Use of climate indices to predict corn yields in southeast USA

INTERNATIONAL JOURNAL OF CLIMATOLOGYInt. J. Climatol. 29: 1680–1691 (2009)Published online 12 December 2008 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/joc.1817

Use of climate indices to predict corn yields in southeastUSA†

Christopher J. Martinez,* Guillermo A. Baigorria and James W. JonesDepartment of Agricultural and Biological Engineering, Institute of Food and Agricultural Sciences, University of Florida, Gainesville, FL, USA

ABSTRACT: The impact of large-scale oceanic and atmospheric climate patterns on county corn yields in Alabama,Florida, and Georgia were evaluated for the period 1970–2005. Associations between detrended corn yield residuals,precipitation, surface temperature, and climate indices were explored by correlation analysis. Significant correlations werefound with indices of the Pacific–North American pattern, tropical North Atlantic and eastern tropical Pacific sea surfacetemperatures, and two indices of the Bermuda high. The summer index of the Bermuda high (BHI) was the only indexto be significantly correlated with yield residuals during the critical summer tasselling period; a time when corn is mostsusceptible to water stress. Due to the high degree of multi-collinearity found between the five indices, leave-n-out cross-validated principal component regression was conducted using all possible combinations of indices to predict corn yieldresiduals. Three indices produced models with the greatest skill using both lagged (known prior to planting) and concurrentindices (cross-validated Pearson’s r: 0.679) and using lagged indices only (cross-validated Pearson’s r: 0.569). Using thecross-validated models 99.2 and 96.9% of predicted county yields showed predictive skill (based on tercile hit scores) usingboth concurrent and lagged indices, and lagged-only indices, respectively. The cross-validated model using lagged-onlyindices indicated the results that can be achieved using known climate index values as early as the winter before the springplanting. Copyright 2008 Royal Meteorological Society

KEY WORDS crop yield forecast; climate; climate indices

Received 7 April 2008; Revised 27 August 2008; Accepted 26 October 2008

1. Introduction

Growers in the United States planted 37.6 millionhectares of corn in 2007, an increase of 19% fromthe previous year, and the highest area since 1944(NASS/USDA, 2007). This increase was due to favour-able corn prices partially caused by increased demandfrom ethanol producers. The area planted with corn in2007 in Alabama, Florida, and Georgia increased by 68%compared to the previous year, and was the largest single-year increase over the past five years (NASS/USDA,2007). As the importance of corn production for feedand fuel increases in the southeast United States, seasonalclimate forecasts can allow farmers to mitigate potentialnegative consequences of variations in climate or takeadvantage of favourable conditions.

To date, most investigations of the effect of large-scale oceanic/atmospheric variables on agriculture inthe southeast United States have been restricted to theEl Nino-Southern Oscillation (ENSO) phenomenon (i.e.Handler, 1990; Hansen et al., 1998, 1999), a major sourceof climate variability affecting many different parts of

* Correspondence to: Christopher J. Martinez, Department of Agricul-tural and Biological Engineering, University of Florida, Gainesville,FL 32611, USA. E-mail: [email protected]† This article was published online on 12 December 2008. An errorwas subsequently identified. This notice is included in the online andprint versions to indicate that both have been corrected 15 April 2009.

the world (Philander, 1990; Trenberth, 1997). Ropelewskiand Halpert (1986) found a consistent ENSO precipitationand temperature signal between October and March in thesoutheast United States; El Nino (La Nina) years werefound to be typically cooler (warmer) and wetter (drier)during these months. However, the use of indices orphases of ENSO alone have been insufficient for planningpurposes in regions where the signal is weak, does notcoincide with the growing season of certain crops, or ismodulated by other climatic signals (Hansen et al., 1999;Podesta et al., 2002; Travasso et al., 2003).

Several associations between indices of large-scaleoceanic/atmospheric variables and climate in the south-east United States have been noted in the literature.Enfield (1996) showed a connection between precipita-tion in the southeast United States and tropical NorthAtlantic sea surface temperatures (SSTs). While Enfieldand Mayer (1997) have shown that 50–80% of the vari-ability of tropical North Atlantic SSTs was associatedwith ENSO, with warming of the Atlantic sector lag-ging the Pacific by one to two seasons, Enfield (1996)found a significant portion that was not an indirect effectof ENSO. Gershunov and Barnett (1998) and Enfieldet al. (2001) indicated that the Pacific Decadal Oscillation(Mantua et al., 1997) and Atlantic Multi-Decadal Oscilla-tion (Kerr, 2000) may modulate the strength of the ENSOteleconnection in the southeast United States over peri-ods of decades. In exploring the relationship between the

Copyright 2008 Royal Meteorological Society

PREDICTING CORN YIELDS IN THE S-E USA 1681

Pacific–North American (PNA) (Wallace and Gutzler,1981) pattern with regional precipitation and temperature,Leathers et al. (1991) found consistently high correlationsbetween the PNA index of Yarnal and Diaz (1986) withautumn, winter, and spring temperatures in the southeastUnited States; however, correlations with precipitationwere comparatively weak. The North Atlantic Oscillation(NAO) has been thought to affect climate in the southeastUnited States during winter months (Rogers, 1984). How-ever, in exploring the relationship of the Palmer DroughtSeverity Index and precipitation in the southeast withthe NAO, PNA, and Southern Oscillation Index (SOI),Yin (1994) and Henderson and Vega (1996) found thatthe NAO was not a major contributor. In their study ofregional precipitation, Henderson and Vega (1996) foundsignificant correlations in all seasons between seasonalprecipitation and an index of the Bermuda high (BHI)used by Stahle and Cleaveland (1992) that were strongerthan that found with the NAO, PNA, or SOI.

