The correct representation of the crop duration within crop models is crucial for the interpretation of the important outputs from the model. For example, if the datasets used for sowing and harvest dates are inaccurate, the simulations could grow crops during the wrong season, thereby affecting the reliability of the simulated water use and crop yield. The main differences between the regional dataset and the global data are for spring wheat. Spring wheat grown in winter is misclassified as winter wheat in the data. This is discussed by as a potential limitation when using the data for tropical and subtropical regions. Spring wheat is the more common type of wheat grown in the South Asia region because minimum temperatures there are not low enough to allow vernalization to take place, which is needed for winter varieties of wheat .

Figure  shows the averaged rice (green rectangles) and wheat (orange rectangles) growing season durations for (diagonal hatching) and the dataset (perpendicular hatching labelled MinAg) overlaid on the present day South Asia averaged precipitation climatology and estimates of the monsoon onset and retreat. This illustrates the differences between the and datasets, showing that in the main growing period for both rice and wheat appears to be during the monsoon. While rice is usually grown during the monsoon it is not typical that wheat should be grown during this period for this region. The growing season durations for the dataset (see Fig. , perpendicular hatching rectangles labelled MinAg) are more typical of this region with rice (green) growing during the monsoon and wheat (orange) growing during the dry season. Figure  highlights that where a global dataset is unable to establish exactly when wheat is grown in tropical regions, an alternative is needed.

Crop models such as those described by and require sowing information such as a sowing date or a sowing window, with the crop model integrating an effective temperature over time as the crop develops. The effective temperature is a function of air or leaf temperature and differs between models. The integrated effective temperature in each development stage is referred to as the thermal time of that development stage ; there may also be an additional photoperiod length dependence. The thermal time in each development stage is typically set by the user and can be calibrated to simulate different varietal properties. Where these varietal properties are unavailable, e.g. for the global analysis in , in order to mimic the spatial variation in the choice of crop variety, these thermal times were determined from sowing and harvest dates and the temperature climatology, which allowed them to vary spatially. This ensures that during the simulation, the crop develops over the course of the crop season starting at the sowing date and ending at approximately the harvest date (i.e. the harvest date is the average over the course of the climatological period used). The use of this predefined thermal time ancillary drives the requirement for providing both a sowing and harvest date. Reliable high-resolution datasets for sowing and harvest dates are often unavailable for either the region or the time period that is needed. In addition, there is a demand for sowing and harvest dates that maintain consistency with the model climate. Therefore, in this paper we propose a new method, outlined in Fig. , for estimating sowing and harvest dates for use in the large-scale modelling of the rice–wheat rotation in South Asia using estimates of monsoon onset and retreat. This method does not require large amounts of data and the user can elect to use either the sowing input data or, if needed, both sowing and harvest data to run their chosen crop model. The main objectives of this study are

to develop a method for determining sowing and harvest dates for modelling the rice–wheat rotation in South Asia based on the ASM and

In order to demonstrate the viability of the methodology outlined in Fig. , we compare the simulated precipitation with observations from the Asian Precipitation-Highly Resolved Observational Data Integration Towards the Evaluation of Water Resources (APHRODITE; ) dataset in Sect. . APHRODITE is a daily, 0.25∘ resolution land-only gridded dataset that is also used in to show that the RCMs in this analysis capture the general hydrology of the region. The monsoon is a highly variable and complex phenomenon that currently not all climate models are able to represent; this may mean that some climate models would not yet be suitable for use with this method, which relies on a good representation of the monsoon. The method presented in Fig.  will become more robust with improving representations of the monsoon in climate models.

The datasets used for sowing and harvest dates include a global dataset, , and a regional dataset, , from the government of India, Ministry of Agriculture and Farmers Welfare. The data are referred to from here on as MinAg data. The MinAg observations of sowing and harvest dates for rice and wheat are given as a range of days of year. The midpoints of these observed ranges are calculated and compared against the midpoints of the model pentads for onset and retreat in day of year. As a post-processing step the differences are then masked using crop areas from the International Crops Research Institute for the Semi-Arid Tropics so that only the areas where rice or wheat is grown are considered.

