* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Regional assessment of climate change impacts on maize
Global warming hiatus wikipedia , lookup
2009 United Nations Climate Change Conference wikipedia , lookup
German Climate Action Plan 2050 wikipedia , lookup
Global warming controversy wikipedia , lookup
Fred Singer wikipedia , lookup
Economics of climate change mitigation wikipedia , lookup
Soon and Baliunas controversy wikipedia , lookup
Heaven and Earth (book) wikipedia , lookup
Michael E. Mann wikipedia , lookup
ExxonMobil climate change controversy wikipedia , lookup
Climatic Research Unit email controversy wikipedia , lookup
Global warming wikipedia , lookup
Climate change denial wikipedia , lookup
Climate resilience wikipedia , lookup
Climate change feedback wikipedia , lookup
Politics of global warming wikipedia , lookup
Climatic Research Unit documents wikipedia , lookup
Instrumental temperature record wikipedia , lookup
Effects of global warming on human health wikipedia , lookup
Climate change adaptation wikipedia , lookup
Climate governance wikipedia , lookup
Carbon Pollution Reduction Scheme wikipedia , lookup
Climate change in Tuvalu wikipedia , lookup
Climate engineering wikipedia , lookup
Citizens' Climate Lobby wikipedia , lookup
Economics of global warming wikipedia , lookup
Climate change in Saskatchewan wikipedia , lookup
Media coverage of global warming wikipedia , lookup
Attribution of recent climate change wikipedia , lookup
Climate sensitivity wikipedia , lookup
Public opinion on global warming wikipedia , lookup
Scientific opinion on climate change wikipedia , lookup
Climate change in the United States wikipedia , lookup
Effects of global warming wikipedia , lookup
General circulation model wikipedia , lookup
Global Energy and Water Cycle Experiment wikipedia , lookup
Solar radiation management wikipedia , lookup
Climate change and agriculture wikipedia , lookup
Climate change and poverty wikipedia , lookup
Effects of global warming on humans wikipedia , lookup
Surveys of scientists' views on climate change wikipedia , lookup
Reg Environ Change DOI 10.1007/s10113-007-0039-z ORIGINAL ARTICLE Regional assessment of climate change impacts on maize productivity and associated production risk in Switzerland Daniele Torriani Æ Pierluigi Calanca Æ Markus Lips Æ Helmut Ammann Æ Martin Beniston Æ Jürg Fuhrer Received: 26 April 2007 / Accepted: 29 September 2007 Springer-Verlag 2007 Abstract A simple model of yield was used along with climate scenarios to assess the impact of climate change on grain maize productivity and associated economic risk in Switzerland. In a first application, changes in the precipitation regime alone were shown to affect the distribution of yield considerably, with shifts not only in the mean but also in the standard deviation and the skewness. Production risk was found to respond more markedly to changes in the long-term mean than in the inter-annual variability of seasonal precipitation amounts. In a further application, yield projections were generated with respect to a full climate scenario, with the emission pathway as specified in the IPCC A2 scenario. Anticipation of the sowing date was found to reduce the negative impact of climate change on yield stability, but was not sufficient to ensure average productivity levels comparable to those observed at present. We argued that this was caused by the reduction in the duration of the growing season, which had a stronger impact than suggested by previous studies. Assuming no change in price relations, the results also revealed a strong increase in production risk with climate change, with more than a doubling in the probability of yield falling short of a critical threshold as compared to today’s situation. D. Torriani P. Calanca (&) J. Fuhrer Air Pollution/Climate Group, Agroscope Research Station ART, Reckenholzstrasse 191, 8046 Zurich, Switzerland e-mail: [email protected] M. Lips H. Ammann Farm Management Group, Agroscope Research Station ART, 8356 Ettenhausen, Switzerland M. Beniston Climate Change and Climate Impacts, University of Geneva, 7 Route de Drize, 1227 Carouge, Switzerland Keywords Maize productivity Production risk Climate change Climate variability Parametric yield model Introduction Climate change as projected by climate models for the twenty-first century has the potential to significantly alter the conditions for crop production, with important implications for worldwide food security (Rosenzweig and Hillel 1998). Referring to the Intergovernmental Panel on Climate Change Special Report on Emissions Scenarios (SRES; Nakicenovic and Swart 2000), Parry et al. (2004) estimated that while global production is likely to remain stable for most of the century, regional differences could grow stronger through time, with only developed countries benefiting from climate change. Regional differences in the response of crop productivity to climate change are also likely to emerge in Europe. As reported by Olesen and Bindi (2002), climate change is expected to have positive impacts only in the northern countries, implying that areas of crop suitability may expand northwards (Olesen et al. 2007). Southern areas, on the other hand, will probably have to face increasing water shortage and incidence of extreme adverse weather events. Without suitable adaptation, implications include lower harvestable yields, higher yield variability and a reduction in suitable areas for traditional crops. In Switzerland, increasing temperature and decreasing summer precipitation could, in the absence of adaptation, also prove adverse to rainfed production of spring and summer crops. On the basis of a temperature increase of 5C and a decrease in summer precipitation of roughly 30%, Torriani et al. (2007) calculated that average yields 123 D. Torriani et al. for grain maize (Zea mays L.) could decrease by 10% even when positive effects of a doubling of the atmospheric CO2 concentration are taken into account. They also found that the coefficient of yield variation could increase by as much as a factor of two, implying depressed yield stability and thus higher production risks. Changes in yield behavior in relation to shifts in climate can become critical for the economy of farms even in areas profiting from favorable conditions at present. An increasing probability of low returns as a consequence of the more frequent occurrence of adverse conditions could prove dramatic for farmers operating at the limit of economic stress. This could be the case in Switzerland, since the projected shortage in water availability during the summer season (Vidale et al. 2007) would more frequently lower the productivity of rainfed crops. Assessing the possible impact of climate change on production risks is therefore necessary to help decision