Value of perfect forecasts of sea surface temperature anomalies for selected rain-fed agricultural locations of Chile

Transcription

1 Agricultural and Forest Meteorology 116 (2003) Value of perfect forecasts of sea surface temperature anomalies for selected rain-fed agricultural locations of Chile Francisco J. Meza a,, Daniel S. Wilks b, Susan J. Riha b, Jery R. Stedinger c a Facultad de Agronomía e Ingeniería Forestal, Pontificia Universidad Católica de Chile, Casilla , Santiago, Chile b Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, NY, USA c School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, USA Received 7 August 2002; received in revised form 10 December 2002; accepted 6 January 2003 Abstract This study evaluates the value of perfect forecasts of El Niño phases for selected rain-fed agricultural locations of Chile. The analysis framework incorporates a soil crop-atmosphere system model and employs an expected utility decision algorithm that reflects a wide range of possible risk attitudes. The value of perfect forecasts is generally greater than zero indicating that real El Niño forecasts could potentially have economic value. Forecast value depends upon crop and location. The value of forecasts increases as the agricultural system becomes more susceptible to climatic variability. Among the regions under study, Temuco (38.5 S) and Valdivia (39.4 S) are likely to see the largest gains from long-term sea surface temperature forecasts Elsevier Science B.V. All rights reserved. Keywords: El Niño forecast; Expected value of perfect information; Chilean agriculture 1. Introduction Chile s agricultural central valley is mainly located between latitudes 29 and 40 south. It is a complex agricultural system where irrigated and rain-fed lands are used to satisfy the internal demand for agricultural products as well as to produce high value crops that are exported. These represent one of the most important sources of income for the country. An El Niño event is an unusual and extensive warming in the central and eastern equatorial pacific. The Southern Oscillation refers to an anomaly in the pressure difference between Tahiti and Darwin. Although those are distinct oceanic and atmospheric processes, their high correlation has resulted in the phenomenon being referred to as the El Niño-Southern Oscillation Corresponding author. Fax: address: fmeza@puc.cl (F.J. Meza). (ENSO). In fact, among the events associated with El Niño is the presence of low (negative) Southern Oscillation index (SOI) values. Rainfall anomalies in central Chile have been investigated and associated with ocean and atmospheric phenomena including the Southern Oscillation index and El Niño events. Anomalously dry conditions are found during positive SOI phase (La Niña event) (Rubin, 1955; Pittock, 1980) and rainfall is exceptionally abundant during El Niño years (Quinn and Neal, 1982; Kane, 1999). A good review on the effects of the Southern Oscillation over South America is provided by Aceituno (1988). The current level of understanding of climatic variability attributable to ENSO, especially in those cases where a subset of events within the regional climate can be identified, provides a good opportunity to explore its impacts over agricultural systems. If a particular region shows an ENSO climatic footprint, /03/$ see front matter 2003 Elsevier Science B.V. All rights reserved. doi: /s (03)

2 118 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) meteorological variables classified according to its different phases (i.e. El Niño, Normal or La Niña) can be used to forecast crop yields and to study their temporal variability. Several studies have investigated the use of climate information and forecasts based on the ENSO phenomenon at different levels of integration and complexity. Regional studies addressing benefits of forecasts for the US economic sector have been carried out by Adams et al. (1995) and Solow et al. (1998). Comparative studies of a location in Argentina and the agriculture of the south-east US describe the potential benefits of climate forecasting for three different types of forecasts (Jones et al., 2000). Comparisons between US and Canadian wheat farmers using SOI based climate forecasts have been described by Hill et al. (2000). Messina et al. (1999) utilize ENSO information for agricultural decisions regarding to optimal land allocation in Argentina. The value of forecast information has been also described for individual farmers in Texas (Mjelde et al., 1997; Mjelde and Hill, 1999). Hammer et al. (2001) provides a comprehensive review on applications and experiences using climate forecasts. The present work shows the applications of perfect forecasts of El Niño phases for rain-fed agricultural locations in Chile. This analysis incorporates two different soil types at each location, analyzing their effect on the potential willingness to pay for information (i.e. differences in the expected utility obtained using forecasts and expected utility based on climatological information), considered over a range of risk preferences. Sections 2 and 3 describe the nature and main features of the model used to address this problem. Section 2 presents the soil crop-atmospheric model. Section 3 develops the economic decision model. Section 4 presents the results for perfect forecasts, describing in detail the impact of perfect information for decisions involving a range of crops, soils and locations. Finally, Section 5 provides conclusions and summarizes relevant issues of the study. 2. Soil crop-atmosphere model The evaluation of the economic consequences of management alternatives under different climatic conditions can be addressed using crop simulation models. Such models integrate the effects of soil, crop, and weather interactions representing the dynamics of crop growth. This section describes the main components of the modeling approach used to evaluate management alternatives subject to different climate patterns. This allows evaluation of the benefits of sea surface temperature forecasts Weather generator Daily meteorological variables are the most important source of temporal variability for crop growth and development. Among them temperature and precipitation have been identified as the major driving variables. They are employed in many studies that investigate the main effects of climate variability on agriculture using crop simulation models (Riha et al., 1996; Wheeler et al., 2000). The inclusion of other relevant variables, such as solar radiation, wind speed, and relative humidity can lead to a better understanding of the effects of climate variability on crop productivity as well as to increase the degree of reliability of the simulated outcomes for exploring different management alternatives. Daily records of meteorological variables are not always available and/or their duration may be insufficient to allow the study of climate variability effects on agricultural crops. To solve this problem stochastic synthetic weather time series can be generated, using random number generators whose outputs have the property of reproducing the main statistical characteristics of the series from which their parameters were fit (Wilks and Wilby, 1999). Those algorithms are commonly known as Weather Generators when used for Monte-Carlo simulation, and were introduced into the crop modeling scheme by Richardson (1981). The science and technology of climate prediction, and the use of indices such as the El Niño and Southern Oscillation to predict likely seasonal to interannual climatic conditions, have reached a point at which there is a possibility to use them not only for early warning systems (Ogallo et al., 2000), but when combined with weather generators, to better address the effects of climate variability on management alternatives. Most of the effort in development of weather generators has been devoted to the proper description of the precipitation process (see Wasami, 1990; Wilks,

