Global crop yields can be lifted by timely adaptation of growing periods to climate change
Rule-based mean sowing and maturity datesLocation- and climate-specific mean crop calendars are computed by combining two rule-based approaches published by19 and22 to simulate sowing and physiological maturity dates of grain crops, respectively. The assumption is that farmers select growing seasons based on the mean climatic characteristics of their specific location and on the physiological limitations (base and optimum temperatures for reproductive growth; sensitivity to terminal water stress) of the respective crop species. Accordingly, they select sowing dates and cultivars with phenologies that, on average, meet these adapted maturity dates.The climate is classified into (i) seasonality types, based on the coefficient of variation of monthly mean temperature and precipitation and (ii) temperature levels, based on the temperature of the warmest month as compared to the base and the optimum temperatures for the crop reproductive growth. Optimal temperatures for sowing, optimal temperature ranges for grain filling, as well as indicators of soil moisture conditions (based on precipitation/potential-evapotranspiration ratio (P/PET)), are defined as global parameters for each crop (Supplementary Table 1) and used as thresholds to identify the best timing for sowing and for the start or end of the crop grain-filling phase. To cope with fluctuations of daily values around these thresholds, mean daily temperature, precipitation and potential evapotranspiration are derived by linear interpolation between monthly values.We distinguish between spring and winter crop types. Maize, rice, sorghum, and soybean are simulated as spring crops only, for wheat we simulate both types. For spring crops, farmers sow the crops at the onset of the wet season (first day of the wettest 120 consecutive days), in case of prevailing precipitation seasonality, or on the day of the year when temperatures increase above crop-specific temperature threshold19 (Supplementary Table 1), in case of temperature-driven seasonality.For wheat, we distinguish three types: winter wheat with vernalization is chosen if monthly temperatures fall below 0 °C, but winter is neither too harsh (temperature of the coldest month is higher than −10 °C), nor too long (temperatures fall below the sowing temperature threshold (12 °C) after 15th September (North hemisphere) or 31st March (South hemisphere)19). Winter wheat without vernalization is grown if winters are mild (the temperature of the coldest month is higher than 0 °C) without dormancy. In this case, wheat is sown 75 days before the coldest month of the year. This rule was arbitrarily chosen based on observed wheat sowing dates in mild winter regions. If the conditions for growing any of the winter-wheat types are not met (winter too harsh and too long), then spring wheat (without vernalization) is chosen. Note that the computed sowing dates do not differ between rainfed and irrigated for any of the crops.The mean maturity date is chosen so that the crop grain-filling phase, the most critical for yield formation, occurs under the least stressful conditions possible in that location and climate as follows. Under precipitation seasonality, grain filling starts towards the end of the rainy season, when a P/PET threshold is crossed. Under temperature seasonality, (a) grain filling of spring crops starts in the warmest month of the year (if summer temperatures are optimal), or right after temperatures return within an optimal range; (b) grain filling of winter crops ends in the warmest month of the year (if summer temperatures are optimal), or right before temperatures exceed the optimal range; (c) eventually, maturity is advanced to escape terminal water stress. Note that the grain-filling phase has a static duration of 60 days for maize and 40 days for all the other crops. This assumption is based on empirical relationships between the total growth period and the post-flowering reproductive phase, showing that the partition between the vegetative and reproductive phase of grain crops follows a saturation curve that levels off after 90–100 days of total growth duration54. Different crops are assumed to have only one crop cycle (sowing-to-maturity) per