makers and stakeholders identify and implement suitable measures of adaptation. The key aspect for quantifying production risk is how the frequency distribution of yield responds to changes in the climatic settings (Kaylen and Korom 1991; Park and Sinclair 1993). There are several ways to infer a distribution of yield from climatic data. A first possibility is to use process-based models of crop growth along with a set of daily weather data spanning a reasonable number of years. This approach is often adopted in regional assessments (e.g., Tubiello et al. 2000; Torriani et al. 2007) when a realistic description of crop physiology is of advantage. A second possibility is to infer the distribution of yield from the distribution of climate using production functions (Hexem and Heady 1978). Models of this kind are widely employed in econometric studies (e.g., Just and Pope 1978; Moss and Shonkwiler 1993; Chen et al. 2004) and also in global assessments (e.g., Parry et al. 2004). Despite obvious limitations with respect to crop physiology, production functions have the advantage of being robust and computationally cheap. In our study we examined the use of yet another type of model, which was proposed by Monteith in the 1970s (Monteith 1972, 1977). It is a parametric model that relates yield to the average climatic conditions throughout the growing season using a set of deterministic equations. As opposed to production functions, the model retains some of the basics of plant physiology and should have for this reason a wider range of applicability. Similarly to production functions, however, it cannot accommodate future management decision taken by farmers on a day to day, seasonal or annual basis. Intended as an extension of the investigation of Torriani et al. (2007), our study considered climate change effects on grain maize production in Switzerland. Maize 123 is one of the most important cereals both for human and animal consumption (Doorenbos and Kassam 1986). According to the statistics of the Food and Agriculture Organization of the United Nations (http://faostat.fao. org/), in the 25 countries of the European Union maize production presently accounts for slightly less than 20% of the total cereal production. In Switzerland, with a nationwide average yield of 9.7 t ha–1 at present, maize production shares an 18% of the total cereal production (statistics of the Swiss Farmers’ Union; http://www. bauernverband.ch/en/). The specific aims of the study were: (1) to demonstrate the reliability of the model approach proposed by Monteith (1972, 1977) in determining the distribution of maize yield in Switzerland under present climatic conditions; (2) to study the sensitivity of rainfed maize production and associated production risk to changes in the precipitation regime; (3) to study the response of maize yield to climate change given a particular climate scenario; and (4) to provide a qualitative measure of how uncertainties in climate projections may affect yield scenarios. The latter issue is explored in more detail, e.g., by Jones (2000), Luo et al. (2005) and Minguez et al. (2007). A word of caution is necessary before proceeding with the exposition. The specific climate scenario used for the analysis (see next section) refers to a threefold increase in the atmospheric CO2 concentration by the end of the century and implies rather drastic changes in the temperature and precipitation regime of the Alpine region. Moreover, as stated above, we do not consider adaptation in cropping practices, nor we take into account changes in the agricultural policy and the regional and global markets, which ultimately would alleviate the negative effects of climate change. In this sense, the analysis provides only upper bounds for what could take place in the real world. It should therefore be seen as a way to address the vulnerability of the present-day agricultural production of the Alpine region. Materials and methods Yield model Developed by Monteith (1972, 1977) the model used for our analysis expresses yield as the product of a radiationdependent potential yield, Ypot, and two limiting factors, gh and gVPD: Y ¼ gh gVPD Ypot ð1Þ Here, h stands for the soil water content, VPD denotes the vapor pressure deficit and Regional assessment of climate change impacts Ypot ¼ erad SRsGS ð2Þ erad being the efficiency of yield formation, SR the average amount of solar radiation received by the crop throughout the growing season and sGS the length of the growing season. Here and in the following, an overbar is used to designate a seasonal mean value. The limiting factors account for two of the most important forms of stress: (1) water stress resulting from shortage of the water supply to the roots; and (2) heat stress resulting from an excessive evaporative demand from the leaves under conditions of elevated levels of the VPD (Monteith 1977). To parameterize gh we rely on the fact that soil water shortage reduces biomass accumulation and evapotranspiration in comparable proportions (Doorenbos and Kassam 1986). This makes it possible to equate gh with the evapotranspiration efficiency. At the seasonal time scale, the latter can be expressed in terms of the ratio between precipitation, P, and potential evapotranspiration, ETpot (Budyko 1974; Milly 1993a, b, 2001). Hence: gh ET P ¼ tanh c ETpot ETpot ð3Þ where c is a crop-specific parameter. To model gVPD, we assume that for values of the VPD in excess of about 5 hPa (C. Körner, personal communication) the transpiration efficiency of crops becomes nearly inversely proportional to the VPD (Tanner and Sinclair 1983). This behavior can be generalized as a threshold response (Thornley and Johnson 2000) as follows: gVPD ¼ m þ ð1 mÞ kn n kn þ VPD ð4Þ where k, m and n are again crop-specific parameters. Model parameterization There are five parameters in Eqs. 1–4: erad, c, k, m and n. Of these, the efficiency of yield formation, which at 350 ppmv atmospheric CO2 concentration is of the order of 0.07 t ha–1 (W m–2)–1, is considered to be specific not only for the crop but also for different cultivars, reflecting among other things disparities in leaf-area development and harvest index (Muchow et al. 1990). Its value was therefore specified separately for each application (see respective sections below) ensuring that computed median yields matched the median values inferred from observations. In contrast, values for the remaining parameters were determined only once because Eqs. 3 and 4 are assumed to reflect general responses of maize to changes in environmental conditions. This was done relying on the information provided by simulations carried out with CropSyst (Stöckle et al. 2003), a soil-plant growth simulator that computes biomass accumulation and phenology for perennial and non-perennial