3 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) ). However, a comprehensive study of climate variability using weather generators must include other variables important to the application at hand, representing their time dependence and mutual correlation in an adequate way. Wilks and Wilby (1999) describe the historical evolution of those models and present a summary of the weather generator components. Typically the precipitation process is modeled in two parts, occurrence and intensity, and the remaining variables are represented using autoregressive models. Daily meteorological variables can also be generated conditioned on climate indices, such as ENSO, to study the impact of its different phases on agricultural systems. For the purposes of this work the El Niño classification proposed by Trenberth (1997) was adopted. Here the region known as Niño 3.4 (5 S 5 N, W) is used to calculate sea surface temperatures (SST) and a sea surface temperature anomaly (SSTA) threshold of ±0.4 C is set to classify years into different El Niño phases (i.e. El Niño, Normal, and La Niña). The parameters included in the weather generator algorithm are conditioned on this classification. Except for the daily mean values for non-precipitation variables, which are allowed to vary on a daily basis, the remaining parameters are considered stationary within each month Precipitation occurrence A common approach to modeling daily precipitation occurrence is to employ a first-order Markov chain. However, it has been demonstrated that this model may not adequately represent the duration of extremely long dry spells for some climates (Wilks, 1999). That particular characteristic is quite common on subtropical climates like the central valley of Chile. For this reason first-order, second-order, and hybrid first/second-order Markov models (Wilks and Wilby, 1999) were tested. The model structure can be generalized as: P hij = Pr{X t = j X t 1 = i, X t 2 = h}, h, i, j = 0, 1 (1) where X t is a discrete random variable over time representing a wet (1) or dry (0) condition on day t. For a first-order Markov chain the state of the random variable X t will only depend on the conditions of the previous day (X t 1 ). This condition can be represented within the selected second-order Markov chain including the constraints: P 001 = P 101 = P 01 (2) P 011 = P 111 = P 11 Here P 01 and P 11 are the transition probabilities of a first-order Markov chain defined as the probability of observing a wet day on day t given a dry day on day t 1, and the probability of observing a wet day on day t given a wet day on day t 1, respectively. Similarly, a hybrid-order model (i.e. a Markov model that extends its memory further back for dry spells only) will be represented as a second-order Markov chain with the constraint: P 011 = P 111 = P 11 (3) The hybrid-order model essentially retains the second-order dependence for dry days, but collapses to first-order dependence for consecutive wet days. The Bayesian information criterion (Schwarz, 1978) was employed to select the best representation among the candidates by maximizing the logarithms of the likelihood function minus a parsimony penalty Precipitation amount In Chile as well as in other subtropical regimes, rainfall amounts are small except for a few occasional heavy rains. Therefore, it is appropriate to model precipitation intensity using a positive and highly skewed probability distribution function (Geng et al., 1986). To represent this feature, gamma distributions are usually chosen (Geng et al., 1986; Katz, 1977). In this study exponential and log-normal distributions were also tested Non-precipitation variables Maximum, minimum and mean daily dew point temperature, as well as mean daily wind speed are represented by a multivariate first-order autoregressive process. The equation that represents the multivariate process can be written as Z(t) = [A]Z(t 1) + [B]ε(t) (4) where Z(t)is a K-dimensional vector of standard Gaussian variables for today s variables, [A] and [B] are K K matrices of parameters (here, K = 4). Finally

