Climate Variability and Rainfed Agriculture in Ceará Brazillhl/crop.pdf · Climate Variability and...
Transcript of Climate Variability and Rainfed Agriculture in Ceará Brazillhl/crop.pdf · Climate Variability and...
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: [email protected]
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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
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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
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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
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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
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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
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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)