“Climate Cost of Cultivation”: A New Crop Index Method to Quantify Farmers’ Cost of Climate Change Exemplified in Rural India

We model the impact of agricultural droughts with a new multi-parameter index (using both climatic and non-climatic parameters) and propose a new risk transfer solution for crop insurance, called Climate Cost of Cultivation (CCC). We used 1979/80 to 2012/13 data relevant for wheat in Bihar, India to test the variation in the CCC values. The variance (risk to farmer) increased significantly in the second half of the period (two-tailed F-test, p=0.00045). We examine the efficiency of CCC by comparing it to typical index insurance (TII), and both indices to wheat yield data (2000/01 to 2012/13). The correlation of CCC index payouts with actual yield losses is improved by a factor of ~3.9 over TII results (76.0 per cent, compared with 19.6 per cent). The pure risk premium of the CCC index is lower by around 90 per cent than the premium of the TII. We also elaborate a method to quantify the premium’s climate change cost component.


Introduction
Years of experience with index-based crop insurance 1 show that uptake has remained very low relative to the target population 2 or arable land, 3 mainly credit-linked, 4 and with only minimal voluntary uptake by farmers. 5 India has the largest agriculture insurance scheme in the world today in terms of the number of policyholders. 6 The Government of India (GoI) has been promoting index-based crop insurance schemes for years. 7 However, voluntary objective would require revisiting the design of index insurance to make it context-relevant. Specifically, a better understanding of location-specific crop production risks 19 requires higher resolution of climate data and the inclusion of certain non-climatic parameters.
We propose a new model that describes production risks better, namely through an improved modelling of the financial impact of drought. By combining climatic and non-climatic parameters, our model addresses the question of the correlation between losses and payouts differently, and contains a formula to calculate the added cost of climate change. We call this the "Climate Cost of Cultivation" (CCC) method.
Readers might be familiar with crop models (that simulate the crop yield based on crop type, weather, soil, pest and disease, and nutrient supply parameters and conditions, as well as farming practices). 20 Unlike crop models, the CCC method estimates the risks to farmers based on the interaction between adverse climatic and non-climatic conditions (the influence of which is recognised in agronomic and soil-water balance models 21 ). Consider a simple example: farmers can decide to irrigate (where irrigation facilities are available) when rainfall is insufficient, rather than suffer crop yield loss; the trade-off is better yield with an increased input cost (irrigation) vs yield loss. Hence, our definition of cost of cultivation combines both increase in irrigation costs, if rainfall patterns are unfavourable, and yield losses, if losses cannot be mitigated easily, for example, in the case of high temperatures. The CCC method aims to quantify the financial implications for farmers of certain climatic conditions by considering the combined effect of increased input costs and yield loss with the severity of these factors, which depends notably on non-climatic parameters.
We demonstrate the improved modelling of the impact of agricultural droughts (hereafter "droughts") with the CCC method by reference to winter wheat in Bihar, India. In Bihar, the rainfall in the winter season is usually very low (on average around 30 mm), providing roughly 10 per cent of the winter wheat water requirement. Therefore, winter wheat is irrigated. Most smallholder farmers in Bihar usually irrigate well below the water required for optimal wheat yield to save the cost and effort involved. The cost comprises the rental charges of tube-well pumps and the diesel fuel to operate the pumps, as most farmers use groundwater for irrigation. Average (or higher) seasonal rainfall can save one to two irrigations in Bihar. Higher soil moisture at the time of sowing, because of above-average precipitation during the preceding monsoon months, can also make a difference.
Typical index insurance (TII) for winter wheat in India, used here as the reference to which we compare the CCC method ("CCC index"), covers yield losses due to high temperature (mean and maximum temperature for different time periods respectively) or excess rainfall, but does not compensate for insufficient rainfall. The CCC method, in addition to losses due to high temperature and excess/untimely rainfall (following a slightly different method), also covers the risk of above-average irrigation costs. In the CCC method we determine the initial seasonal soil moisture as a function of the aggregated pre-season (monsoon) rainfall, to capture the risk of lower soil moisture in the winter (post-rainy) season due to low rainfall during the preceding monsoon. Additionally, daily rainfall during the winter season is incorporated into the daily soil moisture modelling. Incorporating aggregated pre-season and daily seasonal rainfall and non-climatic parameters improves the accuracy of the modelling of droughts and their financial impacts (increased irrigation costs). Stated simply, the CCC method models the random shock of below-average soil moisture for the season (due to unseasonal/insufficient rainfall, high temperatures etc.). This random risk is ignored by TII.
The article is organised as follows: in the next two sections we provide details on the study area, data sources and methods used. The results are presented in the fourth section, discussion in the fifth and conclusions are presented as the last section.