4 120 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) ε(t) is a vector of independent standard normal values, known as white noise or error (Wilks and Wilby, 1999). Parameters for the matrices [A] and [B] can be found by computing the simultaneous and first-lag correlation among the variables, which correspond to the elements of the matrices [R 0 ] and [R 1 ], respectively, and solving the equations (Wilks, 1995): A = [R 1 ][R 0 ] 1 (5) [B][B] T = [R 0 ] [A][R 1 ] T In the parameter fitting procedure wind speed was transformed into an approximately Gaussian variable by taking logarithms of its value, this transformation generally results in better parameter estimates (Stedinger, 1980). The means and variances for each month and El Niño classification were calculated. It is convenient to keep the distinction between wet and dry days, and to model the time series process with different parameters representing the precipitation status, because cloud cover associated with precipitation can influence solar radiation as well as the thermal amplitude (Liu and Scott, 2001). Seasonality in the observed means was modeled by fitting a single harmonic Fourier Series. An algorithm proposed by Epstein (1991) allows a smooth interpolation for the corresponding daily means. Following this procedure, daily variables were expressed as standardized anomalies using the corresponding mean and variance conditioned on the climatic classification, time of the year (day for the case of mean values, and month for variances), and whether or not precipitation was observed. The resulting daily standardized anomalies were used to compute the simultaneous and lagged correlation coefficients that comprise the matrices [R 0 ] and [R 1 ]. Daily solar radiation was not included in the autoregressive process due to the lack of reliable information. It was estimated by empirical equations developed by Bristow and Campbell (1984), and validated for Chile by Meza and Varas (2000). That relationship captures some of the effects of climatic variability as simulated by the weather generator, because it uses thermal amplitude as independent variable Crop model Crop models can capture the major effects of climate variability on crop development and yield, and consequently can be used to explore management alternatives for a better adjustment of agricultural systems to natural climatic variability. Hoogenboom (2000) describes different applications of those models that can be synthesized as strategic and tactical applications, in which crop models are run prior to or right after the planting date to evaluate different management strategies; and forecasting applications by which crop yields are simulated under different climatic scenarios with different objectives ranging from marketing decisions to food security issues. The Erosion Productivity Impact Calculator (EPIC) crop model was used to simulate crop yields under different El Niño scenarios. This model has been validated for different agricultural systems using specific parameters for different crops (Williams et al., 1989). In this study, five different crops were included in the simulation, namely spring and winter wheat, oats, potato and sugar beet. These are the main annual crops in terms of hectares cultivated in Chile. Model parameters were taken from EPIC user s manual (Williams et al., 1990). Actual yield data for the regions under study was not available, therefore it was not possible to perform a site-specific calibration validation study. However, generally applicable parameters are satisfactory for this exploratory study. Even though other crop simulation models with different levels of detail and complexity are available, EPIC provides a fairly good approximation of the crop growth and development under different climatic and management conditions (Kiniry et al., 1995). The main assumption in this study is that EPIC will be sufficiently accurate so that simulated yields reflect the mean and also the variability in observed yields obtained with different agricultural practices. In the literature there are several studies that address crop model performance for different aspects of the soil crop system (some examples can be found in Landau et al., 1998; Cabelguenne et al., 1999; and Roloff et al., 1998). However, crop simulations do not need to provide a prediction of the actual yield in any particular year for the purposes of SSTA forecast valuation Selected locations, soil types and simulation procedure The region under study corresponds to the rain-fed portion of the central valley of Chile. Four

