitivity in a nested modeling system for

South America. Part I: reanalyses boundary forcing. J. Climate, 15, 2437-2453.

Smith, J. W., 1914: The effect of weather upon the yield of corn. Mon. Wea. Rev., 42,

78-87.

Sperber, K. R., and T. N. Palmer, 1996: Interannual tropical rainfall variability in

general circulation model simulations associated with the Atmospheric Model

Intercomparison Project. J. Climate, 9, 2727-2750.

Sun, L., D. F. Moncunill, H. Li, A. D. Moura, and F. D. A. D. S. Filho, 2005: Climate

downscaling over Nordeste Brazil using NCEP RSM97. J. Climate, 18, 551-567

�, D. F. Moncunill, H. Li, A. D. Moura, F. D. A. D. S. Filho, and S. E. Zebiak, 2004:

An operational dynamical downscaling prediction system for Nordeste Brazil and

the 2002-04 real-time forecast evaluation. J. Climate, in review.

Tiedtke, M. 1984: The effect of penetrative cumulus convection on the large-scale flow

in a general circulation model. Beitr. Phys. Atmos., 57, 216-239.

�, 1989: A comprehensive mass flux scheme for cumulus parameterization in large-

29

scale models. Mon. Wea. Rev., 117, 1779-1800.

Uvo, C. B., C. A. Repelli, C. A., S. E. Zebiak, and Y. Kushnir, 1998: The relationships

between tropical Pacific and Atlantic SST and Northeast Brazil monthly

precipitation. J. Climate, 11, 551-561.

Ward, M. N., and C. K. Folland, 1991: Prediction of seasonal rainfall in the north

Nordeste of Brazil using eigenvectors of sea surface temperature. Int. J.

Climatology, 11, 711-743.

�, and L. Sun, 2002: Intensive course on dynamical downscaling of seasonal to

interannual climate predictions. Palisades, New York, USA, January 15 – April 6,

2001. IRI Technical Report, 215pp.

Wilks, D. S., 1999: Interannual variability and extreme-value characteristics of several

stochastic daily precipitation models. Agric. For. Meteorol., 93, 153-169.

30

Figure Captions

Figure 1. Network of rainfall stations in the Sertão Central region of Ceará. Station

locations are marked by small dots.

Figure 2. Raw and smoothed time series of crop data: a) corn yield, b) corn price, c) corn

total value, d) beans yield, e) beans price, and f) bean total value. Units are Kg/ha,

Real/Kg, and million Reais for yield, price, and total value, respectively.

Figure 3. Same as in Fig. 2, but detrended crop data.

Figure 4. Scatter plots of corn yields vs a) Niño3.4 SST anomalies; b) values of the

Atlantic dipole; c) seasonal mean rainfall anomalies; d) values of crop drought index; e)

values of crop flooding index; and f) values of crop weather index. All data are

normalized.

Figure 5. Corn yield anomaly simulations by linear regression using the observed

climatic variables: a) Niño3.4 SST anomalies, b) the Atlantic dipole, c) transformed

seasonal mean rainfall, and d) the weather index. The unit of yield is Kg/ha.

Figure 6. Time series (1971-2000) of observed and model simulated climate anomalies

during FMAM season over the Sertão Central region of Ceará: a) seasonal mean rainfall

anomalies, b) drought index, c) flooding index, and d) weather index. The correlation (r)

between observations and simulations is also shown.

Figure 7. Same as Fig. 5, but predictions.

31

Table 1. Goodness-of-fit statistics for corn yield simulations for the period of 1952-2001.

The coefficient of determination (r2) is expressed as a percentage of 1.0. The unit of the

yield mean absolute error (MAE) is Kg/ha.

Table 2. Goodness-of-fit statistics for corn and bean simulations for the period of 1952-

2001. The values in parentheses are for bean simulations. The coefficient of

determination (r2) is expressed as a percentage of 1.0. The units of mean absolute error

(MAE) are Kg/ha, Real/Kg, and million Reais for yield, price, and total value,

respectively.