Study area
The study was conducted in Bihar, the third most populous Indian state (>100 million persons) and the 12 th largest in terms of area (94,200 km 2 ) located in the eastern part of India. 22 The river Ganges divides Bihar into North Bihar (53,300 km 2 ) and South Bihar (40,900 km 2 ) and contributes significantly to its bio-physical and socio-economic settings. 23 Bihar is prone to waterlogging, floods and droughts. 24 Nearly 81 per cent of the Bihari population is employed in agricultural production. Wheat, paddy, maize and pulses are the principal crops.

Data and methods
In this study, CCC is tested with wheat, a major post-rainy season (Rabi) crop that is largely irrigated. The rabi lasts from November to March. The growth duration of wheat lasts 120 days.

Data used
The relevant parameters we used are described in Table 1.

Methods
The CCC estimation combines the effect of four climatic situations, three with negative implications on crop ((i) water deficit leading to additional irrigation cost; (ii) excess water leading to drainage cost; and (iii) high temperatures leading to yield loss) and one situation with a positive impact on crop yield (increasing concentration of atmospheric CO 2 ). The CCC method does not consider other cultivation costs/risks that we assume to be, by and large, independent of climate. Although waterlogging situations are captured in the CCC method, floods are not, as they are often triggered by heavy rainfall upstream or breaches of river embankments outside the study area. A schematic representation of the method is shown in Figure 1.
Method to calculate costs due to additional irrigation The calculations for water deficiency necessitating irrigation cost are informed by the difference between the daily soil moisture available at root zone and the daily crop water requirement. The crop water requirement is interpreted as the potential crop evapotranspiration ET C . ET C is calculated using the reference evapotranspiration ET 0 and the crop coefficient K C 25 : where ET 0 is the reference evapotranspiration calculated using the FAO Penman-Monteith method and K C is the crop coefficient factor; see Table 2. The crop water requirements are satisfied in the study area by rainfall and groundwater. The soil moisture in the root zone is modelled on a daily basis using the water balance equation. 26,27 This model for soil moisture resembles FAO's CROPWAT model, 25 with a few notable differences: customisation of crop factor, modelling runoff using the Soil Conservation Service (SCS) curve number method, setting initial soil moisture conditions   Standard values for the available water capacity (AWC) for each soil type were considered. 28,29 We set the initial depletion ID at the onset of a crop season as crop, season and year specific (see Table 2). In years with ample rainfall in the off-season preceding the crop season, the initial soil moisture would be higher, and farmers would spend less on irrigation than in years with lower rainfall.
The Geneva Papers on Risk and Insurance-Issues and Practice 286 and interpolated SCS runoff curve number where CN I , CN II , CN III are the curve numbers for three antecedent moisture conditions, namely dry, average condition of moisture and upper limit of moisture. Depending on cover type (here we chose "small grain"), treatment (here "straight row"), hydrological condition (here "good") and hydrologic soil group (soil type dependent) the CN II value is set. 34 The curve numbers CN I , CN III are derived from CN II 35 : (9) In this model any additional water from precipitation after runoff in excess of the amount of water necessary to reduce the root depletion RD i to zero, that is, to reach maximum soil moisture, will be percolating below root zone: We assume that farmers will irrigate the crop rather than incur crop yield loss, but do so as late as they can. The field will be irrigated if the depletion rate (i.e. root zone depletion divided by the maximum soil moisture available to the plant, RD i /(r i *AWC*ID)), reaches or exceeds the critical soil depletion threshold (see Table 2). Though usually the net irrigation amount is the previous day's root zone depletion, during the late stage of the crop cycle, the net irrigation amount is the previous day's root zone depletion times the remaining days until harvest, divided by the length of the late stage in days. This additional rule obviates intensive irrigations just a few days before harvest, which we assume that no farmer would do.
For 1 ⩽ i ⩽ 90 we thus set and for 91 ⩽ i ⩽ 120 we set Furthermore, we assume that farmers in Bihar apply flood irrigation with field efficiency of 70 per cent, that is, only 70 per cent of the gross irrigation will percolate to the root zone of the plant. 25 The gross irrigation amounts were aggregated, I total , for the entire period of 120 days for wheat for every year from 1979/80 to 2012/13.
In Bihar, irrigation is sourced from groundwater that is pumped up with diesel-operated tube-wells (most commonly the 5 horsepower (HP) diesel pumps of 80 per cent efficiency). The irrigation costs depend on two variables: the groundwater depth (assumed to be time constant but spatially variable) and gross irrigation quantum (which varies in space and time).
The cost of irrigation is obtained by multiplying the diesel consumption (1.2 liters per hour for 5 HP (= 5*746 W) pump) by the time the pump needs to draw the gross groundwater amount required, adding a total dynamic head of 15 m to surface level (i.e. 15 m is the equivalent height the water has to be pumped to reflect friction loss and the height reached by the pipe after the pump; the exact value of the total dynamic pump head is specific to each location, and a change in this parameter can lead to changes in the costs). We use a constant diesel price for the entire period under consideration (1979/80 to 2012/13) to reduce confounders, as our study focuses on climate-related variations of cultivation costs only. The assumed diesel price is PPP$3.09 per liter (INR51.69 per liter 36 and at an INR-PPP$ exchange rate of 16.72 in 2013 37,38 ). The cost of irrigation in PPP$ per hectare is then: where ρ water is the density of water, ρ water =1000 kg/m 3 , g is the standard gravity, g=9.81 m/s 2 , and d GW is the groundwater depth.
Method to calculate costs due to excess water When soil moisture exceeds the field capacity, additional rainfall can lead to waterlogging on the soil surface. We assume that farmers drain waterlogged precipitation rather than accept yield loss. The drainage costs depend on rainfall induced runoff. The daily runoff was aggregated over the cultivation period of the crop to compute the surplus water amount. The amount of diesel required to drain the surplus water is calculated assuming a total dynamic head of 10 m. The drainage cost was generated by multiplying diesel amount with the price of diesel: 36 MyPetrolPrice (2015). 37 Year 2013 is taken as the base year as the validation data are available only from 2000/01 to 2012/13. 38 World Bank (2015).