5 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) Table 1 Selected stations, geographic location, annual precipitation, and mean temperature Locality/station name Latitude (S) Longitude (W) Altitude (m) Precipitation (mm) Temperature ( C) Concepción/Carriel Sur Temuco/Maquehue Valdivia/Pichoy Puerto Montt/Tepual meteorological stations were selected to represent the climatic conditions for the locations under study. Data provided by the National Climate Data Center (NCDC) for the period were classified into the three El Niño phases, and the parameters of the weather generator were fit separately to seasons associated with each of the three phases. Table 1 shows the geographic location, total annual precipitation and mean temperature for the stations used. For each location two different soils types were considered to compare the potential benefits of long-term climate forecast under two different yet representative soil conditions. The main difference between the two soils is their maximum rooting depth, and consequently their maximum available water (A w ), defined as the difference in millimeters between two specific points of the soil moisture curve, field capacity and permanent wilting point. Table 2 summarizes the main features of the soils selected for each locality. For each of the soils, crops, and El Niño phases, 500 independent years of meteorological variables were generated using the weather generator algorithm. The EPIC model was run with the initial condition in each year of dry soil at the end of the previous summer. Since the crops studied are not planted until mid-winter or late spring, this feature assures the gen- Table 2 Soil depth and maximum available water (A w ) of eight selected soils of rain-fed Chile s central valley Locality Soil name Soil depth (m) A w (mm) Concepción Caripilun Merilupo Temuco Temuco Ñielol Valdivia Valdivia Rio Bueno Puerto Montt Alerce Puerto Octay eration of totally independent initial soil moisture and weather conditions in successive growing seasons. The differences in rainfall and evaporation between El Niño phases produce changes in the soil water budget prior to the planting date, which contributes to the impact of climatic variability on the future yields. The model simulates optimum crop performance under each soil climate scenario. Additional restrictions associated with crop management such as weed competition, diseases, and nutrient stress are not considered. Only nitrogen fertilization is considered as an operating decision variable; its impact on crop growth and development is modeled using EPIC. 3. Decision model 3.1. Utility functions Optimal selection among alternatives, within a decision framework, requires knowledge of the consequences associated with each alternative, their likelihood or relative frequency of occurrence, and a mathematical formulation of decision makers preferences for the possible results. Utility functions, although not the only plausible approach to represent these preferences, have been widely used to represent risk attitudes. The main characteristics of utility functions are: (a) They are monotonic functions of wealth, income, net benefits, or gains and loss that a decision maker can obtain after selecting a particular alternative. (b) A utility curve shows an upward slope representing the preference for more rather than less, everything else being equal (Clemen, 1996). (c) They can show either decreasing marginal utility, which is associated with a risk-averse decision maker; constant marginal utility referred to as risk neutrality; or increasing marginal utility (risk seeker) (Hardaker et al., 1997).

6 122 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) Even though it is possible to assess empirical utility functions by elicitation techniques based on probability wheels or certainty equivalent methods (Hardaker et al., 1997), the utilities obtained are particular cases corresponding to individual decision makers. The objective of this work is to illustrate and perform an exploratory assessment of the potential value of long-term sea surface temperature anomalies forecasts considering generalized but realistic cases of risk attitude. For this reason, a single algebraic formulation of the utility function is used, varying the shape of the utility function in order to explore the impact of different risk attitudes. Messina et al. (1999) and Letson et al. (2002) have used power functions of wealth in order to represent farmers risk preferences in Argentina. The coefficients of relative risk aversion as defined by Pratt (1964) and Arrow (1965) represent cases of risk-neutral and risk-averse decision makers. This representation has proven useful especially if one desires to model the change in risk attitudes of the decision maker when changes in total wealth are observed. In the present work, a fixed initial wealth is assumed. Risk behavior is represented here by an exponential utility function of the net benefits of a single crop, following the approach taken by Dillon and Scanndizzo (1978). The general formulation is: 1 e δ x U(x) = 1 e δ, δ 0 (6) x, δ = 0 where x is the net benefits from crop yield in a year (1993 dollars), and δ is the risk aversion parameter (dollars 1 ). It can be verified that the marginal utility is always positive but that the relative risk behavior depends upon δ. du(x) > 0 dx δ d 2 U(x) dx 2 > 0 for δ>0 d 2 U(x) dx 2 < 0 for δ<0 d 2 U(x) dx 2 = 0 for δ = 0 Values of δ greater than zero represent risk-seeking decision makers, a decision maker whose utility function has a parameter delta equal to zero is considered as risk-neutral, and negative delta values represent the more typical risk-averse decision maker. Nine values of delta (δ = ; 0.001; ; ; ; 0.0; ; ; and ) were used in this study. These values were found to define utility functions consistent with those found by Dillon and Scanndizzo (1978) for Brazilian farmers and Hildreth and Knowles (1986) for farmers in the US. Even though positive δ values are found in the empirical work of Dillon and Scanndizzo (1978), risk-seeking individuals are not usually viewed as rational decision makers. They have been included in this study to explore the effects of the risk parameter over a wider range of possibilities Actions and events For each crop, location, soil type, and El Niño state, 82 different decision alternatives were evaluated. They represent combinations of three planting dates spaced by 20 days, three plant densities, and nine levels of nitrogen fertilization. One additional alternative represents a situation in which no crop is planted so the farmer will obtain no revenue from farming. For the remaining 81 alternatives, net benefits are calculated as the price of the product times the yield obtained in a particular year-action minus variable and fixed costs. The 1993 price-cost scenario is used in this study and benefits are expressed in dollars per hectare. Price information, input requirements, and costs associated with each crop were obtained from Espinoza (1993). A set of three mutually exclusive and collectively exhaustive events θ j based on SSTA values is considered here, under the assumption that for the growing period (4 6 months depending on the crop) only one of these three events, namely El Niño (j = 1), Normal (j = 2) and La Niña (j = 3), can occur. Changes among these states are assumed not to occur within a particular growing season. Forecasts for periods of time shorter than the growing season are possible, but they introduce additional complications to the format of evaluation, so they are not considered in this initial study. Let NB(D i, θ j, k) be the net benefits associated with decision D i (i = 1,..., 82) for El Niño state θ j