Table 3. Model hindcast validation for the FMAM and MAM seasons during 1971-2000.

The values in parentheses are for the MAM season. The coefficient of determination (r2)

is expressed as a percentage of 1.0. The unit of mean absolute error (MAE) is mm/day for

the seasonal mean rainfall.

Table 4. Goodness-of-fit statistics for corn and bean predictions. Prediction periods are

1971-2000 for yields and values, and 1982-2000 for prices. The values in parentheses are

for bean predictions. The coefficient of determination (r2) is expressed as a percentage of

1.0. The units of mean absolute error (MAE) are Kg/ha, Real/Kg, and million Reais for

yield, price, and total value, respectively.

32

Figure 1. Network of rainfall stations in the Sertão Central region of Ceará. Station locations are marked by small dots.

33

a) Corn Yield

0

200

400

600

800

1000

1200

1950 1960 1970 1980 1990 2000

b) Corn Price

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1950 1960 1970 1980 1990 2000

c) Corn Value

0

50

100

150

200

250

1950 1960 1970 1980 1990 2000

d) Bean Yield

0

100

200

300

400

500

600

700

1950 1960 1970 1980 1990 2000

e) Bean Price

0

0.5

1

1.5

2

2.5

3

3.5

4

1950 1960 1970 1980 1990 2000

f) Bean Value

0

50

100

150

200

250

300

350

400

1950 1960 1970 1980 1990 2000

Figure 2. Raw and smoothed time series of crop data: a) corn yield, b) corn price, c) corn total value, d) beans yield, e) beans price, and f) bean total value. Units are Kg/ha, Real/Kg, and million Reais for yield, price, and total value, respectively.

34

b) Corn Price

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

1950 1960 1970 1980 1990 2000

a) Corn Yield

-600

-400

-200

0

200

400

600

1950 1960 1970 1980 1990 2000

c) Corn Value

-100

-80

-60

-40

-20

0

20

40

60

80

1950 1960 1970 1980 1990 2000

d) Bean Yield

-400

-300

-200

-100

0

100

200

300

400

1950 1960 1970 1980 1990 2000

e) Bean Price

-1.5

-1

-0.5

0

0.5

1

1.5

1950 1960 1970 1980 1990 2000

f) Bean Value

-150

-100

-50

0

50

100

150

1950 1960 1970 1980 1990 2000

Figure 3. Same as in Fig. 2, but detrended crop data.

35

c)

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Rainfall

Yie

ld

r=0.41

e)

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Dro ug ht Ind ex

Yie

ldr=-0.65

a)

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Niño3.4

Yie

ldr=-0.53

b)

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Atlantic Dipole

Yie

ldr=-0.43

d)

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Dry Spell

Yie

ldr=-0.47

f)

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Flooding Index

Yie

ldr=0.22

g)

-3

-2

-1

0

1

2

3

-3 -2 -1 0 1 2 3

Weather Index

Yie

ld

r=-0.78

Figure 4. Scatter plots of corn yields vs a) Niño3.4 SST anomalies; b) values of the Atlantic dipole; c) seasonal mean rainfall anomalies; d) values of crop drought index; e) values of crop flooding index; and f) values of crop weather index. All data are normalized.

36

-600-400-200

0200400600

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Observation Simulationr=0.47

a)

-600-400-200

0200400600

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

r=0.32

b)

-600-400-200

0200400600

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

r=0.44

c)

-600-400-200

0200

400600

1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

r=0.75

d)

Figure 5. Corn yield anomaly simulations by linear regression using the observed climatic variables: a) Niño3.4 SST anomalies, b) the Atlantic dipole, c) transferred seasonal mean rainfall, and d) the weather index. The unit of yield is Kg/ha.