The links that have been found between climate indicesand regional climate in the southeast United Statesidentify them as potential predictors of crop yields inthe region. Over the course of a growing season, cropyields are integrators of climate in space and time.However, particular crops are more sensitive than othersto variations in climate at different stages of growth. Theobjective of this work is to explore the relationship ofcounty-level corn yields, gauge precipitation, and griddedsurface temperatures in Alabama, Florida, and Georgiawith climate indices and to evaluate the potential valueof climate indices as predictors of corn yields.

2. Data

2.1. Corn yields

In the states of Alabama, Florida, and Georgia corn istypically planted between late February and mid-May andharvested between mid-June and mid-September (Maskand Mitchell, 1988; Wright et al., 2004; Lee, 2008).Early planting, while being at risk of freezes, typicallyresults in greater yields compared to late-planted corn.Annual corn yield data (reported here in metric tons perhectare (Mg ha−1)) from 129 counties with significantcorn production (>0.1% of total harvested productionin the three states) and fewer than 10% missing valuesfrom Alabama, Florida, and Georgia were obtainedfrom the NASS/USDA (http://www.nass.usda.gov/) forthe period 1970–2005. Lack of distinction betweenirrigated and rain-fed areas was a source of uncertaintyas irrigation makes crop yields less sensitive to seasonalvariability of precipitation. We assumed that climaticinfluences on corn yields generally occurred at a higherfrequency than non-climatic influences (technologicalimprovements). County corn yields were detrended usinga low-pass spectral smoothing filter (Press et al., 1989)with a 10-year smoothing period to remove an upwardtechnological improvement trend. This smoothing periodwas chosen based on experience with crop yields in this

region (Baigorria et al., 2008a). Corn yield residuals werethen calculated as (mean = 0):

yresidual = yobserved

ytrend− 1

2.2. Precipitation and surface temperature

Monthly precipitation from 166 weather stations inAlabama, northern Florida, and Georgia were obtainedfrom the National Climatic Data Center (http://www.ncdc.noaa.gov) for the period 1970–2005 (Figure 1). Allgauges had fewer than 10% missing values. Missing val-ues were filled using the best nearest-neighbour feature(the precipitation gauge with the strongest correlationis used to provide the missing data point) of the Cli-mate Predictability Tool developed by the InternationalResearch Institute for Climate Prediction and Society(IRI) (http://iri.columbia.edu/outreach/software/). Fillingmissing values using the long-term mean or the geo-graphically nearest gauge yielded similar results. Gaugeprecipitation was then aggregated into three-month run-ning totals.

Monthly gridded surface temperature in the southeastUSA for the period 1970–2005 were obtained from theNational Centers for Environmental Prediction/NationalCenter for Atmospheric Research (NCEP/NCAR) reanal-ysis project (Kalnay et al., 1996) and were obtained fromIRI (http://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NCEP-NCAR/.CDAS-1/.MONTHLY/.Diagnostic/.surface/.temp/). Gridded surface temperatures were thenaggregated into three-month running averages.

2.3. Indices of climate variability

We used indices of ENSO, SSTs in the tropical NorthAtlantic (TNA), the PNA, and the BHI. The ENSO indexwas the raw average monthly SST anomalies used by

Figure 1. Rain gauges used in this study.

Copyright 2008 Royal Meteorological Society Int. J. Climatol. 29: 1680–1691 (2009)DOI: 10.1002/joc

1682 C. J. MARTINEZ ET AL.

the Japanese Meteorological Agency (JMA, 4 °N–4 °S,90° –150 °W) and was obtained from the Center forOcean-Atmospheric Prediction Studies (COAPS) (ftp://www.coaps.fsu.edu/pub/JMA SST Index/) at FloridaState University. The JMA index was chosen to repre-sent ENSO based on previous work conducted within theSoutheast Climate Consortium (http://www.secc.coaps.fsu.edu/) that has established its usefulness in the region(in addition, the JMA index exhibited the strongest cor-relation with corn yield residuals in the proceeding anal-ysis compared to other indices of ENSO evaluated). TheTNA SST anomaly index (5.5° –23.5 °N, 15° –57.5 °W)of Enfield et al. (1999) was obtained from the EarthSystems Research Laboratory, Physical Science Divi-sion of the National Oceanic and Atmospheric Admin-istration (http://www.cdc.noaa.gov/ClimateIndices/). Anindex of the PNA was constructed from monthly 500 hPastandardized geopotential height anomalies (z) from theNCEP/NCAR reanalysis project (Kalnay et al., 1996),obtained from IRI (http://iridl.ldeo.columbia.edu/SOUR-CES/.NOAA/.NCEP-NCAR/.CDAS-1/.MONTHLY/.Intrinsic/.PressureLevel/.phi/), using the three grid pointsof Horel and Wallace (1981):