crops at a daily time step. Inferring the parameters directly from the analysis of field experiments would have been the preferred alternative. However, the available data were too scarce to treat the effects of the individual stress factors separately. CropSyst results considered to parameterize Eqs. 3 and 4 are essentially those described in Torriani et al. (2007). Maize yields were simulated for Waedenswil (8410 E, 47130 N, 463 m a.s.l.), a representative location on the Swiss Plateau, using daily meteorological data for 1981– 2003 provided by the Swiss Federal Office of Meteorology and Climatology to drive the model. Given the relatively narrow spectrum of precipitation amounts and air humidity levels in the daily observations and the need to ensure the general validity of Eqs. 3 and 4, these primary simulations were supplemented with additional runs driven with synthetic precipitation and air humidity data. A first set of synthetic data was generated to parameterize gh, whereby observed daily rainfall amounts were reduced in turn by 20, 40 and 60%, leaving all other variables unchanged relatively to the baseline. A second set of data was prepared specifying relative humidity in the range 10–100%. This second set was used to parameterize gVPD. For all CropSyst simulations, soil hydraulic properties were specified with respect to a soil texture with clay, silt and sand fractions of 38, 36 and 26%, respectively, relative soil organic matter content of 2.6%, along with optimal nitrogen fertilization and automatic irrigation. The sowing date was set at day of the year (DOY) 130 and harvest was assumed to take place 5 days after maturity. Base temperature of 7C and cut-off temperature of 20C were specified to calculate growing degree days (GDD) (Stöckle et al. 2003). As shown in Fig. 1, in simulations with CropSyst most of the biomass accumulation takes place during a so-called linear growth phase (see also Goudriaan and Monteith 1990; Monteith 2000; Yin et al. 2003). The linear growth phase is easily identified when time is expressed in GDD units. In practice, start and end of the linear growth phase were defined in correspondence to GDD thresholds of 400 and 1,250C-days, respectively, coinciding with DOY 182 and 273 at Waedenswil. The linear growth phase was then used as a reference for calculating the seasonal mean values of T, SR, VPD and P needed in Eqs. 1–4. Following Calanca (2004), ETpot was estimated from the seasonal mean net radiation, NR; using the Priestley-Taylor (1972) equation: 123 D. Torriani et al. Fig. 1 Biomass accumulation in the years 1981–2003 as a function of growing degree days. Simulations with CropSyst for the test site Waedenswil. The values of 400 and 1,250C-days used to delimit the linear growth phase are highlighted with vertical lines ETpot ðdesat dTÞT NR ¼a ðdesat dTÞT þ c Lv ð5Þ where a = 1.26 is the Priestley-Taylor coefficient, ðdesat dTÞT the slope of saturation vapor pressure function of temperature, evaluated at T; c the psychrometric constant and Lv the latent heat of vaporization. In turn, net radiation was inferred from solar radiation using a linear relation (Davies 1967): NR ¼ a þ bSR ð6Þ with coefficients a = –20 W m–2 and b = 0.62 determined using accurate radiation measurements carried out at Payerne (6570 E, 46490 N, 490 m a.s.l.) within the framework of the Baseline surface radiation network (BSRN) (Ohmura et al. 1998). In summary, based on the results presented in Fig. 2 and assuming for this site an efficiency of yield formation erad = 0.069 t ha–1 (W m–2)–1, values of c = 1.33, k = 7.494 hPa, m = 0.251 and n = 1.607 were determined for the parameters appearing in Eqs. 3 and 4. Model testing To test the validity of our approach, yield distributions were computed for two other locations on the Swiss Plateau, Wynau (7470 E, 47150 N, 422 m a.s.l.) and Taenikon (8540 E, 47290 N, 536 m a.s.l.), and contrasted with distributions inferred from a census of yield data collected between 1975 and 2001 by the Swiss Federal Research Station Reckenholz-Tänikon (ART 2002). The nationwide census refers to a few thousand prototype farms spread all 123 Fig. 2 Relationships between gh and the ratio P=ETpot (top panel) and between gVPD and VPD (bottom panel). Results of simulations with CropSyst for Waedenswil over the Swiss territory and provides information on geographic location, cultivated area, crop productivity and production costs. Unfortunately, the number and location of farms substantially varied from year to year. Moreover, there is no information available in the census concerning cultivars used and specific management practices. It is therefore meaningless to compare model results and observations on a farm unit basis. For this reason, yield data from farms located within a distance of 15 km from the respective meteorological stations were spatially aggregated to provide regional mean yields. For both locations, daily climatic data for 1981–2003 were again obtained from the Federal Office of Meteorology and Climatology. To compute seasonal statistics, the limits of the linear growth phase were adjusted according the annual course of GDD. As before, base temperature of 7C and a cut-off temperature of 20C were used to infer the GDD from temperature. For GDD limits of 400 and 1,250C-days, start and end of the linear growth phase Regional assessment of climate change impacts were found to coincide, respectively, with DOY 169 and 254 at Wynau, and DOY 171 and 260 at Taenikon. Values of the radiation use efficiency of 0.067 and 0.061 t ha–1 (W m–2)–1 were specified for Wynau and Taenikon, respectively. All other parameters (c, k, m and n) were assigned the same values as in the Waedenswil runs and ETpot was again computed using Eq. 5, with seasonal mean net radiation given by Eq. 6. Economic framework The economic framework adopted for the analysis considers production risk as the long-term probability that actual yield, Y, falls short of a critical threshold, Ycr, viz.: Risk ¼ ProbfY Ycr g FðYcr Þ ð7Þ where F(Y) is the yield distribution function with the associated mass probability function f(Y). To define Ycr we assumed that this threshold corresponds to long-term shut-down decision taking place when the total revenue becomes equal to the costs of production: pYcr vðYcr Þ ð8Þ where p is the price of grain yield and v(Y) the specific production costs. Ycr for today’s conditions in Switzerland was determined using prices and costs published by Lips and Ammann (2005). A summary of the most important entries is given in Table 1. Some of the costs in the economic accountancy Table 1 Economic accountancy of maize production in Switzerland Yield (t ha–1) depend on the level of yield. Hence, Ycr was initially calculated for yield levels of 7.5, 8.5, 9.5, 10.5 and 11.5 t ha–1, resulting