The Geneva Papers on Risk and Insurance-Issues and Practice
Method to calculate high temperature losses The relationship between high temperature and yield loss is complex and only partially understood. [39][40][41] Open field investigations, 42,43 laboratory experiments 44,45 and computer simulations 43,[46][47][48][49][50][51] have been conducted to assess the impact of temperature on crop yield. Based on studies conducted for wheat, 41,[52][53][54][55] we assume a yield loss of 8 per cent respectively per 1°C above-seasonal-average maximum temperature in the reference period (1979/80 to 2012/13) plus 1°C. For the calculation, we used crop yield data for Bihar for the year 2012/13 as a reference. For every season with yield loss, we multiplied the percentage of loss by the proxy for the market price of wheat, set at the Bihar government minimum support prices for 2012/13, which was 0.81 PPP$/kg. 56 Method to calculate CO 2 fertilisation Long-term experiments have revealed that an increase in atmospheric CO 2 has a positive impact on yield for some crops. [57][58][59][60] We assume 0.028 per cent increase in wheat yields with a 1 ppm increase of CO 2 in the atmosphere. 61 In the time period considered here, the CO 2 concentration has increased from 336.78 ppm in 1979 to 393.82 ppm in 2012. The annual change in yield due to CO 2 -effect was calculated with reference to 2012 leading to lower yields in the past, ceteris paribus.