There are a wide variety of metrics for estimating the monsoon onset and retreat. Some are specific to agriculture and include a representation of breaks in the monsoon . More general metrics include a combination of meteorological variables, such as 850 hPa wind and precipitation as in , or only use precipitation, such as in and the Normalized Pentad Precipitation Index (NPPI) . The NPPI and methods both use a long-term climatological average of precipitation because the model data are too noisy to calculate the monsoon statistics per year. Agricultural-specific definitions of monsoon onset and retreat represent breaks in the monsoon which can adversely affect the germination of crops. However, these metrics are not as effective when used in conjunction with long-term average precipitation fields such as those used here. This is probably because the breaks that occur in the monsoon are quite variable from year to year and are smoothed out within the climatology. The approach by defines monsoon onset as the pentad in which the relative rainfall exceeds 5 mm day-1 during the May–September period. However, regrid to the GPCP rainfall dataset , which is much coarser resolution than the APHRODITE data used here. The NPPI metric uses Eq. () to estimate monsoon onset, retreat, peak, and duration. NPPI=P-PminPmax-Pmin, where P is the unsmoothed pentad precipitation climatology and Pmin and Pmax are the annual minimum and maximum at each grid box respectively. The monsoon onset is then defined as the pentad in which the NPPI exceeds 0.618 for the first time and withdrawal as the last time the NPPI drops below this threshold in the year. The NPPI only reaches a value of 1.0 once in the annual cycle, which corresponds to the monsoon peak. In the NPPI method the only regridding that takes place is to ensure that the model and observations are on the same grid; as they are both 25 km resolution there is no loss of resolution in doing this. The threshold for NPPI is also independent of the resolution of the data, which is not the case for the method. The NPPI metric has been successfully applied previously by to analyse the monsoon in models of a similar resolution to the simulations used here (see Fig. ). Therefore in this analysis in the same way that use the 1981–2000 climatology, we use a 1990–2017 climatology. The pentad provided by the NPPI is representative of the climatological period and therefore cannot be compared to a particular year; however, the pentad can be used to find the 5-day window for the climatological period during which onset and retreat typically occur, which can then be compared to APHRODITE observations also averaged for that period. We use the NPPI metric to calculate the pentad of the monsoon onset, retreat, peak, and duration for the APHRODITE observations and the three HNRCM simulations.

We use estimates of the monsoon onset and retreat together with present day rules on sowing and harvest for rice and wheat, referred to as crop rules, to calculate the sowing and harvest dates relative to the monsoon (see Fig. ). This method allows any crop model that uses, for example, a driving dataset similar to APHRODITE or the HNRCMs to derive sowing and harvest dates that are consistent with the monsoon of the driving data (see Fig. ). Thus, the crop is grown at the appropriate time of the year; i.e rice is kept during the monsoon period and wheat is sown and harvested during the dry season. The monsoon is a highly variable phenomenon; however, the use of a long-term average (climatology) to calculate the monsoon statistics smooths out their large inter-annual variability. This highlights the consistency between the sowing and harvest dates and the monsoon statistics. Therefore we do not expect the monsoon statistics to be exactly the same as the observed sowing and harvest dates. Rather, this method relies on consistency between the climatological estimate of the monsoon statistics and the sowing and harvest dates across the region. The introduction of a crop rule then moves the monsoon statistic to more closely reflect the observed sowing and harvest dates. This means that even if the difference between the most relevant monsoon statistic and the observed sowing or harvest date is large then the difference is similar across India. Although these sowing and harvest events may not always be dictated entirely by the monsoon, the phenomenon provides the broader seasonality associated with the crop seasons in this region. The consistency between the crop practices and the monsoon statistics across the region provides the empirical relationship exploited here to estimate the sowing and harvest dates for use in both present day and future crop simulations. These sowing and harvest dates are not really intended to offer advice to farmers on when to sow or harvest on a year to year basis; rather, it provides a way for sowing and harvest dates to remain relevant to this major climatological feature. A key assumption is that the monsoon remains a defining feature of the crop seasons for South Asia in the future.

The method summarized in Fig.  is applied to two future periods using the ECHAM5 and HadCM3 RCM simulations (described in Appendix ). Global mean temperatures are used (within the High-End cLimate Impacts and eXtremes project, HELIX) to define the future climate in terms of specific warming levels (SWLs), i.e considering a 2, 4, and 6 ∘C world. The use of time periods is much more common than SWLs; however, SWLs enable the analysis to focus less on the climate scenarios and more on what the world will look like at 2, 4, and 6 ∘C . This will differ depending on when the threshold is passed. The SWL approach is therefore a benefit as it means that new scenarios that are developed as part of new model intercomparison projects can be compared against older ones from previous projects. Although the older scenarios may not contain the most up-to-date socio-economic information, they are no less likely than the newer scenarios. The simulations used here are for the period 1965 to 2100 and therefore only the 2 ∘C threshold for global mean temperature is actually passed during these simulations. For HadCM3 this occurs in 2047 and for ECHAM5, 2055. Therefore the two future periods used in this analysis are 2040–2057 and 2080–2097. The 2040–2057 period is chosen because it includes the year that the global mean temperature exceeds 2 ∘C in the two simulations, and the 2080–2097 period is chosen because it is furthest into the future in these simulations and therefore likely to show the greatest warming. The length of the two future analysis periods has been chosen for consistency with the ERA-Interim RCM simulation, which is only available for the period 1990–2007. Although the threshold of 2 ∘C is exceeded globally it is important to note that the relationship between the projected global mean change in temperature and the regional climate change in temperature for South Asia is complicated. Heat and moisture and how they vary across the globe are not evenly distributed, with land warming faster than the ocean ; therefore the actual temperature change experienced in South Asia may be higher than the global mean change.