in values of 8.05, 8.12, 8.18, 8.21 and 8.24 t ha–1, respectively. A linear relation was then fitted to these results and used to determine Ycr for the full range of yields. In the simulations with climate scenarios, market prices and production costs were left unchanged in view of the large uncertainties concerning their future evolution. Again, ignoring adaptation by farmers and policy makers to the new climatic conditions implies that our results merely provide an upper bound of the possible impacts. Climate scenarios Torriani et al. (2007) calculated yield scenarios for 2071–2100 using climate projections inferred from simulations with HIRHAM4, the regional climate model (RCM) of the Danish Meteorological Institute (Christensen et al. 1998). With a spatial resolution of 50 km · 50 km, these regional climate simulations were originally carried out as a contribution to the PRUDENCE project and are available though the project webpage (http://prudence.dmi.dk/, accessed 24/09/2007). Details of the model setup and data processing can be found in Christensen et al. (1998) and Christensen and Christensen (2007). All PRUDENCE experiments included a baseline or control run for 1961–1990 and a climate scenario for 2071– 2100 (Christensen and Christensen 2007). The emission scenario adopted for the HIRHAM4 experiment was the IPCC SRES A2 scenario (Nakicenovic and Swart 2000). 7.5 8.5 9.5 10.5 11.5 Seeds (CHF ha–1) 272 272 272 272 272 Fertilizer (CHF ha–1) Plant protection (CHF ha–1) 249 217 249 217 249 217 249 217 249 217 Cleaning and drying (CHF ha–1) 805 912 1,019 1,127 1,234 Hail insurance (CHF ha–1) 61 69 77 85 93 Other direct costs (CHF ha–1) 7 7 7 7 7 Costs Labor costs (CHF ha–1) 764 764 764 764 764 Machinery costs (CHF ha–1) 1,345 1,359 1,368 1,368 1,368 Land value (CHF ha–1) 718 718 718 718 718 Interest rate costs (CHF ha–1) 38 40 43 46 49 Other indirect costs (CHF ha–1) 728 728 728 728 728 Benefits Data are for the year 2005. ‘‘Other benefits’’ refers to the average indemnities received by the farmers from the hail and other insurances Producer benefits (CHF ha–1) 3,375 3,825 4,275 4,725 5,175 Direct payments (CHF ha–1) 1,600 1,600 1,600 1,600 1,600 Other benefits (CHF ha–1) 41 41 41 41 41 Balance (CHF ha–1) –187 130 453 785 1,116 Critical yield threshold (t ha–1) 8.05 8.12 8.18 8.21 8.24 123 D. Torriani et al. The corresponding CO2 level was about 800 ppmv by 2100 (three times the pre-industrial value), which provided an upper bound for the ensemble of projections discussed in the Third Assessment Report of IPCC (Houghton et al. 2001). Given the biases in reproducing current climatic conditions with the regional climate models used in PRUDENCE (Frei et al. 2003; Frei 2007; Jacob et al. 2007), an anomaly approach was chosen to derive a climate distribution for the time window 2071–2100. The procedure can be outlined as follows. Let mX and sX be the long-term average and corresponding inter-annual standard deviation of a series of In addition, let the absolute and seasonal mean values X: relative anomalies of a long-term mean be denoted by Dm and dm, respectively, and the relative anomaly of the interannual standard deviation be denoted by ds. Using superscripts BASE and SCEN to designate baseline and scenario, these anomalies are defined by: Dm mSCEN mBASE X X dm mSCEN X mBASE X 47150 N, 608.98 m a.s.l) closest to the station of Waedenswil. Since changes in temperature affect the timing and length of the growing season, two scenarios were generated. The first one (referred to as SC) was calculated assuming the same limits for the linear growth phase as in the baseline. The second one (referred to as AD) was derived assuming anticipation of the sowing and harvest dates in response to higher temperatures. For the second scenario, start and end of the linear growth phase were recalculated from the annual course of the GDD using thresholds of 400 and 1,250C-days as in the baseline. These limits were found in correspondence to DOY 155 and 223, respectively. The data in Table 2 show that differences between the two scenarios are appreciable. Compared to SC, the AD scenario is characterized by a small change in precipitation, a less severe increase in the seasonal mean VPD and a more substantial increase in daily mean incoming solar radiation. ð9Þ ð10Þ Results Model test and sSCEN ds XBASE sX ð11Þ The next step consists in employing the anomalies to generate in a consistent way a series of seasonal mean values XSCEN valid for the scenario from the series of observed seasonal mean values XOBS : This can be achieved letting: ds XSCEN ¼ mOBS þ Dm þ XOBS mOBS X X ð12Þ The results of the model test are presented in Fig. 3 showing that the simulated probability distribution functions closely matched those inferred from the census data. At Wynau the median yield was of 8.6 t ha–1 and the interquartile range was of 1.0 t ha–1 for the modeled and 1.2 t ha–1 for the observed distribution. At Taenikon median yield was of 8.2 t ha–1, with simulated and observed inter-quartile ranges of 1.1 t ha–1 and 1.4 t ha–1, respectively. Appreciable differences between simulated and observed yield distributions were found in the details. For or OBS mOBS XSCEN ¼ mOBS ds X dm þ X X ð13Þ depending on whether the shift in the long-term mean is given in absolute or relatively to the baseline. Obviously, the first-term on the right-hand side of (12) and (13) represents the adjustment of the long-term mean, whereas the second-term reflects the inflation or suppression of inter-annual variability, i.e., of mean departure of an individual year from the long-term mean. It is easy to show that Eqs. 12 and 13 satisfy (10) and (11). Four our analysis, absolute changes in the long-term mean were assumed for T and VPD; while relative changes were assumed for P and SR: All anomalies were derived from the HIRHAM4 results for the grid-point (8350 E and 123 Table 2 Absolute (D), respectively relative anomalies (d) for the long-term mean value and inter-annual standard deviation of seasonal mean temperature (T), precipitation (P), solar radiation (SR) and vapor pressure deficit (VPD) Parameter Scenario SC Scenario AD Mean SD Mean SD T D = + 5.1C d = 1.15 D = +5.0C d = 1.25 P SR d = 0.77 d = 1.10 d = 0.73 d = 0.60 d = 1.03 d = 1.26 d = 1.01 d = 1.04 VPD D = +2.3 hPa d = 2.74 D = +1.6 hPa d = 1.96 Results inferred from the HIRHAM4 simulations. Values in the first two columns refer to the scenario without shift in the growing season (SC); values in the third and fourth column refer to the scenario with anticipation of sowing and harvest dates (AD) Regional assessment of climate change impacts Fig. 3 Histogram (bars), empirical probability density function (thin continuous line) and modeled probability density function of maize yield (thick dashed line) at