Calculation of the CCC values and the CCC index
The CCC values in each location are calculated as the sum of costs due to deficient rainfall (irrigation costs), excessive rainfall (drainage costs) and maximum temperature (yield losses) minus the positive impacts of atmospheric CO 2 (fertilisation leading to higher yields).
Based on the calculated CCC values, for each location the CCC index payout has been defined as • 0, if the CCC value was below the average of all years, • the positive deviation, if the CCC value was above the average.
The average CCC values were calculated location-specific for the years 2000/01 to 2012/ 13 (with the exception of 2009/10, for which official cost of cultivation records were unavailable) for the purpose of this comparison. The CCC index payout is thus defined as the positive deviation of the CCC values in each location from the temporal average. Although the CCC values reflect location-specific heterogeneities (soil type, groundwater depth, micro-climate), which cannot be insured, the CCC index in each location measures the positive deviation of the CCC values from the temporal average, which can be insured. The heterogeneities can then be reflected in the pricing and design of the CCC index.
All maps shown in this article were generated using ArcGIS software version 9.3.

Comparing the CCC index to a typical index insurance
To assess the effectiveness of the CCC index in reducing the risk to farmers, we compared the CCC and TII payouts with cost of cultivation data available for wheat at plot level. 62 We have taken all points which are sampled each year by the Government of Bihar for the purpose of collecting cost of cultivation data at farm level. 63 The cost of cultivation data set contains all costs, such as inputs, irrigation and labour, plot size and crop yield. Irrigation costs constitute the major climate-related costs. Therefore, we determined the net income subject only to the yield income and irrigation costs with fixed prices at 2012/13 levels (0.81 PPP$/kg for wheat produce, 2.39 PPP$ per hour of irrigation) to remove the inflation in costs and to allow for comparison with the CCC values. Other costs (e.g. human labour, seeds, pesticides, fertiliser) were ignored, because they are either independent of climatic conditions or negligible.
The yield data were de-trended to remove the effect of technological advancements and to calibrate the data at 2012/13 levels following the approach of Deng et al. 64 and Ye et al. 65 The plot level trends were calculated by first determining the slopes of the linear trends of the average yield on Bihar level through ordinary least squares (OLS) regressions. For each plot in each sample period the linear trend was calculated through OLS regression under the constraint that the slope of the trend at plot level was set as the Bihar level one.
The net income was calculated as the difference between de-trended yield income and irrigation costs. Only plots with at least two years of net income data were considered. The expected yield was set at the mean value and plots were considered to have zero loss in years where the actual yield was equal to or larger than the expected yield, while in the other years, the loss was equal to the shortfall. 62 Collected from sampled plots in sampled villages by the Directorate of Economics and Statistics (DES), Dept.
of Agriculture and Cooperation, Ministry of Agriculture, Govt. of India. 63 Every three years, the DES samples new villages, but within a sampling period, the villages and plots remain the same. Each year, the cost of cultivation data cover around 40-50 villages across the state of Bihar. In each village, data on plots of approximately 3-8 farmers are captured. 64 Deng et al. (2007). 65 Ye et al. (2015).

290
Decomposition of pure risk premium into "normal" and "climate change increment" The CCC captures the most important climate-related input parameters and quantifies the risk to farming holistically. Therefore, statistically significant different CCC values (in mean, variance or both) in two (non-overlapping) extended time periods indicate climatic changes from one period to the other. In this case the pure risk premium of the CCC index can be decomposed into a "normal" pure risk component, PR normal , and a "climate change increment" pure risk, PR CC , in the following way for the time periods given by t 1 <t 2 ⩽ t 3 <t 4 : where PR(t a, t b ) is the pure risk premium based on (historic) CCC values in the time period t a <t b . The time period from t 1 to t 2 would indicate the base/reference period before climatechange.

Results
We compute the CCC by considering its four climatic components (deficient rainfall, excessive rainfall, maximum temperature and atmospheric CO 2 ) from 1979/80 to 2012/13 (for which data were available). Moreover, for each year from 2000/01 to 2012/13 (where wheat data were available), we calculated the average loss and the correlation between average loss and average CCC index payout for all plots representing the sample for Bihar state. The risks of farming without insurance are reflected by standard deviations of the average losses, and the risks of farming with insurance are reflected by the differences of average losses after considering average CCC index payouts. The benchmark for comparison of the performance of the CCC index is a typical weather index insurance product (TII) which was sold for winter (Rabi) wheat season 2013 in Bihar; we compare the correlation between losses and payout, and risk reduction properties.