7 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) (j = 1, 2, 3) and the year k (k = 1,..., 500). The expected utility for any decision D i under a SSTA scenario θ j is estimated as 500 EU(D i,θ j ) = 1 U[NB(D i,θ j,k)] (7) 500 k= Value of information The expected utility provides an evaluation of the consequences of different actions for each SSTA state. It is at this point where the risk aversion parameter can play an important role modifying the shape of the net benefits function, producing expected utilities that are different from the utility associated with the expected net benefits. The rational decision maker selects the alternative that maximizes the probability-weighted expected utility, where the probabilities are determined by the available information (i.e. historical information of SSTA, an imperfect forecast, or perfect information). The forecasts will produce a set of conditional probabilities for the three SSTA classes in the upcoming growing season (P Θ F (θ f)). Provided that the probabilities of the El Niño phases for the growing season (P Θ (θ j )) can be obtained from the historical record, it is possible to calculate the relative frequencies with which the forecast are issued if they are unbiased or if their bias is known. Let f m (f 1 = El Niño, f 2 = Normal, f 3 = La Niña ) be the forecast for the SSTA scenario in the next growing season with relative frequencies given by P F (f m ). The conditional probabilities for El Niño phases given the forecast (P Θ F (θ f)) satisfy the following relationship: P Θ (θ j ) = 3 P Θ F (θ j f m ) P F (f m ) (8) m=1 Perfect SSTA information will correspond to the case where the conditional probability of a given SSTA condition given the forecast is equal to one for the scenario forecasted and zero for the remaining cases. Climatological information, referred to here as historical records of SSTA, can be represented within this scheme as conditional probabilities for climatic conditions equal to the relative frequencies with which they are observed, and independent of the forecast type. Imperfect information is an intermediate situation where there is error associated with the forecast but the resulting conditional probabilities differ from the climatological relative frequencies. In this paper, the probability-weighted expected utilities for perfect SSTA information and climatological (i.e. historical) information are evaluated. Realistic, simple imperfect forecast results are described in Meza and Wilks (2003). Under the maximization of expected utility criterion, the expected utility for climatological information (EUCI) is the one obtained when an optimal decision is made without SSTA forecast, and would be calculated as 3 EUCI = max [P Θ (θ j ) EU(D i,θ j )] (9) i j=1 The expected utility corresponding to perfect SSTA information (EUPI) can be calculated as 3 EUPI = P Θ (θ j ) max[eu(d i,θ j )] (10) i j=1 To calculate the value of information it is necessary to assess a single monetary value for the utilities, with and without information. The certainty equivalent, defined as the inverse of the utility function evaluated at the probability-weighted expected utilities, represents the amount of money that the decision maker is willing to exchange for any particular scenario yielding an uncertain outcome (Hardaker et al., 1997). Following the nomenclature used in this work, the certainty equivalent of climatological information (CECI) and perfect information (CEPI) are obtained as: CECI = U 1 (EUCI) (11) CEPI = U 1 (EUPI) where U 1 (y) = ln(1 (1 eδ ) y) (12) δ The expected value of a perfect SSTA forecast will be the net increase in the certainty equivalent of the decision taken with information, relative to climatological information as the baseline. Thus, the expected value of perfect information (EVPI) is: EVPI = CEPI CECI (13)