Wynau (top panel) and Taenikon (bottom panel). The density functions were calculated using a kernel density estimation with Gaussian kernel instance, the modeled distribution at Taenikon was negatively skewed, while a symmetric distribution was suggested by the census data. Since the number of data available in the census varied from a minimum of 2 in 1997 to a maximum of 13 in 1988 at Wynau, and from a minimum of 4 in 1987 and 2000 to a maximum of 18 in 1989 at Taenikon, it could not be excluded that the comparison suffered from a sampling bias in the census. Denoting by hPi the total amount of rainfall throughout growing season, long-term averages mhPi between 200 and 500 mm and corresponding inter-annual standard deviations shPi in the range 50–150 mm were specified to reasonably cover current and future rainfall regimes (see, e.g., Vidale et al. 2007). A distribution of climate was obtained for each combination of long-term mean and inter-annual standard deviation by first defining the distribution of hPi. Since precipitation amounts are constraint to be non-negative, hPi was modeled by means of the gamma distribution, with shape and scale parameters calculated using the moment estimators (Wilks 2006). The gamma distribution is commonly used in meteorology and climatology to represent variations in rainfall amounts (e.g., Ison et al. 1971; Stern and Coe 1984; Wilks 1990). Distributions of T; SR and VPD were then generated taking into account their relation to hPi. It was assumed that each of T; SR and VPD consists of the sum of a deterministic term, linearly depending on hPi, and a normally distributed stochastic component with zero mean and appropriate standard deviation. Deterministic and stochastic components were fitted to the observed climatology (Fig. 4) and were assumed valid for every other combination of mhPi and shPi. For each of P; T; SR and VPD, a set of 30,000 realizations was drawn at random from the respective distributions. Results of the sensitivity analysis are displayed in Fig. 5. The distribution of maize yield responded markedly to changes in mhPi and shPi. Under current conditions (dots in Fig. 5) mean, standard deviation and skewness of the distribution were of 8.5 t ha–1, 0.75 t ha–1 and 0.1, respectively. Decreasing mhPi or increasing shPi depressed mean yield and yield stability, made the skewness increasingly negative, and increased the risk of falling short of the critical yield Ycr. The sensitivity of the production risk to shifts in shPi appeared to be less pronounced than for the moments of the distribution. This reflects the fact that in the framework of Eqs. 7 and 8 risk was primarily determined by the overall level of productivity and only secondarily by the spread and asymmetry of the distribution. Sensitivity analysis: response to changes in the precipitation regime Case study: a maize yield scenario for 2071–2100 In a first application, Eqs. 1–4 were used to study the response of the yield distribution and associated production risks to changes in precipitation regime, including shifts in both the long-term mean and the inter-annual variability. To provide a possibility for comparison with the results presented in Torriani et al. (2007), the analysis was conducted with respect to the station of Waedenswil. Yield distributions calculated for the HIRHAM4 scenarios are presented in Fig. 6. Despite disparities in the two scenarios (Table 2), the simulated yield distributions were similar. The median yield was of 7.3 t ha–1 for SC and 7.2 t ha–1 for AD. These values should be contrasted with the 8.5 t ha–1 obtained for the baseline, which indicates that climate change is likely to have a negative impact on 123 D. Torriani et al. Fig. 4 Deterministic (left) and stochastic (right) components of seasonal mean air temperature (top), solar radiation (middle) and VPD (bottom). Data are for Waedenswil, valid for 1981– 2003. The panels on the righthand side show both the empirical distribution of the residuals (histogram and dashed line) as well as the assumed zero-mean normal distribution (continuous line) Fig. 5 Nomograms (isolines) displaying the sensitivity of long-term mean (top left), interannual standard deviation (top right), and skewness (bottom left) of maize yield, as well as the sensitivity of production risk (bottom right) to changes in mean (mhPi) and standard deviation (shPi) of seasonal precipitation amounts. Results are for Waedenswil. Current climatic conditions are indicated with a dot. Mean and standard deviations of yield are in units of t ha–1, skewness is dimensionless, and risk is in % 123 Regional assessment of climate change impacts Fig. 6 Histogram (bars) and modeled probability density function of maize yield for the baseline climate (BL, thin continuous line), and modeled probability density functions valid for the two climate scenarios, without (SC, dashed line) and taking into consideration a shift in timing and length of the growing period (AD, dotted dashed line). The density functions were calculated using a kernel density estimation with Gaussian kernel yield, irrespective of whether or not an anticipation of the growing season is taken into account. Differences between the two scenarios were more pronounced concerning yield stability. Inter-quartile ranges of 2.1 and 1.3 t ha–1 were computed for SC and AD, respectively. Both values were higher than the inter-quartile range calculated for the baseline (1.0 t ha–1). In view of the specific climate settings, the fact that the overall yield levels in SC and AD were comparable is surprising. A closer look at the individual terms in Eqs. 1 and 2 revealed, however, different backgrounds. Potential yield was higher in SC (14.1 t ha–1) than in AD (12.0 t ha–1), thanks to the longer period available for biomass accumulation (91 against 68 days) and despite lower levels of solar radiation (204 against 234 W m–2 as an average throughout the linear growth phase). Dissimilarities between the two scenarios were also found with respect to the limiting factors (Fig. 7). In SC, shifts in climatic conditions resulted in a more severe limitation of productivity, both with respect to soil water shortage (median value of gh & 0.89, as opposed to 0.98 in the baseline) as well as heat stress (median value of gVPD & 0.59, as opposed to 0.69 in the baseline). In AD, anticipation of the sowing date was effective in reducing the impact of decreased summer precipitation on yield formation. As seen in Fig. 7, the distribution of gh was very close to the distribution inferred for the baseline (median value of nearly 0.97 in both cases). On the other hand, increasing temperature and VPD lowered productivity in AD as well (median value of gVPD & 0.62, as opposed to 0.69 in the baseline). Fig. 7 Histograms (bars) and probability