The climatology in Fig.  shows that on average the observed rice and wheat sowing and harvest dates from MinAg align well with the monsoon onset and retreat in the simulations. Observed rice sowing dates generally compare well with the monsoon onset in the model as shown in Figs.  and .

The monsoon onset and retreat estimates are provided in days of year (pentads) and therefore with a range of plus or minus 2.5 days. The MinAg observations are also provided in days of year with a range that varies from plus or minus 15 days depending on the location. Figure  shows the range of the MinAg sowing and harvest observations for each state; the full sowing or harvest window is shown by the downward grey triangles, with the midpoints shown by black triangles joined by a black line. Figure  considers the midpoints of these two ranges in order to summarize how well aligned the monsoon onset range is to the observed range of rice sowing dates, i.e. how the 5-day onset windows coincide with the observed sowing window. If the monsoon onset range is completely within the range of sowing days provided by the observations, this is classed as a “hit” (shown by the blue regions). If the monsoon onset range is completely outside the range of observed sowing days, this is classed as a “miss” (shown by the red regions). The yellow regions in Fig.  show the places where the monsoon onset overlaps the range of observed sowing days but does not completely fall within it; these regions are labelled “overlaps”. Figure  has only a small area of red indicating that monsoon onset is, for large parts of India, within the range of days of rice sowing. In each plot shown in Fig.  the region that is red or yellow is different, and this makes it difficult to say if one dataset is better than another. ECHAM5 appears to have the smallest total area in red or yellow, which is probably because ECHAM5 tends to have an earlier onset than the other datasets and in general that makes it closer to the rice sowing dates. Table  lists the differences between the monsoon statistics (onset and retreat) and the relevant sowing and harvest dates for each crop calculated for each of the simulations and the APHRODITE observations and averaged for India. Table  shows that on average across India rice sowing occurs between 10 and 20 days prior to the averaged modelled monsoon onset (third block, Table ). We would not expect the different datasets to give the same results; however, Table  shows that they are relatively consistent with each other and, importantly, with observations as illustrated by the APHRODITE data. Table  highlights the fact that on average APHRODITE requires a larger crop rule than the simulations for rice sowing; however, this is not always the case for sowing or harvest and rice or wheat. The crop rules used here are based on the 1990–2007 period for which ERA-Interim has the earliest onset (see Fig. ). ECHAM5 has the smallest crop rule to move it towards the rice sowing date but the highest variance in the mean difference between the monsoon onset and the MinAg rice sowing date. APHRODITE has the largest crop rule for rice sowing, indicating that the weighted average of the APHRODITE monsoon onset is further from the rice sowing date than for other datasets.

In general the differences between rice harvest and monsoon retreat are larger but still consistent across the region (see Fig. ), with rice harvest occurring on average 30–40 days after monsoon retreat (see fourth block, Table ). Wheat sowing tends to occur approximately 60–70 days after monsoon retreat (see Fig.  and first block, Table ) and wheat harvest tends to occur approximately 90–101 days before monsoon onset (see Fig.  and second block Table ). These values (given in Table ) provide the RelMonsooncroprule values introduced in Sect.  used to adjust the monsoon statistics and calculate the new sowing and harvest dates based on the monsoon. There are small regions with different monsoon characteristics and therefore much earlier sowing days, for example for rice sowing in the southern and far north of India. These regions have a direct impact on the values (minimum, maximum, mean, and standard deviation) given in Table , which are averages for the whole of India and are discussed in more detail in Sect. . Figure  highlights the fact that the average sowing and harvest dates for rice and wheat are closely aligned with the monsoon precipitation from all three RCM simulations.