PNA = 13

[z(55 °N, 115 °W) − z(30 °N, 85 °W)

−z(45 °N, 165 °W)

]

These three grid points correspond to southwestCanada, southeast United States, and the North PacificOcean south of the Aleutian Islands, respectively. Follow-ing Stahle and Cleaveland (1992), the BHI was derivedby an exploratory analysis of standardized monthlymean sea level pressure from the NCEP/NCAR reanal-ysis project (Kalnay et al., 1996), obtained from IRI(http://iridl.ldeo.columbia.edu/SOURCES/.NOAA/.NCEP-NCAR/.CDAS-1/.MONTHLY/.Intrinsic/.MSL/.pressure/) in the area of the western periphery of the BHIover the Atlantic Ocean (25° –50 °N, 50° –0 °W). The BHIwas constructed as the difference between standardizedmonthly mean sea level pressure anomalies at an Atlanticgrid point and a grid point near New Orleans, Louisiana(30 °N, 90 °W), and effectively indicates the approximateposition of the western edge of the BHI (Stahle andCleaveland, 1992; Henderson and Vega, 1996; Katz et al.,2003; Diem, 2006). Following Stahle and Cleveland’s(1992) approach, the Atlantic grid point was selectedas that found to be most strongly correlated with cornyield residuals. All climate indices were composited into3-month moving averages for analysis.

3. Methods

3.1. Principal Component Analysis

County yield residuals, gauge precipitation, and griddedsurface temperatures were summarized using PrincipalComponent Analysis (PCA). Each dataset was convertedinto standardized anomalies prior to PCA (mean sub-tracted from each precipitation and temperature obser-vation, and each observation in each dataset was divided

by its standard deviation yielding mean = 0 and standarddeviation = 1). PCA is an efficient data-reduction tech-nique that successively maximizes the variance of thedataset explained by each successive principal compo-nent (PC). Separate S-mode PCAs (locations as variables(rows) and time series as observations (columns)) wereconducted on each dataset. The first PC (PC1) was used tospatially aggregate the time series of each dataset. Sum-marizing the data using PC1 considerably reduces theeffects of possible erroneous values in the original data(Widmann and Schar, 1997).

3.2. Association of precipitation and surfacetemperature with yield residuals

Linear correlation analyses were performed to identifysignificant relationships between PC1 of corn yield resid-uals with PC1 of precipitation and surface temperature.Periods where PC1 of precipitation and surface tempera-ture showed maximum correlation with yield residualswere retained for further analysis. Linear correlationswere then explored between PC1 of precipitation andsurface temperature during these periods with the climateindices.

3.3. Association of yield residuals with climate indices

Linear correlations were performed to identify signifi-cant relationships between climate indices and PC1 ofyield residuals. Correlations with concurrent (during thegrowing season) and lagged (prior to the growing sea-son) climate indices were evaluated, and the most sig-nificant relationships were selected for discussion andfurther analysis. To evaluate the potential predictabilityof yield residuals with combinations of climate indices,regression analysis was performed. It is known that manylarge-scale circulations are interrelated, and that one may‘carry’ the signal of another. For this reason, it is oftendifficult to ascribe causal mechanisms with complete con-fidence and standard multiple linear regression may notprovide a stable relationship when more than one predic-tor is included in the model. To remedy this, PrincipalComponent Regression (PCR) was conducted using theClimate Predictability Tool developed by IRI.

The PC scores of the climatic indices were used aspredictors in regression to eliminate multi-collinearities(Jolliffe, 2004). While PCR typically results in theuse of fewer predictor variables (PCs) in forming theregression equation, there is no corresponding reduc-tion in the number of original variables (in this case,climate indices) since the PCs are (by definition) lin-ear combinations of them. This can hamper subsequentinterpretation of the resulting regression equation. Jol-liffe (2004) described several techniques for input vari-able selection in PCR; however, there is no singlebest method. In this study, successive PCR was con-ducted using all possible combinations of the climateindices (input variables) and the ‘best’ PCR model (themodel showing the highest cross-validated skill, as dis-cussed below) for each number of indices was retained.



PCR models were discussed in two groups: the mod-els showing the highest cross-validated skill using con-current (values known only after planting) and lagged(known prior to planting) indices, and those using laggedindices only. The group of models using both concur-rent and lagged indices demonstrates the skill that canbe achieved with ‘perfect’ climate knowledge, while thegroup of models using lagged-only indices demonstratesthe skill that can be achieved using observed informa-tion prior to planting and can be useful for future fore-casts.