density functions for the two limiting factors, gVPD (top) and gh (bottom). Results are shown for the baseline (BL, thin continuous line), the scenario without adaptation (SC, dashed line) and the scenario accounting for anticipation and shortening of the growing season (AD, dotted dashed line). The density functions were calculated using a kernel density estimation with Gaussian kernel For present-day conditions, production risk was estimated at 28%. At first sight this value may appear high, but it could be explained by the fact that average productivity during the period 1981–2003 (8.5 t ha–1) was significantly lower than in 2005 (9.5 t ha–1), the year taken as the reference for the economic analysis. Production risk increased considerably as a consequence of climate change, attaining 67% in SC and 79% in AD. Uncertainties in the projections There are many sources of uncertainties in climate projections (e.g., Wigley and Raper 2001; Déqué et al. 2007), and their implications should be considered in impact studies. With respect to the Alpine region, variations across the PRUDENCE scenarios have been quantified by Frei 123 D. Torriani et al. (2007), Christensen and Christensen (2007) and Déqué et al. (2007) for seasonal mean temperature and precipitation. Despite differences in the specific aims, the number of scenarios and greenhouse-gases emission pathways examined, these analyses concurred in indicating that the average spread of the projections is of the order of 10–30% around the ensemble mean values. Note that following Déqué et al. (2007), we considered the inter-model standard deviation as the metric for quantifying the dispersion. Unfortunately, none of the aforementioned studies considered uncertainties in the projections of other climatic parameters, nor did they attempt to quantify the uncertainties related to changes in the inter-annual standard deviation. Based on the results presented by Déqué et al. (2007) we therefore assumed that uncertainties in both the absolute and relative anomalies of Table 2 can be represented by a normal distribution with coefficient of variation of 20%. For precipitation and VPD, the assumed uncertainty is of the same order as the inter-annual variability under present-day climatic conditions. We sampled each distribution 10,000 times, assuming statistical independence of the anomalies, and repeated the calculations reported in the previous section for each of the 10,000 realizations of climate. We then summarized the outcome with respect to the uncertainty in mean yield and production risk. As shown in Fig. 8, uncertainties in mean yield were nearly normally distributed. This reflected an almost linear mapping of the uncertainties in the climate scenario. At 2.0 t ha–1 the standard deviation of the distribution was equivalent to a coefficient of variation of 18%, slightly less than the mean uncertainty level imposed on the climate anomalies. Production risk, on the other hand, is constrained in the interval 0–100%. It follows that the distribution of the associated uncertainties can become highly asymmetric. As seen in Fig. 8 this was indeed the case with respect to AD. Taking a median risk of 81% as a reference, the results of Fig. 8 implied that the probability of a very low or a very high risk was not negligible, with a probability of 10% to have either a risk of less than 30% or a risk higher than about 90%. Discussion and conclusions Regional assessments of the effects of climate change on crop production are needed at various decision levels, and they are necessary to quantify the economic impacts at the farm and regional scale. Of the various aspects related to climate change, the possible increase in climate variability has been recognized in recent years as one of the most critical issues (Mearns et al. 1997; Porter and Semenov 123 Fig. 8 Uncertainties in the projections for mean yield (top) and risk (bottom) as calculated for the scenario AD. Shown is the empirical distribution function obtained by assuming normally distributed uncertainties in the climate anomalies of Table 2 with coefficient of variation of 20 % 2005). In this paper we demonstrated that a simple model of crop yield operating at the seasonal time scale can be a reliable tool for regional impact studies. We also showed that such a model can be linked to a very basic economic model, providing means for characterizing, at least in a qualitative way, the expected effects of climate change on production risks. Shifts in yield and yield stability largely depend on assumptions about future emissions, the climate projections, and the downscaling procedure used to generate the climatic data at the regional scale typically required as input to crop models. Olesen et al. (2007) noted that for a site-based analysis the method used for downscaling is more crucial than the choice of a specific climate scenario. They also pointed out that use of climate model outputs directly as input to the crop is not appropriate. Following this recommendation, in our study we relied on the application of climate anomalies inferred from a regional climate scenarios as adjustment factors to an observed Regional assessment of climate change impacts climatology, including shifts in both the long-term mean conditions and the inter-annual variability of climate. Out of the several scenarios available from the PRUDENCE project, we chose the HIRHAM4 scenario in order to be consistent with an earlier analysis (Torriani et al. 2007). Comparison of the anomalies given in Table 2 with the values published by Christensen and Christensen (2007) and Déqué et al. (2007) shows that this particular scenario represents the upper limit of the ensemble of simulations available in PRUDENCE, at least with respect to changes in summer temperature and precipitation. This needs to be taken into account when interpreting the results. In a first application of the yield model, we found that changes in the precipitation regime alone have important consequences not only for mean yield but also for the distribution of yields, with yield stability decreasing with decreasing mean and increasing variability of seasonal rainfall, in agreement with studies in other regions (cf. Fuhrer 2006). Taking into account changes in temperature, solar radiation and VPD provided a more differentiated picture. Ruling out adaptation, mean yield was found to decrease from 8.5 to 7.3 t ha–1, in good agreement with the results presented in Torriani et al. (2007). A similar decrease in mean productivity was also found by Tubiello et al. (2000) for an Italian location, but their results were obtained assuming irrigated maize production. Many studies (e.g., Tubiello et al. 2000; Torriani et al. 2007) regard anticipation of sowing date of spring/summer crops as an effective