8 124 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) The value of information should never be less than zero, and should be strictly positive if at least one of the optimal actions associated with the forecast information differs from the one selected without forecast unless different decisions yield the same outcomes. Note that the estimate of the EVPI is also a random variable that depends on the precision of the computed values (i.e. the length of the crop simulation), the estimate of its variance is presented in the Appendix A. 4. Results 4.1. Climatological differences between SSTA states During the rainy season (May to September), El Niño years show higher values of total precipitation in all locations. Differences up to 40% in average total precipitation can be observed when El Niño and La Niña years are compared. Both precipitation occurrence and daily precipitation amount are affected by the El Niño phenomenon. Except for the case of Puerto Montt, relative frequencies of days with precipitation are higher during El Niño than during La Niña years. Differences between average precipitation intensity are also present, being higher in El Niño years and decreasing in magnitude as we move southward. Mean maximum, minimum, dew point temperatures and wind speed of wet and dry days are less influenced by El Niño and La Niña years when compared within their corresponding category (i.e. wet or dry days). However, there are important differences between wet and dry days that will result in different temperature and wind statistics because of the greater frequency of wet days in El Niño seasons. While average maximum temperatures are 1 or 2 C higher on dry days, minimum temperatures are 2 or even 3 C lower. Dew point temperature and wind speed are higher on wet days than in dry days. These differences will be summarized by the crop and expressed as yield variability and changes in rate of development. Selected parameters of the weather generator algorithm for Concepción comparing El Niño and La Niña years are shown in Tables 3 and 4. Table 3 illustrates, on a monthly basis, the main differences in the precipitation process. Unconditional relative frequen- Table 3 Unconditional relative frequencies of precipitation days (π), mean daily precipitation intensity (µ), and expected monthly total precipitation (R) for El Niño and La Niña years at Concepción Month π µ (mm per day) El Niño years January February March April May June July August September October November December La Niña years January February March April May June July August September October November December R (mm per month) cies of precipitation days are obtained from the corresponding transition probabilities of a second-order Markov chain for El Niño and La Niña years. As mentioned above the relative frequency of precipitation Table 4 Mean annual values of non-precipitation variables for dry and wet days under El Niño and La Niña years at Concepción El Niño years Dry days Wet days La Niña years Dry days Wet days Maximum temperature ( C) Minimum temperature ( C) Mean dew point temperature ( C) Mean wind speed (m/s)

9 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) days is higher during El Niño years. Mean precipitation intensity is derived from the parameters of the fitted Gamma distribution function. The product of the shape (alpha) and scale (beta) parameters corresponds to the mean value for precipitation intensity. The expected monthly precipitation value is also reported in Table 3 as a summary of the differences between El Niño and La Niña years. Table 4 shows the mean annual values of maximum temperature, minimum temperature, mean daily dew point temperature and mean daily wind speed comparing dry and wet days under different climatic scenarios Value of perfect information Using historical information from 1950 to 1999 about the monthly sea surface temperatures in the equatorial Pacific stratified according to the El Niño classification, it is possible to obtain the relative frequencies of the three different phases of El Niño for each growing season. For winter wheat, spring wheat and oats the growing season considered here goes from June to December. The relative frequencies of El Niño, Normal, and La Niña, for winter-grown crops are P Θ (θ 1 ) = 0.34; P Θ (θ 2 ) = 0.36 and P Θ (θ 3 ) = 0.30, respectively. Sugar beet and potato have a growing season that covers 6 months, starting in October and ending in March. The relative frequencies of El Niño phases for these crops are P Θ (θ 1 ) = 0.33; P Θ (θ 2 ) = 0.41 and P Θ (θ 3 ) = A simulation model is used to capture the main effects of climatic variability. As a result, modeled yield values are high in comparison to those normally observed in the regions under study. If the model does not show bias in the yield estimates the results could be interpreted as an upper bound of the monetary net benefits that farmers would have obtained if they would have applied the state of the art technology in terms of weed control, fertilization (other than nitrogen), and pest management. In addition, soil nitrogen concentrations were set to relatively low values in all locations. The integrated model, under those conditions, selected optimal nitrogen fertilization levels slightly higher than the ones normally adopted by farmers. Three of the locations selected show, in general, economic values of perfect SSTA forecasts greater than zero. Even though the location of Puerto Montt presents differences in the climatic regime among the phases of El Niño, such differences are not sufficient for the decision model to select different best management alternatives. At Puerto Montt, the best strategy for any of El Niño phases turns out to be no different from the one based on climatological information. Results for the other locations and soil types are presented in the subsections below. With few exceptions, the farmer s risk attitude does not affect the selection of optimal alternatives. However, the magnitude of the risk parameter does introduce changes on the valuation of the net benefits (i.e. expected utilities). In those cases, the value of information reflects the farmer s willingness to pay for the information, and its change in magnitude is usually a consequence of the utility curve rather than a different decision alternative selected Results for Concepción Because it is a shallow soil, Caripilun only produces non-zero values for perfect information when either winter wheat or potato are grown. Moreover, the nature of this soil and climatic system forces the farmer, represented by the decision model, to select an alternative different than fallow conditions during El Niño years only. The remaining crops are not attractive alternatives because they do not produce yields that are sufficiently large to obtain, on average, positive net benefits for the Neutral or La Niña years. The interpretation of the results under this situation is therefore not straightforward. If the farmer decides to carry out an agricultural activity in this region with this soil he would need to pursue a completely different production system, involving extensive forage crops and animal production instead of annual crops. This hypothetical system falls out of the scope of our study. Merilupo soil, unlike Caripilun, has a higher water holding capacity, providing a better environment for an annual crop production system. Fig. 1 and Table 5 show the results of the expected value of perfect information for the crops under study on Merilupo soil, and the differences between optimal alternatives selected under different SSTA scenarios for each value of δ. Values in italic face represent selected decisions that differ from the one selected using historical information of the SSTA. The value of perfect SSTA information is found here for spring wheat with a range between 10 and 14 dollars/ha decreasing as the