Cross-validation was used in the selection of PCsto include in the regression models to reduce artificialskill (Efron and Gong, 1983). Leave-three-out cross-validation was used whereby a 3-year moving windowis left out of the regression and the middle year ispredicted at each step (and used to calculate errorstatistics). PCs were included in the model consecutively(in order of variance) since non-consecutive selectionof PCs may result in regression coefficients of thepredictors (climate indices) having the opposite signof their initial correlation with the predictand (yieldresiduals); resulting in a model that would not beconceptually acceptable (Garen, 1992). Non-consecutiveselection of PCs also implies that there are major modesof variability in the predictors that are unrelated tothe predictand (i.e. a significant portion of the variancein the PCs is unrelated to yield residuals). In thiscase, it would be desirable to remove the offendingvariables in question from the PCR (if possible) sincethey may not be optimal for forecasting, resulting in amore parsimonious model (Garen, 1992; Hidalgo et al.,2000).

The cross-validated skill of the model results was eval-uated using the mean squared error (MSE) between thecross-validated predictions and observations, and usinga Goodness of Fit Index (GFI), defined as the averagePearson’s correlation between the cross-validated pre-dictions and observations. In addition, the Spearman’srank correlation (ρ) and bias are presented. The use-fulness of the models in predicting county-level yieldresiduals were evaluated using the tercile hit score (per-centage of forecasts of the correct tercile category).Use of categorical tercile forecasts may be of par-ticular value since knowing if yields are expected tobe ‘above’, ‘below’, or ‘normal’ should provide ade-quate information for decision making. Using the ter-cile hit score a result of 33.3% is expected by chancealone, indicating no skill, while a result of 100% wouldindicate perfect skill. The usefulness of the models inpredicting county-level yield residuals over time wereevaluated using the percentage of counties with cor-rect forecasts (tercile ‘hits’) for each year. The ‘best’(>66.6% of counties of the correct tercile forecast)and ‘worst’ (<33.3% of counties of the correct tercileforecast) were then used as a diagnostic of the PCRmodels.

4. Results and discussion

4.1. Principal Component Analysis

The results of the PCAs of corn yield residuals, pre-cipitation, and temperature are listed in Table I. PC1 ofeach dataset showed all positive loadings (all observationlocations were in phase). For surface temperature and pre-cipitation, the second PC explained a significant, althoughreduced percent of variance compared to PC1. Signifi-cant relationships were not found in successive analyseswith the second PCs of these variables and will not beaddressed further.

4.2. Association of precipitation and surfacetemperature with yield residuals

PC1 of corn yield residuals showed significant correlationwith PC1 of precipitation between April and June (AMJ),and June and August (JJA) (Figure 2), with the high-est correlation between May and July (MJJ) (r = 0.692,p < 0.001). The MJJ season corresponds to the typi-cal timing of tasselling (the emergence of pollen-bearingtassel-like inflorescence at the top of the plant) of cornin the southeast United States, during which corn is mostsusceptible to water stress (Hansen et al., 1998; Baigorriaet al., 2007, 2008b). PC1 of corn yield residuals showedsignificant correlation with PC1 of surface temperaturebetween AMJ and July–September (JAS) (Figure 2) withthe highest correlation in JJA (r = −0.694, p < 0.001).This negative correlation with surface temperature corre-sponds to the results found by Lobell and Asner (2003)who noted significant negative correlation of temperaturewith corn yields in the southeast and Midwest, and posi-tive correlation in the northern Great Plains. The negativecorrelation with surface temperature is likely due to short-ened grainfill periods due to higher temperatures (Phillipset al., 1999). The MJJ and JJA values of PC1 of precip-itation and temperature, respectively, were retained forfurther analysis with climate indices.

4.3. Association of precipitation and surfacetemperature with climate indices

In constructing the BHI, two Atlantic grid points of sealevel pressure were found to have maximum correlationwith yield residuals at different times of year (discussedfurther below). The first grid point was located at 32.5 °N,65 °W (index denoted BHI1) and the second grid point

Table I. Percent variance explained by the first five principalcomponents of corn yield residuals, surface temperature, and

precipitation.

PC Corn yieldresiduals

Surfacetemperature

Precipitation

1 57.2 58.5 48.92 6.3 19.9 10.83 5.4 7.2 4.64 4.1 5.1 4.05 2.7 3.0 2.0



Figure 2. Pearson’s correlation of the first principal component ofsurface temperature and precipitation with the first principal componentof corn yield residuals. Dashed lines indicate significance at p = 0.05.

was located at 40 °N, 60 °W (index denoted BHI2). Boththe BHI1 and BHI2 (each constructed as the gradient ofstandardized sea level pressure anomalies between theAtlantic grid point and 30 °N, 90 °W, as previously men-tioned) showed greatest correlation with MJJ of PC1 ofprecipitation in the MJJ season (r = 0.657, p < 0.001and r = 0.543, p < 0.01, respectively) (Figure 3(a)) andwith JJA of PC1 of surface temperature in the JJA sea-son (r = −0.454, p < 0.01 and r = −0.361, p < 0.05,respectively) (Figure 3(b)). The BHI1 showed strongercorrelation with JJA of PC1 of surface temperature inDecember–February (DJF) (r = −0.293, p < 0.10) andFebruary–April (FMA) (r = −0.357, p < 0.05) com-pared to the BHI2 (Figure 3(b)).