The monsoon-derived sowing and harvest dates are calculated by applying the RelMonsooncroprule for each model (see Table ) to the simulated monsoon onset and retreat fields (see Fig. ). Here we compare these with the gridded observations to see how well the method performs for the present day. The monsoon-derived sowing and harvest dates are compared with the MinAg observations using regional maps and an analysis for each state area in order to show the differences in the method across India.

Figure  shows the monsoon-derived estimates of rice sowing dates (left column) compared with MinAg observations (right column). Figure  shows the same plots for rice harvest, with plots for wheat shown in Figs.  and  for sowing and harvest respectively. The RelMonsooncroprule values for wheat for both sowing and harvest are much larger than those for rice, but there is still good agreement between the monsoon-derived estimates and the MinAg observations across the region. On average the monsoon-derived estimates of sowing and harvest dates are within 4 days of the midpoints for the sowing and harvest dates for rice and within 7 days of the midpoints for sowing and harvest dates for wheat. There is some variation across India with some regions showing larger differences, but generally the monsoon-derived estimates for sowing and harvest dates are within the range provided by the observations across much of the region for both crops.

Figure  shows the average crop duration for each state where MinAg observations were available for the 1990 to 2007 period alongside the crop duration for each of the four sets of monsoon-derived estimates using the Fig.  method. In the majority of states shown in Fig.  the sowing and harvest dates calculated using the Fig.  method were within the range of the MinAg observations for rice and wheat sowing and harvest dates; however, the overall performance was better for rice compared with wheat and sowing compared with harvest in each crop. Figure  also highlights the difference in both the observed and simulated crop duration between the two crops with rice having a shorter season than wheat. In general across most of the states with available data the method provides a reasonable estimate of the sowing date, harvest date, and crop duration. Even where the method does not quite capture the observed sowing and harvest dates, the method is often just outside the observed range.

In order to establish how well the method performs overall, we use Fig.  to assess if the results using the method are good, poor, or fair compared to the MinAg data. Where the monsoon-derived sowing and harvest dates from three of the four datasets using the method are within the range of the MinAg data as shown in Fig. , the results of the method are said to be “good” for a state. The results of the method are said to be “fair” where two datasets are within the range of the MinAg data and “poor” where the sowing and harvest dates fall outside the observed range. In this analysis only the state of Assam did not have any “good” scores for rice or wheat sowing or harvest. Most of the scores for most states for sowing and harvest as well as wheat and rice had a score of good or fair.

In general the regions where the monsoon-derived sowing and harvest dates are not as close to the MinAg observations tend to be the states in the south, such as Andhra Pradesh and Karnataka, or to the north of India, such as Jammu and Himachal Pradesh. This is supported by the maps, particularly for rice for these regions (in Figs.  and ), which show that the method does not perform as well for some of these states. These differences may be explained by the differing monsoon characteristics in these regions compared to the rest of India; these are highlighted in Fig.  and discussed further in Sects.  and . Assam in the north-east of India is also noticeable compared with the other states in Fig. , with the rice crop season in the MinAg data displaced to an earlier part of the year. Assam tends to plant predominantly rice with three distinct rice seasons (autumn, winter, and summer) rather than a rice–wheat rotation . In this analysis we use data for the Kharif paddy rice crop from the MinAg dataset, which is planted and harvested earlier in Assam than in other states, with sowing in February–March and harvest in June–July .

As a demonstration of the method summarized in Fig. , the HELIX SWLs (described in Sec.) are used to select two future periods: 2040–2057 and 2080–2097. Considering only these future periods, spatially HadCM3 and ECHAM5 show quite different future climates. HadCM3 shows a similar onset to the present day for 2040–2057 (see Fig. a and c) but a later onset compared with the present day for 2080–2097 (see Fig. a and c). ECHAM5 shows an earlier onset compared with the present day for the 2040–2057 period (see Fig. b and d) but much later for the 2080–2097 period (see Fig. b and d). This suggests high variability in monsoon onset in these simulations. In fact, monsoon onset, peak, retreat, and duration all show a large degree of variability as shown in Fig.  in which each statistic has been averaged for South Asia. Each point in Fig.  represents a 17-year time slice from between 1970 and 2097 for each of the APHRODITE, ECHAM5, HadCM3, and ERA-Interim datasets. Figure  supports the points made regarding the spatial plots and also shows how the four monsoon statistics change between the 17-year time slices. The 2040–2057 period has a much earlier onset for ECHAM5 than all the other periods except the 2000–2017 period, which is similar (see Fig. a). For most of the periods ECHAM5 has an earlier onset than HadCM3; this is also true of the retreat (see Fig. b), but the duration is usually longer for ECHAM5 compared with HadCM3 (see Fig. d).