Climatic and non-climatic parameters affecting farm losses
For all 12 Rabi wheat seasons where crop data were available, we calculated plot-level farm net income losses. The results are shown in Table 3: We regress the farm net income loss against climatic (seasonal rainfall, pre-season rainfall and average maximum temperature) and non-climatic parameters (groundwater depth and soil type that inform available water capacity and infiltration rate).
The regression illustrates that the influence of seasonal rainfall, pre-season rainfall, seasonal maximum temperature and the infiltration rate of the soil is statistically significant, while the R 2 value is still very low (0.006967). As expected, farmers incur lower losses when seasonal and pre-season rainfall are adequate and atmospheric CO 2 increases, and more losses when average maximum temperatures are high. One would expect that losses increase as irrigation water is fetched from greater depth, but the regression did not confirm significant losses due to groundwater depth increases.

CCC calculation: Temporal and spatial variation
We use data for 34 years (from 1979/80 to 2012/13) and 45 locations where the Government of Bihar collected crop yield and irrigation data. The CCC in each of the 1,530 points (34×45) is the sum of costs due to deficient rainfall, excessive rainfall and maximum temperature minus the positive impacts of atmospheric CO 2 . The total CCC and each of its components and the CCC index payouts are shown in Table 4. The CCC index payouts are determined for each location as the positive deviation from the temporal average of the CCC values and thus the index insures against one or several of the following weather-related adverse events on crops: high maximum temperatures, higher than average irrigation costs due to insufficient rainfall (during the season and before the season) and/or due to higher evapotranspiration (e.g. because of higher temperature), and excess rainfall costs. Table 4 informs firstly the relative contribution of the various components of the CCC towards its results. The irrigation costs comprise 91.8 per cent of the total costs for rabi wheat in Bihar, which is understandable, as rainfall is minimal during that season and wheat requires well-defined quantities of water. The second highest contribution to CCC comes from excessive heat (contribution of only 1.8 per cent to the overall CCC), but its standard deviation is comparatively high (17.9 PPP$/ha vs 35.0 PPP$/ha for total CCC); this parameter leads to losses in 7 of the 34 years analysed, with a significant impact in 2005 (96.2 PPP$/ha) and in 2008 (48.1 PPP$/ha). The impact of excess rainfall is negligible. And, the CO 2 fertilisation effect increased from −31.3 to 0 PPP$/ha in the study area, as CO 2 concentration increased by 57.04 ppm from 1979 to 2012. The large contribution of irrigation costs to the CCC does not imply that the CCC index payouts are dominated by the variations in irrigation costs. Consider that the correlation of CCC index payouts with irrigation costs is 70.2 per cent, while it is 89.2 per cent with high temperature losses.
The CCC would display an increasing and statistically significant trend over the period, which, however, disappears due to the effect of increasing CO 2 . This is shown in Figure 2. Figure 2 also illustrates the temporal variations. We divided the period of 34 years into two equal phases (1979/80 to 1995/96 and 1996/97 to 2012/13). Although the mean CCC value for all 45 locations was essentially similar in the two phases (265.3 vs 269.8 PPP$/ha), the standard deviation (which is a measure for the farmers' risk) increased from 19.3 to 47.1 PPP$/ha (two-tailed F-test, p=0.00045) and this difference is statistically significant and material (Table 4). As we assume that non-climatic parameters remain constant during the study period, this result clearly indicates that climatic parameters (e.g. untimely rainfall, heat waves) have caused that increase in farmers' risk exposure. The increase in risk is also reflected in higher average CCC index payouts: 15.1 PPP$/ha in phase I compared with 23.7 PPP$/ha in phase II (+56.7 per cent) (Table 4). This temporal comparison makes it possible to quantify the increase in farmers' climate change-related risks (the longer the studied time period, and inclusion of the pre-climate change scenario period, should provide a more robust analysis of the impact of climate change). In this example, the climate change-related increase was 8.6 PPP$/ha, that is, 36.2 per cent of the current risk premium of 23.7 PPP$/ha. This calculation makes it possible, for the first time, to identify the share of costs that should be reduced from premiums payable by farmers if the "polluter pays" principle is applied.
In Table 4 we show the temporal variation in CCC, and in Figure 3 we show the spatial variation, for the entire time-period and the two partial phases. As can be seen, notwithstanding the slight changes in rainfall and temperatures over the 34 years across Bihar, North and South Bihar represent low and high CCC values respectively.   Higher average CCC values reflect spatial heterogeneity, but do not per se result in higher CCC index payouts.
We examine in detail the specific influence on the spatial CCC profile of climatic (aggregated seasonal and pre-season rainfall and average maximum temperature) and nonclimatic parameters (groundwater depth, available water capacity and infiltration rate of soil) (Figure 4). The analysis (compare Figures 3 and 4) indicates that the largest influence on the spatial CCC profile is due to groundwater depth.
When groundwater depth increases uniformly by 1 m, the CCC values increase by 13 PPP $/ha on average (see the "Methods" section for the calculation model). This result is not negligible, and justifies the argument that irrigation costs (and groundwater depth, as irrigation costs increase linearly as groundwater depth increases) should not be ignored in the design of index insurance of crops that are usually groundwater irrigated.