year, therefore neither multi-cropping systems nor crop rotations are accounted for in the decision-making rules. A detailed description of the rules and parameterization can be found in refs. 19, 22.Simulated crop calendars reflect current farmers’ managementSimulated historical crop calendars, driven by the bias-corrected climate dataset WFDEI23, largely agree with observations11,12,13. We compare results both at the country and grid-cell level because, although the observed crop calendars used here are gridded datasets, their underlying sources are often reported per country. The country-level comparison highlights that the agreement is good for most countries, importantly, including those with large cropland area. The area-weighted Mean Absolute Error (MAE) is close or well below 30 days for all considered crops (Fig. 4). The simulated crop calendars compare well with the observed data also at the grid-cell level. Large areas, including major agricultural regions of importance for global yields, show deviations within ±15 days for both sowing and maturity dates (Supplementary Table 2 and Supplementary Figs. 21–24). However, evaluating the accuracy below 30 days is limited by the time resolution of the observations, which is either (i) monthly11 and converted by us into daily values, by taking the mid-day of the reported month, or (ii) daily12,13, but resulting from averages over large time windows (often > 1 month). Overall, the accuracy of the model is in line with the original evaluations of this rule-base method19,22, as well as with other studies simulating average growing periods across large regions18,20.Fig. 4: Evaluation of simulated crop calendars.Country-level comparison of simulated and observed sowing (A) and maturity (B) dates (day of the year) for five crops. Each circle refers to a country and a crop, the size of the circle is scaled according to the cropland area per country. The area-weighted Mean Absolute Error (MAE, days) is reported for each crop. Crop-calendar simulations are based on WFDEI reanalysis climate forcing23 for the period 1979–2012. The observed crop calendar includes different sources11,12,13.Full size imageSimulation of daily crop phenology and yields with the LPJmL crop modelWe perform a modeling experiment across the global land grid at 0.5° × 0.5° resolution. We used the LPJmL5 crop model24,25 to simulate daily growth and phenological development of five crops, driven by climate projections from four General Circulation Models (GCMs) GFDL-ESM2M, HadGEM2-ES, IPSL-CM5A-LR and MIROC5 under the Representative Concentration Pathways 6.0 (RCP6.0) as provided in bias-adjusted form from the CMIP5 archive by the ISIMIP2b project42. Irrigated and rainfed production systems are simulated separately on their current harvested areas11, which is also used to compute total crop yields at grid-cell and global scale, as the product of yield by crop-specific area. A first 5000-year spin-up simulation is used to initialize all model pools (e.g., soil carbon and nitrogen content). A second spin-up simulation of 390 years is used to introduced effects of historical human-driven land-use change on these pools. A change in cropping area for the future scenarios is not considered in this study.Phenological development is simulated based on the thermal-time model, including the effect of vernalization. All crops are assumed to be insensitive to photoperiod, due to a lack of parameters for multiple-crops and global-scale simulations. Previous global studies15,18 that have focused on maize and wheat only, have found lower performances in the growing-period simulations when using a photo-thermal model, compared to a temperature-only driven approach and thus recommend caution when using the photoperiodic response. State-of-the-art global crop models13,16 also typically do not consider sensitivity to photoperiod or assume that the photoperiodic response of the cultivars chosen in each location are perfectly tuned to the given conditions.Sowing dates are prescribed based on the external rule-based algorithm. Crop cultivars are parametrized based on the phenological units required to reach the corresponding maturity dates (TUreq, °C days). In line with15, TUreq are derived consistently with the phenological module of the crop model LPJmL for each grid cell, crop, and rule-based computed growing period from the respective climate input. They are calculated as the sum of daily mean air temperature increments above a crop-specific base temperature (TU) (Supplementary Table 1) between rule-based sowing and maturity. In addition, winter-wheat cultivars require effective vernalization days (VUreq), that range between 0 (mild winters) and 70 (cold winters), depending on the temperature of the 5 coldest months (Eq. (1))15,18.$${{{{{mathrm{V}}}}}}{{{{{{mathrm{U}}}}}}}_{{{{{{{mathrm{req}}}}}}}}=frac{70}{5}times left(1-frac{{T}_{m}-3}{10-3}right)$$