The strongest correlation of the PNA with MJJ ofPC1 of precipitation occurred in the January–March

Figure 3. Pearson’s correlation of the BHI1, BHI2, and PNA indiceswith (a) MJJ of the first principal component of precipitation, and(b) JJA of the first principal component of surface temperature. Dashed

lines indicate significance at p = 0.05.

(JFM) season (r = −0.352, p < 0.05) (Figure 3(a)) andthe strongest correlation with the JJA of PC1 of surfacetemperature occurred in the FMA season (r = 0.488,p < 0.01) (Figure 3(b)). These correlations of the PNAwith precipitation in MJJ and surface temperature in JJAare of opposite sign compared to those reported in theliterature for winter and the early spring months (Leatherset al., 1991; Henderson and Vega, 1996).

The JMA did not show significant correlation withMJJ of PC1 of precipitation (Figure 4(a)), but showedhighest significant correlation with JJA of PC1 surfacetemperature in the previous August–October (ASO−1)season (r = 0.348, p < 0.05) (Figure 4(b)).

The TNA also did not exhibit significant correlationwith MJJ of PC1 of precipitation (Figure 4(a)), butwas significantly correlated with JJA of PC1 of surfacetemperature (Figure 4(b)) with the highest occurring inthe March–May (MAM) season (r = 0.456, p < 0.01).

4.4. Association of climate indices with yield residuals

The correlation of PC1 of corn yield residuals withclimatic indices is shown in Figure 5. The association ofyield residuals with each climate index is first discussedindividually, after which the association of combinationsof indices and the relative uniqueness of their effect onclimate in the study area is discussed. Cross-validatedforecast equations are then developed using PCR toeliminate multi-collinearities between the indices.

4.4.1. El Nino-Southern Oscillation

The PC1 of corn yield residuals showed maximumcorrelation with the JMA index in the July–September

Figure 4. Pearson’s correlation of the JMA and TNA indices with(a) MJJ of the first principal component of precipitation, and (b) JJAof the first principal component of surface temperature. Dashed lines

indicate significance at p = 0.05.



Figure 5. Pearson’s correlation of the climate indices with the firstprincipal component of corn yield residuals. Dashed lines indicate

significance at p = 0.05.

season of the previous year (JAS−1) (r = −0.426, p <

0.01) (Figure 5). Correlations were negative, indicatingthat the cooler (warmer) and wetter (drier) winter andspring conditions associated with El Nino (La Nina) inthe area were associated with reduced (increased) yields.

4.4.2. Pacific–North American pattern

The PC1 of corn yield residuals showed strongest neg-ative correlation with the PNA in the DJF (r = −0.533,p < 0.001) season (Figure 5). Thus, the positive (neg-ative) phase of the PNA during winter, and associatedcooler (warmer) and wetter (drier) conditions were asso-ciated with reduced (increased) corn yields. Wetter thannormal antecedent conditions may cause growers to delayplanting, possibly resulting in an overall reduction inyields. Alternately, the warmer conditions experiencedunder the negative phase could result in better growingconditions soon after planting since correlations of thePNA have been shown to be much stronger with temper-ature compared to precipitation in the southeast (Leatherset al., 1991). Earlier planting in the region is known totypically result in increased yields. The PNA may be oneof the avenues by which tropical Pacific SSTs associatedwith ENSO affect the southeast United States (Wang,2002). Horel and Wallace (1981) noted that the PNAin DJF tends to be positive during El Nino events, andmaximum correlation occurs with the SOI in the previoussummer.

4.4.3. Tropical North Atlantic SSTs

The PC1 of corn yield residuals was negatively correlatedwith the TNA, indicating that warming (cooling) in thetropical Atlantic was associated with reduced (increased)

corn yields (Figure 5). The correlation was strongestin MAM of the current year (r = −0.437, p < 0.01),coinciding with the reported lag of the Atlantic warmingin response to tropical Pacific warming (Enfield andMayer, 1997). Enfield (1996) found that correlations withthe TNA may not simply be an indirect response toENSO. However, the results found here are inconclusivein this regard as the correlations of the JMA andTNA share the same sign. Moreover, the timing ofmaximum correlation of the two indices with yieldresiduals coincides with the effect of ENSO (Enfieldand Mayer, 1997). Thus, the correlation found herewith the TNA could largely be a proxy for PacificSSTs.

4.4.4. Bermuda high

As previously noted, exploration of the gradient ofstandardized monthly mean sea level pressure betweenthe western Atlantic and near New Orleans revealedtwo Atlantic grid points that exhibited maximum cor-relation with yield residuals at different times of theyear. The first was located at 32.5 °N, 65 °W (BHI1),and the second was located at 40 °N, 60 °W (BHI2).The Atlantic grid point for the BHI2 is identicalto that found by Stahle and Cleaveland (1992) andused by Henderson and Vega (1996). The BHI1 corre-lated to yield residuals most strongly in the DJF sea-son (r = 0.494, p < 0.01), while the BHI2 correlatedmost strongly in the MJJ season (r = 0.503, p < 0.01)(Figure 5).