Performance and sensitivity analysis of the CCC index
The calculation of CCC is based on climatic and non-climatic parameters (most importantly temperature, seasonal and pre-season precipitation, groundwater depth and soil type). The CCC captures three climatic situations with negative implications on crops, namely water deficit leading to additional irrigation cost, excess water leading to drainage cost and high temperatures leading to yield loss. The CCC index indemnifies against  above-average CCC values. In this section we compare the plot-level net income losses (NIL) with the CCC index and TII payouts. We also analyse how much the incorporation of non-climatic parameters improves the performance of the CCC, and the impact of ignoring the climatic conditions leading to additional irrigation costs or high temperature losses. We will also see how much better than the TII the CCC index captures agricultural droughts. We consider the following six CCC options (in addition to the CCC index with no changes) leading to different CCC index payouts: 1. CCC with constant groundwater depth (fixed at the spatial average of 3.75 m), that is, groundwater depth is not considered as a parameter; 2. CCC with constant soil type (namely loam, the most prevalent soil type in the study area), that is, soil type is not considered as a parameter; 3. CCC with constant groundwater depth and soil type, that is, Options 1 and 2 combined; 4. CCC with constant initial soil moisture (fixed at the temporal and spatial average of 59.6 per cent), that is, year-to-year variations in aggregated pre-season rainfall are ignored; 5. CCC with no irrigation cost component, that is, additional irrigation costs due to insufficient precipitation or higher evapotranspiration are ignored; 6. CCC with no high temperature loss component, that is, yield losses due to above-average maximum temperatures are ignored, and the CCC is mainly due to additional irrigation costs. However, high temperature leading to higher evapotranspiration and hence irrigation costs is still considered.
We did not consider the CCC option that ignores costs due to excess rainfall, as these costs are negligible in the non-rainy season studied here (see also Table 4). The comparison of plot-level NIL, CCC index and TII payouts are shown in Table 5.
The CCC index (no change) performed better than any of the partial CCC options examined, in terms of correlation with NIL and the reduction of risk, estimated by comparing the standard deviation of loss and loss minus payout for the cases of uninsured and insured, respectively (correlation: 76.0 per cent; risk reduction: −34.5 per cent). The largest contribution to the correlation of the CCC index payouts with NIL is the high temperature loss component; CCC Option 5 (ignoring irrigation costs, i.e. mainly considering high temperature losses) unveils a correlation of 66.9 per cent. However, CCC Option 6 (ignoring high temperature losses, i.e. mainly considering above-average irrigation costs) yields non-negligible correlation of 51.0 per cent. Hence, the combination of high temperature losses and above-average irrigation costs is required to achieve a correlation of 76.0 per cent. Compare that with the TII with a correlation of 19.6 per cent with NIL. It is recalled that TII includes high temperature losses and excess rainfall similar to the CCC but not the risk of insufficient rainfall (in other words the impacts of agricultural droughts) and the consequential need for additional irrigation. Including a simple cover that protects against insufficient rainfall to the TII would most likely not improve the performance of the TII much; one might hypothesise that a better calibration of the strikes and notionals of the TII high temperature cover could perhaps improve the correlation with losses (maybe comparable to CCC Option 5), which would still fall short of the results we have for the unmodified CCC of 76.0 per cent.
The mean of the CCC index payouts is 22 PPP$/ha, while the mean payout under TII is 251 PPP$/ha or about 11.4 times larger than CCC index. Considering that the CCC index reduces the risk by 34.5 per cent, compared with the almost quadrupled risk effect of the TII (+300.8 per cent), the TII payout seems incongruous.
Ignoring pre-season rainfall (CCC Option 4) reduces the correlation by 2.2 percentage points from 76.0 per cent (CCC index, no change) to 73.8 per cent and the risk reduction by even 9.4 percentage points from −34.5 to −25.1 per cent. This indicates that including the aggregated pre-season rainfall in the agricultural drought modelling is justified.
CCC Option 3 (with non-climatic parameters constant) reduced the correlation with NIL by 1.4 percentage points to 74.6 per cent and the risk reduction by 3.0 percentage points to −31.5 per cent, which shows that including non-climatic parameters improves the correlation in a modest way for the winter wheat.