measure of adaptation to increasing temperature and decreasing water availability. In these earlier studies anticipating the date of sowing had indeed a positive effect on yield levels, but our results indicated that this might not generally be true. Although average climatic conditions were more favorable in AD than in SC, shortening of the growing period (–25% relative to the baseline) resulted in a considerable loss of productivity. Therefore, to take advantage of more favorable conditions during spring time, cultivars with higher thermal time requirements would be required (Torriani et al. 2007). Anticipation of the growing season had, however, a positive effect on yield stability. While yield variability more than doubled in SC, as compared to the baseline, the increase was of only 30% in AD. For a critical yield of about 8.1 t ha–1, this did not necessarily imply lower production risks. It is clear that quantifying the economic implications of climate change requires the understanding of yield behavior in a specific economic context. Accordingly, assessing production risk solely on the basis of shifts in the distribution of yield can be misleading. Several aspects were not addressed by our analysis. For instance we ignored the positive effects of elevated CO2 concentration on maize productivity. Most studies conducted so far assumed that maize yields would improve roughly by 10–15% for a doubling of CO2 (Sinclair and Rawlins 1993; Parry et al. 2004). This could have been considered by adjusting erad (Sinclair and Rawlins 1993) and by modifying gh and gVPD to reflect acclimation as an increase in transpiration efficiency (Polley 2002; Fuhrer 2003). However, the extent of the CO2 effect has recently been questioned (Long et al. 2006). Furthermore, we did not attempt to account for technological advances in production, including crop improvements through breeding (Duvick 2005; Sinclair and Muchow 2001) or switching to cultivars with higher thermal time requirements (Torriani et al. 2007). Also, we disregarded the possibility that farmers can opt among a variety of crops and reduce the overall economic risks by choosing those responding more positively or less negatively to climate change. Mendelsohn et al. (1994) and more recently Mendelsohn and Reinsborough (2007) and Mendelsohn et al. (2007) showed that allowing for a palette of crops the effects of global warming on farms’ value are significantly lower than estimated for a single crop with the help of traditional production functions. Finally, we adopted an economic framework in which critical yield was only dependent on today’s prices and costs. A more realistic assumption would have been that such a critical yield threshold reflects the evolution of the prices and costs relations. For instance, Parry et al. (2004) considered higher prices in response to lower crop productivity worldwide, but for Switzerland lower crop prices could be expected in view of the changes in the agricultural policy prompted by the harmonization with the Common Agricultural Policy of the European Union or in response to outcomes of negotiations of the World Trading Organization. In any case, making realistic projections remain a difficult task. In this sense, the assumption of constant prices and costs was not more arbitrary than any other hypothesis. Acknowledgments This work was supported by the Swiss National Science Foundation through the National Centre of Competence in Research on Climate (NCCR Climate). Climatic data were provided by the Swiss Federal Office of Meteorology and Climatology, while results of the HIRHAM4 simulations were provided through the PRUDENCE data archive, funded by the EU through contract EVK2CT2001-00132. The authors would like to thank Prof. C.O. Stöckle for the internship granted to D.S.T. at Washington State University, Pullman (USA). Analyses and graphics were produced using the open-source software package R. Special thanks are due to the R Development Core Team (URL: http://www.r-project.org/, accessed 24/09/2007). Two anonymous reviews were very helpful for improving the manuscript. References ART (Agroscope Reckenholz-Tänikon) (2002) Ergebnisse der Zentralen Auswertung von Buchhaltungsdaten (Results of the central 123 D. Torriani et al. accounting assessment). Report available from the Research Station Agroscope Reckenholz-Tänikon, Ettenhausen, Switzerland Budyko MI (1974) Climate and life. Academic, New York Calanca P (2004) Interannual variability of summer mean soil moisture conditions in Switzerland during the 20th century: a look using a stochastic soil moisture model. Water Resour Res 40:W12502. doi:10.1029/2004WR003254 Chen CC, McCarl BA, Schimmelpfenning DE (2004) Yield variability as influenced by climate: a statistical investigation. Clim Change 66:239–261 Christensen OB, Christensen JH, Machenauer B, Botzet M (1998) Very high-resolution regional climate simulations over Scandinavia—present climate. J Clim 11:3204–3229 Christensen JH, Christensen OB (2007) A summary of the PRUDENCE model projections of changes in European climate by the end of this century. Clim Change 81:7–30 Davies JA (1967) A note on the relationship between net radiation and solar radiation. Quart J Roy Meteor Soc 93:109–115 Déqué M, Rowell DP, Lüthi D, Giorgi F, Christensen JH, Rockel B, Jacob D, Kjellström E, de Castro M, van den Hurk B (2007) An intercomparison of regional climate simulations for Europe: assessing uncertainties in model projections. Clim Change 81:53–70 Doorenbos J, Kassam AH (1986) Yield response to water. FAO Irrigation and Drainage Paper 33. Food and Agriculture Organization of the United Nations, Rome Duvick DN (2005) The contribution of breeding to yield advances in maize (Zea mays L.). Adv Agron 86:83–145 Frei C, Christensen JH, Déqué M, Jacob D, Jones RG, Vidale PL (2003) Daily precipitation statistics in regional climate models: evaluation and intercomparison for the European Alps. J Geophys Res 108. doi:10.1029/2002JD002287 Frei C (2007) Die Klimazukunft der Schweiz (The future of Climate in Switzerland). Report published by the Swiss Advisory Body on Climate Change (OcCC), Bern, pp. 12–16. The report is available at http://www.occc.ch Fuhrer J (2003) Agroecosystem responses to combinations of elevated CO2, ozone, and global climate change. Agric Ecosyst Environ 97:1–20 Fuhrer J (2006) Agricultural systems: sensitivity to climate change. CAB Rev Perspect Agric Vet Sci Nutr Nat Resour 1:052. doi: 10.1079/PAVSNNR20061052 Goudriaan J, Monteith JL (1990) A mathematical function for crop growth based on light interception and leaf area expansion. Ann Bot 66:695–701 Hexem RW, Heady EO (1978) Water production functions for irrigated agriculture. The Iowa State University Press, Ames Houghton JT, Ding Y, Griggs DJ, Noguer M, van der Linden