These indices of the BHI may experience maximumcorrelation with yield residuals at different times ofthe year due to the northerly migration of the highbetween winter and late spring (Sahsamanoglou, 1990;Davis et al., 1997). Correlations with the two indiceswere positive, indicating that larger (smaller) sea levelpressure gradients across the southeast are associatedwith increased (reduced) corn yields. During summers,the BHI extends westward and its anti-cyclonic flowbrings hot humid air to the southeast (Keim, 1997).Positive values of the index indicate enhanced mois-ture advection and higher precipitation potential in theregion (Stahle and Cleaveland, 1992). The time periodof maximum correlation of the BHI1 with yields maybe a proxy of the PNA, since the two indices sharea center of action in their calculation (in the southeastUnited States) and exhibit maximum correlation in thesame season. Wang (2002) noted that a possible path-way for ENSO-related Pacific SST anomalies to affectthe Atlantic region is via the PNA, and that it maybe possible for this connection of ENSO through thePNA to then affect the BHI. Changes in the BHI dur-ing winter could then affect tropical Atlantic SSTs inthe spring (Wang, 2002; Hasanean, 2004). The highcorrelation of the BHI2 in MJJ is particularly signifi-cant since this corresponds to the tasselling period ofcorn in most of the study area, during which yieldsare very susceptible to water stress (Hansen et al.,1998).



Table II. Pearson’s correlation between 3-month-averaged climate indices used in this study.

BHI1DJF BHI2MJJ PNADJF JMAJAS−1 TNAMAM

BHI1DJF 1 – – – –BHI2MJJ 0.218 1 – – –PNADJF −0.556∗∗∗ 0.325 1 – –JMAJAS−1 −0.159 −0.142 0.579∗∗∗ 1 –TNAMAM −0.469∗∗ 0.009 0.472∗∗ 0.483∗∗ 1

∗, ∗∗ , ∗∗∗ Significant at p < 0.05, 0.01, and 0.001 levels, respectively.

Table III. Cross-validated Principal Component Regression models showing greatest skill for each number of indices included.The PCR models showing greatest skill using concurrent and lagged and lagged-only indices are shown in bold-face and were

used to reconstruct county yield residuals in Figure 6.

# Indices Indices included in model # of PCs Cross-validated statistics Regression coefficients

GFI ρ MSE Bias BHI1 BHI2 JMA PNA TNA

5 BHI1 BHI2 JMA PNA TNA 2 0.666 0.673 40.0 0.00 1.93 2.67 −1.06 −2.23 −0.844 BHI1 BHI2 JMA TNA 2 0.659 0.731 40.8 0.02 2.78 3.34 −1.55 – −1.733 BHI1 BHI2 JMA 1 0.679 0.599 38.8 0.11 3.24 3.10 −2.73 – –3 BHI1 JMA PNAa 1 0.569 0.567 48.6 0.12 1.98 – −2.03 −2.56 –2 BHI1 BHI2 1 0.594 0.538 46.7 0.21 3.52 3.52 – – –2 BHI1 PNAa 1 0.550 0.531 50.0 0.16 2.83 – – −2.83 –1 PNAa 1 0.477 0.468 55.5 0.12 – – – −4.58 –

a Best models using lagged-only indices.

4.4.5. Interaction of climatic indices and theuniqueness of climate signals

While several of the climate indices showed strong,significant relationships with PC1 of corn yield residuals,these results are confounded by the fact that thereare strong relationships between the climate indices(Table II). Some of the indices share centers of actionand show concurrent correlations with yield residuals(BHI1 and PNA). Others show correlations at lag timesthat coincide with time periods when the indices areknown to be most strongly connected (JMA and PNA,JMA and TNA). The presence of the Pacific signalin the TNA may also be reinforced by its correlationwith the BHI1 and PNA. A connection between Pacificwith spring or summer climate could be indicated bythe (weak) correlation (p < 0.10) between the winterPNA and summer BHI2 (Table II). Thus, there are likelyredundancies in using all these indices to predict yields.

In an effort to assess the predictability of PC1 ofcorn yield residuals with combinations of climate indices,regression analysis was conducted. Due to the highcorrelations between the indices, PCR was conducted(using the 3-month averaged index values identifiedabove) to eliminate the multi-collinearities between theindices.

4.4.6. Principal component regression

PCR was conducted, using cross-validation, with allpossible combinations of indices (yielding a total of 31PCR models). The intent of the regression was to identify

the most important combinations of concurrent (valuesknown only after planting) and lagged (known prior toplanting) indices as they relate to corn yield residuals,as well as to identify the combinations of lagged-onlyindices that could be used to forecast yields in the future.The group of models using both concurrent and laggedindices demonstrates the skill that can be achieved with‘perfect’ climate knowledge, while the group of modelsusing lagged-only indices demonstrates the skill that canbe achieved using observed information prior to planting.