37

a) Seasonal Rainfall Anomaly

-6

-4

-2

0

2

4

6

1970 1975 1980 1985 1990 1995 2000

Observation RSMr=0.84

b) Drought Index

-200

-100

0

100

200

1970 1975 1980 1985 1990 1995 2000

r=0.74

c) Flooding Index

-20

-10

0

10

20

1970 1975 1980 1985 1990 1995 2000

r=0.84

d) Weather Index

-3

-2

-1

0

1

2

3

1970 1975 1980 1985 1990 1995 2000

r=0.69

Figure 6. Time series (1971-2000) of observed and model simulated climate anomalies during FMAM season over the Sertão Central region of Ceará: a) seasonal mean rainfall anomalies, b) drought index, c) flooding index, and d) weather index. The correlation (r) between observations and simulations is also shown.

38

-600

-400

-200

0

200

400

600

1970 1975 1980 1985 1990 1995 2000

Observation Prediction

r=0.44

a)

-600

-400

-200

0

200

400

600

1970 1975 1980 1985 1990 1995 2000

r=0.70

b)

Figure 7. Same as Fig. 5, but predictions.

39

Table 1. Goodness-of-fit statistics for corn yield simulations for the period of 1952-2001. The coefficient of determination (r2) is expressed as a percentage of 1.0. The unit of the yield mean absolute error (MAE) is Kg/ha. Predictor Niño3.4 SST Atlantic Dipole Seasonal Rainfall Weather Index r2 21.7 10.4 19.2 56.8 MAE 128.4 144.0 130.5 91.0 d 0.61 0.49 0.59 0.85

40

Table 2. Goodness-of-fit statistics for corn and bean simulations for the period of 1952-2001. The values in parentheses are for bean simulations. The coefficient of determination (r2) is expressed as a percentage of 1.0. The units of mean absolute error (MAE) are Kg/ha, Real/Kg, and million Reais for yield, price, and total value, respectively.

Yield Price Value

Predictor Seasonal Rainfall

Weather Index

Seasonal Rainfall

Weather Index

Seasonal Rainfall

Weather Index

r2 19.2(9.2) 56.8(35.9) 13.9(18.8) 22.2(32.5) 15.9 60.3(19.4) MAE 130.5(67.5) 91.0(55.0) 0.068(0.34) 0.063(0.31) 28.7 19.0(34.4) d 0.59(0.48) 0.85(0.73) 0.51(0.58) 0.62(0.71) 0.55 0.87(0.59)

41

Table 3. Model hindcast validation for the FMAM and MAM seasons during 1971-2000. The values in parentheses are for the MAM season. The coefficient of determination (r2) is expressed as a percentage of 1.0. The unit of mean absolute error (MAE) is mm/day for the seasonal mean rainfall.

Seasonal Rainfall Drought Index Flooding Index Weather Index r2 70.2(69.8) 54.2(59.6) 71.0(68.9) 47.4(32.7) MAE 0.83(0.98) 78.0(61.9) 5.6(4.9) 0.64(0.83) d 0.89(0.89) 0.76(0.75) 0.53(0.55) 0.84(0.75) Variance Ratio 0.71(0.68) 0.68(0.62) 0.59(0.56) 0.54(0.49)

42

Table 4. Goodness-of-fit statistics for corn and bean predictions. Prediction periods are 1971-2000 for yields and values, and 1982-2000 for prices. The values in parentheses are for bean predictions. The coefficient of determination (r2) is expressed as a percentage of 1.0. The units of mean absolute error (MAE) are Kg/ha, Real/Kg, and million Reais for yield, price, and total value, respectively. Yield Price* Value

Predictor Seasonal Rainfall

Weather Index

Seasonal Rainfall

Weather Index

Seasonal Rainfall

Weather Index

r2 19.1(8.0) 49.5(35.7) 34.0(30.4) 26.3(42.3) 16.8 48.6(21.6) MAE 135.4(63.3) 105.9(50.8) 0.047(0.36) 0.048(0.31) 34.9 25.4(38.2) d 0.60(0.48) 0.82(0.74) 0.73(0.70) 0.69(0.79) 0.59 0.81(0.60)