PJ, Dai X, Maskell K, Johnson CA (2001) Climate change 2001: the scientific basis. Contribution of working group I to the third assessment report of the intergovernmental panel on climate change. Cambridge University Press, Cambridge Ison NT, Feyerherm AM, Bark LD (1971) Wet period precipitation and the gamma distribution. J Appl Meteor 10:658–665 Jacob D, Bärring L, Christensen OB, Christensen JH, de Castro M, Déqué M, Giorgi F, Hagemann S, Hirschi M, Jones R, Kjellström E, Lenderink G, Rockel B, Sánchez E, Schär C, Seneviratne SI, Somot S, van Ulden A, van den Hurk B (2007) An intercomparison of regional climate models for Europe: design of the experiments and model performance. Clim Change 81:31–52 Jones RN (2000) Analysing the risk of climate change using an irrigation demand model. Clim Res 14: 89–100 Just RE, Pope RD (1978) Stochastic specification of production functions and economic implications. J Econom 7:67–86 123 Kaylen MS, Korom SS (1991) Trend, weather variables, and the distribution of U.S. corn yields. Rev Agric Econ 13:249–258 Lips M, Ammann H (2005) Vollkostenkalkulationen für Ackerkulturen (full cost calculations for field crops). Agrarforschung 13:228–231 Long SP, Ainsworth EA, Leakey ADB, Nösberger J, Ort DR (2006) Food for thought: lower-than-expected crop yield stimulation with rising CO2 concentrations. Science 312:1918–1921 Luo Q, Jones RN, Williams M., Bryan B, Bellotti W (2005) Probabilistic distributions of regional climate change and their application in risk analysis of wheat production. Clim Res 29:41–52 Mearns LO, Rosenzweig C, Goldberg R (1997) Mean and variance change in climate scenarios: method, agricultural applications, and measures of uncertainty. Clim Change 35:367–396 Mendelsohn R, Nordhaus WD, Shaw D (1994) The impact of global warming on agriculture: a Ricardian analysis. Amer Econ Rev 84:753–771 Mendelsohn R, Reinsborough M (2007) A Ricardian analysis of US and Canadian farmland. Clim Change 81:9–17 Mendelsohn R, Basist A, Kurukulasuriya P, Dinar A (2007) Climate and rural income. Clim Change 81:101–118 Milly PCD (1993a) An analytic solution of the stochastic storage problem applicable to soil moisture. Water Resour Res 29:3755– 3758 Milly PCD (1993b) A minimalist probabilistic description of root zone soil water. Water Resour Res 37:457–463 Minguez MI, Ruiz-Ramos M, Diaz-Ambrona CH, Quemada M, Sau F (2007) First-order impacts on winter and summer crops assessed with various high-resolution climate models in the Iberian Peninsula. Clim Change 81:343–355 Monteith JL (1972) Solar radiation and productivity in tropical ecosystems. J Appl Ecol 9:747–766 Monteith JL (1977) Climate and the efficiency of crop production in Britain. Phil Trans R Soc Lond B 281:277–294 Monteith JL (2000) Fundamental equations for growth in uniform stands of vegetation. Agric Forest Meteorol 104:5–11 Moss CB, Shonkwiler JS (1993) Estimating yield distributions with a stochastic trend and nonnormal errors. Amer J Agr Econ 75:1056–1062 Muchow RC, Sinclair TR, Bennett JM (1990) Temperature and solar radiation effects on potential maize yield across locations. Agron J 82:338–343 Nakicenovic N, Swart R (eds) (2000) Special report on emission scenarios. Intergovernmental panel on climate change. Cambridge University Press, Cambridge Ohmura A, Gilgen H, Hegner H, Müller G, Wild M, Dutton EG, Forgan B, Fröhlich C, Philipona R, Heimo A, König-Langlo G, McArthur B, Pinker R, Whitlock CH, Dehne K (1998) Baseline surface radiation network (BSRN/WCRC): new precision radiometry for climate research. Bull Amer Meteor Soc 79:2115– 2136 Olesen JE, Bindi M (2002) Consequences of climate change for European agricultural productivity, land use and policy. Eur J Agron 16:239–262 Olesen JE, Carter TR, Dı́az-Ambrona CH, Fronzek S, Heidmann T, Hickler T, Holt T, Minguez MI, Morales P, Palutikof JP, Quemada M, Ruiz-Ramos M, Rubæk GH, Sau F, Smith B, Sykes MT (2007) Uncertainties in projected impacts of climate change on European agriculture and terrestrial ecosystems based on scenarios from regional climate models. Clim Change 81:123–143 Park WI, Sinclair TR (1993) Consequences of climate and crop yield limits on the distribution of corn yields. Rev Agric Econ 15:483– 493 Parry ML, Rosenzweig C, Iglesias A, Livermore M, Fischer G (2004) Effects of climate change on global food production under SRES Regional assessment of climate change impacts emissions and socio-economic scenarios. Global Environ Change 14:53–67 Polley HW (2002) Implications of atmospheric and climate change for crop yield and water use efficiency. Crop Sci 42:131–140 Porter JR, Semenov MA (2005) Crop responses to climatic variation. Phil Trans R Soc B 360:2021–2035 Priestley CHB, Taylor RJ (1972) On the assessment of surface heat flux and evaporation using large-scale parameters. Mon Wea Rev 100:81–92 Rosenzweig C, Hillel D (1998) Climate change and the global harvest. Oxford University Press, New York Sinclair TR, Rawlins SL (1993) Inter-seasonal variation in soybean and maize yields under global environmental change. Agron J 85:406–409 Sinclair TR, Muchow RC (2001) System analysis of plant traits to increase grain yield on limited water supplies. Agron J 93:263– 269 Stern RD, Coe R (1984) A model fitting analysis of daily rainfall data. J Roy Stat Soc A 147:1–34 Stöckle CO, Donatelli M, Nelson R (2003) CropSyst, a cropping system simulation model. Eur J Agron 18:289–307 Tanner CB, Sinclair TR (1983) Efficient water use in crop production: research or re-search? In: Taylor HM, Jordan WR, Sinclair TR (eds) Limitations to efficient water use in crop production. Madison (USA). Am. Soc. Agronomy, Crop Science Soc. Amer., Soil Science Soc. Amer. pp 1–27 Thornley JHM, Johnson IR (2000) Plant and crop modelling. A mathematical approach to plant and crop physiology. Blackburn, Caldwell Torriani DS, Calanca P, Schmid S, Beniston M, Fuhrer J (2007) Potential effects of changes in mean climate and climate variability on the yield of winter and spring crops in Switzerland. Clim Res 34:59–69 Tubiello FN, Donatelli M, Rosenzweig C, Stöckle CO (2000) Effects of climate change and elevated CO2 on cropping systems: model predictions at two Italian sites. Eur J Agron 13:179–189 Vidale PL, Lüthi D, Wegmann R, Schär C (2007) European summer climate variability in a heterogeneous multi-model ensemble. Clim Change 81:209–232 Wigley TML, Raper SCB (2001) Interpretation of high projections for global-mean warming. Science 293:451–454 Wilks DS (1990) Maximum likelihood estimation for the gamma distribution using data containing zeros. J Clim 3:1495–1501 Wilks DS (2006) Statistical methods in the atmospheric sciences. 2nd edn. Academic, London Yin X, Goodrian J, Lantinga EA, Vos J, Spiertz HJ (2003) A flexible sigmoid function of determinate growth. Ann Bot 91:361–371 123