The PCR results using all possible combinations ofindices are shown in Table III. Only the PCR modelsshowing the highest cross-validated skill (highest GFIand lowest MSE) for a given number of indices areshown. Using both concurrent and lagged indices, thePCR model for the BHI1, BHI2, and JMA indices showedthe highest cross-validated skill, indicating the redun-dancy of using four or five indices. With the excep-tion of the 1-index model in Table III, the PCR mod-els showing greatest skill using both concurrent andlagged indices all contained the BHI1 and BHI2. Theinclusion of the BHI2 indicates the importance of thisindex in relation to summer climate in the southeastUnited States (Stahle and Cleaveland, 1992; Hender-son and Vega, 1996). Following these two indices, themost important was the JMA index which appearedin three of the models. The PNA showed the great-est cross-validated skill of all of the 1-index models(by definition 1-index models are identical to simpleregression without PCR). Of this group of models show-ing the highest cross-validated skill, all but the 1-index



model (the PNA) requires information known only afterplanting.

Of the seven possible models using combinations oflagged indices only (i.e. all possible combinations ofthe BHI1, JMA, and PNA indices), values of whichare known prior to planting and may thus be useful forforecasting, the PCR model using the BHI1, JMA, andPNA indices (the maximum number possible) showed thegreatest cross-validated skill (Table III). Compared to thebest model using both lagged and concurrent indices, the3-index model using lagged-only indices resulted in areduction of the GFI by 0.11 and increase in MSE of9.8. The 1-, 2-, and 3-index models using lagged-onlyindices all contained the PNA, and can thus be employedat the end of February to forecast yields for the currentyear’s growing season (both the BHI1 and PNA use DJFvalues). Following the PNA index, the BHI1 index wasincluded in the 2- and 3-index models with greatest cross-validated skill.

County corn yield residuals were reconstructed usingthe results of the PCR models with greatest cross-validated skill (Table III) using concurrent and laggedindices (Figure 6(a)) and lagged-only indices (Figure6(b)). Using both concurrent and lagged indices 93.8%

of predicted county yields were found to be significant(at p < 0.05), while using lagged-only indices 80.6% ofpredicted county yields were significant. Also shown, arethe time series (Figure 6(c) and (d)) of the cross-validatedPCR models showing greatest skill compared to PC1 ofcorn yield residuals. It is evident from the time series thatwhile the PCR models generally follow the fluctuationsof PC1 of corn yield residuals there are some years whenthe models were unable to reproduce.

The error associated with the cross-validated countyyields using the PCR models showing greatest skillusing concurrent and lagged and lagged-only indicesis shown in Figure 7. The error in yields gener-ally followed a normal distribution with the errorof the predictions using lagged-only indices showinglarger variance and a positive skewness. Using con-current and lagged indices, 60.1% of the predictionsfell within +/−0.5 Mg ha−1 and 93.8% were within+/−1.5 Mg ha−1. Using lagged-only indices, 60.2% ofpredictions were within +/−0.5 Mg ha−1, and 91.2%within +/−1.5 Mg ha−1.

The accuracy of the cross-validated county yieldresidual forecasts in both space and time were evalu-ated using categorical tercile forecasts (Figure 8). For

Figure 6. Cross-validated Pearson’s correlation of predicted county corn yield residuals using concurrent and lagged indices (a), lagged-onlyindices (b), and the time series of the first principal component of corn yield residuals compared to the cross-validated principal componentregression model using concurrent and lagged indices (c), and lagged-only indices (d). Correlations of county yield residuals >0.33 are significant

at p < 0.05. The PCR models in (c) and (d) were used to reconstruct the predicted county corn yield residuals in (a) and (b), respectively.



Figure 7. Relative frequency of error of cross-validated county cornyields using both concurrent and lagged indices (a) and lagged indices

only (b).

comparison, tercile forecasts using only the JMA indexare also shown. This comparison allows any improve-ment in skill of the PCR models to be evaluated rela-tive to using only the JMA index. In addition, use ofthe JMA index only is of value, even if at lower skill,since it provides the longest lead-time compared to theother models. County hit scores ranged from 30.6 to72.2% and from 25.0 to 72.2% using both concurrentand lagged indices (Figure 8(a)) and lagged-only indices(Figure 8(b)), respectively, while hit scores using onlythe JMA index as a predictor ranged from 25.0 to 63.9%(Figure 8(c)). In Figure 8(a) and (b) county forecasts thatshowed low or no skill were generally located on theedges of the domain. This is likely due to the domaindependence of PCA when used to aggregate a dataset(Jolliffe, 2004); the loadings of PC1 of county corn yieldresiduals were greatest near the center of the domain withthe densest data (PC1 loadings not shown).

The hit score across all counties showed large year-to-year variability (Figure 8(d), (e) and (f)) with thepercentage of counties with correct tercile forecastsranging from 3.1 to 98.4%, 7.0 to 98.4%, and 3.1to 98.4% using both concurrent and lagged indices(mean: 50.9%), lagged-only indices (mean: 50.8%), andthe JMA index only (mean: 41.3%), respectively. Toinvestigate the year-to-year variation of correct forecasts,standardized seasonal index values were separated intothree categories: ‘low’, ‘high’, and ‘mid’; defined asvalues below, above, or within ±0.5 standard deviation ofthe mean. Forecasts were then evaluated for years of highforecast skill (>66.6% of counties forecasted correctly)and low forecast skill (<33.3% of counties forecastedcorrectly) in Table IV. For high forecast skill years theindex values tended to fall in the low or high categories,with the exception of the PNA index. For low forecastskill years the index values tended to fall in the midcategory. Notable in the low forecast skill years is the

occurrence of one to two years with a low value forthe JMA index (approximately coinciding with La Ninaevents) indicating that La Nina years were generally wellforecasted (at least with >33.3% of counties with correctforecasts) as were El Nino years (to a lesser extent)compared to neutral.