Discussion
We set out to prove that the inclusion of certain climatic and non-climatic parameters in the design of index insurance can deliver a better estimate of farmers' risks, lead to a better correlation between losses and payouts, and quantify the added cost to farmers of the impact of climate change. We demonstrated the results by reference to winter wheat in Bihar, India by comparing a new method (which we call "Climate Cost of Cultivation" or CCC) to the TII in use in India, and to alternative options of CCC with fewer parameters.
The CCC index provides a more robust modelling of farmers' risk exposure compared with TII notably because the CCC refines the estimate of agricultural droughts in the nonrainy season by considering the residual impact of precipitation in the preceding (rainy) season on soil moisture and conducting a detailed daily soil moisture modelling (which incorporates daily seasonal rainfall, temperature data and non-climatic parameters). This calibration of the index to soil moisture variations rather than to the observation of a single climatic parameter during the season is novel. It registers a better understanding of farmers' risk of agricultural drought even in regions that are otherwise rich with groundwater, like Bihar. The advantage of such a region is that irrigation is possible and practiced, and, as irrigation compensates for drought conditions, there is every justification to include irrigation costs in the CCC, considering that the purpose of index insurance is to compensate farmers for the adverse impact of unstable or changing patterns of climate on crop yields. Including irrigation costs is another important innovation of the CCC model.
The basic thought underlying the CCC model is that index insurance should include, additional to climatic parameters, other parameters that influence the economic results of farming. The parameters with which we demonstrated the usefulness of the model for a specific crop (wheat), season (rabi) and location (Bihar) were chosen in order to model the daily soil moisture at root level, which is the major indicator both for plant growth and for additional irrigation costs (and for which many of the climatic parameters are essentially proxy indicators). Obtaining meaningful results on soil moisture necessitates the inclusion of soil properties (e.g. available water capacity-portion of water that can be absorbed by plant roots-and infiltration rate) and groundwater depth, in areas relying on groundwater irrigation for plant growth. TII does not incorporate non-climatic parameters and does not allow to compensate for additional irrigation costs in the non-rainy season. During low rainfall periods, farmers replenish low soil moisture levels through irrigation to reduce or avoid crop yield reduction. In Bihar, as in other parts of the world where groundwater can be pumped for irrigation, the cost of each water unit pumped is directly linked to the depth from which the water is fetched, and the cost of the energy required (in Bihar this is mainly diesel, to operate tube wells). Therefore, we included in the CCC method both groundwater depth and the estimated cost of diesel, in addition to soil properties.
We show that an increase in groundwater depth increases not only the cost of cultivation, but also farmers' risks. Including the cost of irrigation in the CCC index makes it possible to compensate farmers for that financial loss.
In Bihar, groundwater levels are shallow and do not fluctuate much spatially, which explains the modest contribution of this parameter to the CCC performance and why groundwater depth did not exhibit a statistically significant impact on net income losses (Table 3). Nonetheless, inclusion of groundwater depth and soil type improved the performance of the CCC compared with options which ignored these parameters partially The Geneva Papers on Risk and Insurance-Issues and Practice (Table 5). And, it stands to reason that the impact of groundwater depth on improving the CCC will be bigger in regions where groundwater depth varies spatially more than in Bihar.
Table 5 also reveals that neglecting additional irrigation costs (CCC Option 5) or high temperatures (CCC Option 6) reduces the performance of the CCC more significantly.
We conclude that the first important insight arising from the findings is that both climatic and non-climatic parameters have to be included in index design to model farming risks more accurately.