(1)
where Tm is the mean temperature of the month.From the day of sowing, effective TU for phenological development are accumulated daily, as the difference between the mean air temperature on that day and the crop-specific base temperature for phenological development (Eq. (2)). The vernalization effectiveness is computed daily by a scaling factor (0–1), which is then multiplied to the TU (Eq. (2)). For crops that are insensitive to vernalization, VUd is set equal one.$${{{{{mathrm{T}}}}}}{{{{{{mathrm{U}}}}}}}_{{{{{{{mathrm{req}}}}}}}}=mathop{sum }_{d=1}^{{ndays}}left({max }left(0,{T}_{d}-{T}_{{base}}right)times mathop{sum }_{0}^{d}{{{{{mathrm{V}}}}}}{{{{{{mathrm{U}}}}}}}_{d}right)$$
(2)
where the scaling factor VUd is computed by a three-stage linear response function with a range of optimal temperatures (Eq. 3). Temperature for effective vernalization range between −4 °C and +17 °C, with an optimum range between 3 °C and 10 °C.$${{{{{{{mathrm{VU}}}}}}}}_{d}=left{begin{array}{cc}left({T}_{d}-left(-4right)right)/left(3-10right) & {{{{{{mathrm{if}}}}}}}-4 , < ,{T}_{d} , < , 3\ 1 & {{{{{{mathrm{if}}}}}}};3,le ,{T}_{d},le, 10\ left(17-{T}_{d}right)/left(17-10right) & {{{{{{mathrm{if}}}}}}};10 , < ,{T}_{d} , < , 17\ 0 & {{{{{{mathrm{otherwise}}}}}}}end{array}right}$$
(3)
In this study, we have removed the effect of vernalization on slowing down TU accumulation until 10% of the total vernalization requirements is reached. In this way, the crop can accumulate both vernalization units and heat units in fall, so that there is some leaf growth before winter (in LPJmL, the LAI curve depends on accumulated heat units).The LPJmL model simulates phenology as one single phase from emergence to maturity. Although the flowering stage is not simulated as an explicit break point, the fraction of above-ground biomass that is allocated to the storage organs (fHI) depends on the phenological progress (fTUreq, fraction of TUreq that have been fulfilled), with the bulk of the storage organs start filling up after 40% of TUreq have been reached (Eq. (4)). In line with this, the LAI curve reaches a plateau when 45% (wheat) or 50% (other crops) of the TUreq are fulfilled, which could be considered a proxy of the flowering stage.$${{{{{{mathrm{fHI}}}}}}}=100times frac{{{{{{{{mathrm{fTU}}}}}}}}_{{{{{{{mathrm{req}}}}}}}}}{100times {{{{{{{mathrm{fTU}}}}}}}}_{{{{{{{mathrm{req}}}}}}}}+{{exp }}^{11.1-10.0times {{{{{{{mathrm{fTU}}}}}}}}_{{{{{{{mathrm{req}}}}}}}}}}$$
(4)
Crop biomass growth is simulated by daily carbon accumulation and allocation to different plant organs (roots, leaves, storage organs, mobile reserves, and stem). The fraction of carbon allocated to each pool is a function of the fraction of completed phenological progress. Water stress increases allocation to the roots and reduces allocation to the leaves. The daily Net Primary Production (NPP) is the result of the Gross Primary Production (daily gross photosynthesis) reduced by the respiration costs. Gross photosynthesis is simulated as a function of absorbed photosynthetically active radiation, CO2 atmospheric mixing ratio, air temperature, day length, and canopy conductance. Photosynthesis rate is given by the minimum between light-limited and Rubisco-limited photosynthesis rates, with distinguished pathways for C3 and C4 crops. Respiration is tissue-specific and it is also driven by temperature. If accumulated NPP is insufficient to satisfy all organ demands, allocation follows a hierarchical order from roots, to leaves, to storage organs, and consequently penalizing the harvest index. Crops are subject to yield failure due to frost events (daily minimum temperature More