10 126 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) Fig. 1. Expected value of perfect information at Concepción (Merilupo soil) for three crops. risk parameter increases, representing 5 10% of the certainty equivalent that the farmer would have obtained using climatological information. Among the different SSTA states (i.e. El Niño, Normal, La Niña, and Climatology), optimal strategies differ only in the amount of nitrogen fertilization. Early sowing dates (mid-august) are preferred to late ones since they are associated with higher amounts of rainfall during the Table 5 Differences between selected alternatives at Concepción under different SSTA states (θ j ) and risk attitude (δ) Crop Soil θ j Risk parameter (δ, 10 3 ) Fertilization rate (kg N/ha) Spring wheat Merilupo θ θ θ Sowing date (Julian day) Potato Merilupo θ θ θ Fertilization rate (kg N/Ha) Potato Merilupo θ θ θ Italic values represent selected strategies that differ from the climatological one.

11 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) upcoming growing season. Plant densities on the order of 2,000,000 plants/ha provide the highest net benefits in all scenarios. Fertilization rates of 150 kg nitrogen (N)/ha rather than 200 kg N/ha are selected during La Niña years. Potato exhibits the greatest monetary values for perfect information, ranging from 18 to 50 dollars/ha. The value in this case represents 3 5% of the certainty equivalent associated with the expected net benefits obtained using only climatological information. Planting dates and fertilization rates are the main components of the differences observed between SSTA states. During El Niño years early planting dates (mid-september) and fertilization rates of 100 kg N/ha are chosen by the decision model, whereas during the other years the rate of fertilization is increased by 50 kg N/ha and planting dates are delayed 1 month. For the case of decisions based on climatological information there is an increase in the fertilization rate from 100 to 150 kg N/ha as the farmer becomes a risk-taker. Winter wheat shows a very modest result in the expected value of perfect information, being less than 1 dollar/ha. Although the value of perfect information is positive, it is unlikely that a farmer would profit much from using SSTA forecasts for the selection of management alternatives Results for Temuco The result for the value of perfect SSTA forecasts and the differences between selected alternatives at Temuco are shown in Fig. 2 and Table 6, respectively. On the Temuco soil only sugar beet does not present EVPI greater than zero, indicating that for this crop the strategy selected under climatological information cannot be improved by using perfect El Niño forecasts. Among the other crops, winter-grown cereals have the smallest values for perfect forecasts, indicating that the differences on the alternatives selected are not translated into large changes in the net benefits obtained. Spring wheat, however, reaches a value of 30 dollars/ha, which is five or six times higher than the value found for winter wheat and oats. This value represents 6 8% of the certainty equivalent obtained when no forecast is used. Early sowing dates (mid-august) are selected in all years. Plant densities of 3,000,000 plants/ha and fertilization levels of 200 kg N/ha are the best strategy for El Niño years whereas low densities and relatively low fertilization rates (150 kg N/ha) give the best economic combination for La Niña years. The most important case for this soil and location is potato. The value of perfect forecasts is the largest found for this location. As in the case of spring wheat, potato growth and development have a strong dependence on spring summer conditions, making it advisable to select different strategies when a forecast is released. In this case the value of perfect information decreases as the risk parameter increases. EVPI for potato under this condition can reach values of 160 dollars/ha, being no less than 100 dollars/ha for the decision maker whose utility function reflects a higher risk preference. This represents 10% of the certainty equivalent obtained by a farmer that does not consider SSTA forecasts in the decision making process. In this case, changes in fertilization rates and planting dates are mainly responsible of the differences in expected utilities. While 150 kg N/ha produces the best results under El Niño and Normal years, 100 kg of nitrogen is the best strategy for La Niña conditions. Early planting dates are preferred in El Niño and Neutral years. The second soil selected in this study (Ñielol), has a larger water holding capacity. It shows a significant value of perfect information for all crops except for spring wheat. Winter wheat and potato show values of perfect information in the order of 20 dollars/ha. Those values are 10 and 1%, respectively of the certainty equivalents obtained by a farmer whose decisions are based on climatological information. The selection of plant densities in both cases is not affected by El Niño forecasts. Fertilization rate is increased from 150 to 200 kg N/ha in La Niña years, representing the best way to take advantage of the forecast for winter wheat. For potato late planting dates are selected during La Niña years keeping the same fertilization level in all years. In this soil, even sugar beet has a chance to be grown with management conditions that differ among El Niño phases and produce changes in net benefits up to 50 dollars/ha, representing 15% of the certainty equivalent obtained without information. As in the case of potato, selection of the optimal sowing date becomes the best way to improve net benefits in La Niña years and therefore obtain monetary benefits from perfect forecasts.