5. Concluding remarks

PCA was used to summarize precipitation, surface tem-perature, and county corn yield residuals from Alabama,Florida, and Georgia to reduce the dimensionality of thedatasets. The association of corn yield residuals with pre-cipitation and surface temperature was evaluated by linearcorrelation. The association of corn yield residuals, sea-sonal precipitation, and surface temperature (that showedthe strongest correlation with yield residuals) with climateindices was then evaluated by linear correlation. Cornyield residuals exhibited statistically significant correla-tion with each of the indices evaluated. MJJ precipitationonly showed significant correlation with three of the fiveindices and JJA surface temperature showed significantcorrelation with all five indices. The timing of maximumcorrelation of the climate indices with MJJ precipitationand JJA surface temperature often did not match the tim-ing of maximum correlation of the indices with corn yieldresiduals.

While ENSO is known to affect winter and early springclimate in the southeast United States, the JMA index(as well as other indices of ENSO, results not presented)showed the lowest significant correlation with yield resid-uals of the five indices evaluated. The greatest correlationwith yield residuals was found with the PNA index,followed by the BHI2, BHI1, TNA, and JMA indices,respectively. While not exhibiting the greatest correla-tion, the JMA index did show significant correlation atthe largest lead-time (JAS of the previous year) of all theindices, indicating its potential value for forecasting cornyields in the region. The BHI1 and PNA exhibited max-imum correlation in the DJF season prior to the growingseason, while the TNA and BHI2 exhibited maximumcorrelation during the growing season (MAM and MJJ,respectively).

PCR models using all possible combinations of indiceswere developed to determine the best (showing greatestskill according to the GFI and MSE) PCR model usingconcurrent and lagged and lagged-only indices and toeliminate multi-collinearities between the indices. Usingboth concurrent and lagged indices and lagged-onlyindices, the best cross-validated PCR models containedthree indices. Using both concurrent and lagged indicesthe best PCR model contained the BHI1, BHI2, andJMA indices, while using lagged-only indices the modelcontained the BHI1, JMA, and PNA indices (the maxi-mum possible). Reconstruction of county yields using thecross-validated predictions of the PCR models showedthat 93.8 and 80.6% of the predicted county yields werestatistically significant using concurrent and lagged and



Figure 8. Cross-validated hit scores of predicted county corn yield residuals using concurrent and lagged indices (a), lagged-only indices (b),the JMA index only (c), and percent of counties with correct tercile forecasts over time using concurrent and lagged indices (d), lagged-only

indices (e), and the JMA index only (f). [Correction made here after initial publication.]

lagged-only indices, respectively. Evaluating the countyyield forecasts using the tercile hit score showed that 98.4and 97.6% of counties had some skill greater than thatexpected by chance (hit score >33.3%), however, skillacross counties varied greatly year to year. The resultsof the PCR model using lagged-only indices demon-strated the results that can be achieved using observedclimate index values known as early as the winter beforethe spring planting. The PCR model using lagged-only

indices showed better skill compared to using the JMAindex only (89.9% of counties showing skill greater thanchance), however, by itself, the JMA index can be usedto make forecasts with the longest lead-time (JAS of theprevious year) of all the indices evaluated.

Two final caveats must be made on the use of monthlyvariables to predict crop yields and the use of county-level data. Crop yields are known to be highly sensi-tive to the distribution of precipitation within a given



Table IV. Diagnostic of index values for years of High and Low forecast skill for the PCR model using concurrent and laggedindices, lagged-only indices, and the JMA index only. Values show the category of each index in High and Low forecast skill

years.

High Forecast Skill Years (>66.6% of Counties with correct tercile forecasts)

Concurrent and Lagged Lagged-Only JMA Only

BHI1 BHI2 JMA BHI1 JMA PNA JMA

Low 4 6 5 5 5 3 4Mid 3 2 3 2 2 4 1High 5 4 4 4 4 4 4

Total: 12 12 12 11 11 11 9

Low Forecast Skill Years (<33.3% of Counties with correct tercile forecasts)

Concurrent and Lagged Lagged-Only JMA Only

BHI1 BHI2 JMA BHI1 JMA PNA JMA

Low 3 3 1 0 1 3 2Mid 3 3 5 5 5 3 9High 2 2 2 4 3 3 5

Total: 8 8 8 9 9 9 16

month, particularly during crucial periods such as at tas-selling for corn. Monthly or 3-month-averaged variablessuch as the climate indices used here are not capableof capturing this short-term variability. Similarly, pre-cipitation magnitudes and distributions within a givenmonth can vary greatly within a county, resulting in dif-ferent yields that are not resolved using county-level yieldinformation. Nevertheless, the techniques used can beuseful for forecasting corn yields in the southeast UnitedStates.

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Use of climate indices to predict corn yields in southeast USA