In order to illustrate the method for deriving sowing and harvest dates, Fig.  shows the annual cycle of precipitation averaged for South Asia for the two future periods (panel a shows 2040–2057 and panel b shows 2080–2097) in the same way as the present day is shown in Fig. . The crop sowing and harvest dates used to provide the growing season durations in each of the plots shown in Fig.  for each of the simulations are calculated using the method described in Fig. . This shows that the proposed method provides an estimate of sowing and harvest dates that ensures the crops can continue to be grown in the simulation when the climate is most appropriate rather than being fixed to the present day observed values.

In general the method described by Fig.  works well across most of India for the present day, with the monsoon-derived estimates of sowing and harvest dates falling within the range of days for sowing given by the observations and therefore providing a good estimate of the crop duration for most states (see Fig. ). However, there are regions where the estimated sowing and harvest dates do not compare as well against present day observations. Rice sowing is generally closely associated with ASM onset across most of central India; however, in the south of India there is a small region where the differences between the observations of sowing dates and the monsoon are larger than everywhere else (see Fig. ). In Sect.  this region is shown to have different monsoon characteristics to the rest of India. This part of India includes the state of Tamil Nadu, which is located on the lee side of the Western Ghats and therefore does not receive the large amount of ASM rainfall that is commonly associated with this part of the world. Tamil Nadu receives up to 50 % of its annual rainfall during October–December via the less stable North-east (NE) Monsoon. The NE Monsoon is therefore more important for water resources for this part of India than the ASM, which accounts for approximately 30 % of the annual rainfall for this region . These differing monsoon characteristics mean that different agricultural practices are required to cultivate rice in this part of the country. This is illustrated by Fig. a, which shows that the southern region of India with differing monsoon characteristics irrigates rice more intensively than other parts of India. In the Tamil Nadu region, rivers are usually dry except during the monsoon months and the flat gradients mean there are few locations for building reservoirs; therefore approximately one-third of the paddy rice crop is irrigated from a large network of water tanks . The southern states of India have the highest density of irrigation tanks with large numbers also found in Andhra Pradesh and Karnataka; these are also regions shown to have a high irrigation intensity in Fig. . Rice harvest is typically not as closely associated with the monsoon onset as rice sowing, which usually requires the monsoon to be fully established before planting.

The widespread irrigation of wheat shown in Fig. b has less of an impact on the estimates of wheat sowing and harvest dates because this crop is less closely linked to the monsoon onset than rice. Therefore the regional differences between the MinAg observations and the monsoon-derived sowing and harvest dates for wheat are not as large as some of those for rice (see Sect. ). Given that the method has provided reasonable estimates of sowing and harvest dates for most of India, it would be useful and interesting to extend this method to improve it for the south of India.

The analysis of the future monsoon onset, retreat, peak, and duration shown in Sect.  shows how changeable the ASM is for these simulations between time periods. show that there is a high model agreement within the ensemble from the Coupled Model Intercomparison Project Phase 5 (CMIP5) for an earlier onset and later withdrawal in the future that therefore indicates a lengthening monsoon duration. However, the simulations presented here do not show this with Fig. , instead highlighting the large amount of variability in the ASM for this region. It is possible that an increase in the monsoon duration does occur in these simulations for some parts of South Asia, but this detail is lost through averaging over the region or as a result of the time periods selected. also suggest that there is medium confidence within the CMIP5 ensemble that the ASM rainfall will increase to the end of the century. The simulations presented do indicate this as shown by the time series in Fig. .

Assuming that crops continue to be grown in accordance with the monsoon, Sect.  shows that the method described in Sect.  provides a good estimate of sowing and harvest dates for the two future periods shown. Spatial plots of the sowing and harvest dates for the two future periods (not shown) are similar to those in Sect.  for the present day with the south of the Indian peninsula continuing to show different monsoon characteristics (see Sect. ) to the rest of India in the future, resulting in later estimated sowing and harvest dates for this region.

The proposed method successfully adjusts the sowing and harvest dates when the monsoon begins earlier in the future simulations and therefore provides a good estimate of sowing and harvest dates for the two future periods considered. This is a key benefit of using this method as it simulates the decision a farmer might take to sow before the usual observed date if the monsoon arrived early. This method therefore provides the capability for climate simulations to replicate the type of adaptation response that would happen in the real world. This method would also be useful for other regions that have a crop calendar that is similarly defined such as the SSA; this is a multiple cropping region with sowing and harvest dates closely associated with the main rainy season .