12 128 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) Fig. 2. Expected value of perfect information at Temuco for four crops. (a) Temuco soil, (b) Ñielol soil Results for Valdivia Fig. 3 and Table 7 show the main results of the expected value of perfect information and the differences between selected alternatives under different SSTA scenarios at the location of Valdivia. The differences between soil depths and water holding capacities are considerable in this case. The Valdivia soil, even though deep enough to provide an adequate supply of water during scarcity periods, provides a more favorable environment for adopting management

13 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) Table 6 Differences between optimal selected alternatives at Temuco location under different SSTA states (θ j ) and risk attitude (δ) Crop Soil θ j Risk parameter (δ, 10 3 ) Plant density (plants/m 2 ) Spring wheat Temuco θ θ θ Fertilization rate (kg N/ha) Spring wheat Temuco θ θ θ Sowing date (Julian day) Potato Temuco θ θ θ Fertilization rate (kg N/Ha) Potato Temuco θ θ θ Fertilization rate (kg N/Ha) Winter wheat Ñielol θ θ θ Sowing date (Julian day) Potato Ñielol θ θ θ Sowing date (Julian day) Sugar beet Ñielol θ θ θ Fertilization rate (kg N/ha) Sugar beet Ñielol θ θ θ Italic values represent selected strategies that differ from the climatological one. alternatives which can take advantage of forecasts of El Niño phases. Once again, crops cultivated during spring summer season show the highest values of perfect information reflecting their susceptibility to changes in the climatic regime associated with El Niño phases, and the possibility to select different management alternatives. Potato varies from 50 to 250 dollars/ha, representing 3 9% of the certainty equivalent associated with climatological information. In this case, the differences in the net benefits obtained by the farmer are explained by changes in fertilization rate and planting date. While early planting dates (mid-september) and fertilization rates of 200 kg N/ha are selected as the best strategy for El Niño years, 150 kg N/ha and late planting dates (mid-october) are preferred during the rest of the years. Cereal crops show values on the order of dollars/ha, representing 4 10% of the certainty equivalent associated with climatological information. Fertilization rate is in those cases the best way to take advantage of perfect forecast being increased from 150 to 200 kg N/ha during El Niño

14 130 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) Fig. 3. Expected value of perfect information at Valdivia for five crops. (a) Valdivia soil, (b) Rio Bueno soil.

15 F.J. Meza et al. / Agricultural and Forest Meteorology 116 (2003) Table 7 Differences between optimal selected alternatives at Valdivia location under different SSTA states (θ j ) and risk attitude (δ) Crop Soil θ j Risk parameter (δ, 10 3 ) Fertilization rate (kg N/ha) Spring wheat Valdivia θ θ θ Sowing date (Julian day) Potato Valdivia θ θ θ Fertilization rate (kg N/ha) Potato Valdivia θ θ θ Fertilization rate (kg N/ha) Winter wheat Rio Bueno θ θ θ Fertilization rate (kg N/ha) Potato Rio Bueno θ θ θ Plant density (plants/m 2 ) Potato Rio Bueno θ θ θ Italic values represent selected strategies that differ from the climatological one. years. Sugar beet in this soil only will be grown in preference to fallow during El Niño years, but unlike the case discussed for Concepción, there are several feasible alternatives related to the annual crop production system. Given this particular situation, the value of perfect information for this crop is high, ranging from 110 to 210 dollars/ha. The second soil, Rio Bueno, has smaller EVPI values. Here winter wheat, oats and potato show EVPI on the order of 20 dollars/ha, representing 7 10% of the certainty equivalent obtained without information for the cases of winter wheat and oats and less than 1% for the case of potato. In the case of oats and winter wheat fertilization rate is increased during La Niña years from 100 to 150 kg N/ha, being the main cause of the differences in the net benefits and consequently of the value of perfect information found in this study. Differences in the expected value of perfect information for potato are explained by changes in optimal plant density, which increased from 45,000 to 55,000 plants/ha during El Niño years. Crops cultivated during spring summer growing seasons show in general higher potential for climate forecasts. Even in La Niña years, the amount of winter precipitation is sufficient to meet crop water requirements so water stress is less likely to occur. Spring and summer seasons are characterized by higher air temperatures, lower dew point temperatures and higher solar radiation, which are in turn translated into higher potential transpiration rates. If the season is anomalously dry as in La Niña years, it is more likely for the crop to experience water stress and to exhibit reduced yields. This situation becomes more critical when soils have lower water holding capacities because the stored water from winter will help to face only a small fraction of the dry season. In these