The second essential insight is that the CCC informs the assessment of the risk to farmers due to climatic changes over time, and by how much. The increase in average CCC index payout, and hence in the pure risk premium, has been material for winter wheat in Bihar (+56.7 per cent during 1996/97 to 2012/13 compared with 1979/80 to 1995/96; see Table 4). However, as already mentioned, the robust analysis of the impact of climate change should be based on longer time periods and should comprise a pre-climate change scenario. Respecting this caveat, climate change has already increased the cost of index insurance and this increase might be ongoing, which in turn could lower the likelihood that smallholder farmers in developing countries would buy index insurance. The first counter-measure would be to remove the share of the premium that reflects climate change trends (and the justification why farmers, whose carbon signature is negligible, should not be required to pay the climate change-related surcharge is known and self-explanatory). We have shown how the principle of "polluter-payer" can be applied. Applying this principle would reduce the cost of the premium significantly and enhance the likelihood that farmers would buy index insurance that compensates their risks. Considering that the incremental climate change-related addition to the pure risk premium is specific to each location, crop and season, our CCC method offers an actionable method to contextualise the quantification of this cost component, so that its subtraction from premiums could be applied in practice.
The third important insight is that the CCC index offers a much better correlation between farmers' net losses and payouts than TII (76.0 vs 19.6 per cent). Applying an index that offers a much-improved correlation between losses and payouts leads to a significant reduction in farmers' risks, measured as the standard deviation of CCC-adjusted net farm income losses. Not only would that translate into lower premiums, which in the analysed context was lower by 91 per cent compared with TII, but the lower premiums would suffice to sustain the index insurance as a business, since the payouts would be lower in years of little or no loss. The CCC thus points a way to reduce farmers' basis risk drastically (i.e. the risk of mismatch between incurred losses and index-triggered payouts) as well as the cost of crop insurance.
Lastly, we submit that risk exposure cannot be treated as "one size fits all", even if this is the prevailing practice now. Within the new CCC method, we incorporated spatial heterogeneities because of varying groundwater depth, soil type and microclimate. We suggest that arable areas that represent systemically higher risk should command a higher premium, just as lower risk areas should command lower premiums. Spatial heterogeneities would feed into the insurance design, to apply justified differential premiums and payouts. For example, farmers could choose an insurance package where groundwater depth and soil type are one of the parameters customised to their conditions. Although the CCC method seems to be data intensive, all the data are available for all of India and most of the data are freely accessible to a global extent; regional information (like soil type, groundwater depth, rainfall and temperature) is available in most countries Nihar Jangle et al. Climate Cost of Cultivation: A New Crop Index through local authorities. In our study area, we assumed that groundwater depth was constant over the last decades, as data did not suggest otherwise. However, if groundwater levels vary, the CCC method can easily be adjusted to accommodate this calibration of the index. For other regions of investigation, the irrigation cost module in the CCC method would have to be adapted to the different irrigation sources and facilities used: for instance, in regions which are entirely rain-fed, water stress would not lead to additional input costs due to irrigation, but would affect yield losses (which can be incorporated into the CCC). In the analysis of CCC for wheat in Bihar, we identified that crop losses were associated with extended periods of high maximum temperatures. Similarly, for other crops, other parameters might be more relevant, for example, high/low minimum temperature, high wind speeds etc.
The discussion leads to the conclusion that CCC can be applied to other crops, seasons and locations once the necessary calibration is done; and the method explained in this article shows the way how to do this. Some crops might require the elaboration of other permutations of CCC that include other or additional relevant parameters, both climatic and non-climatic parameters.
The CCC method is subject to some limitations. For one, certain weather-related risks are not purely local, for example, floods are sometimes caused by weather conditions upstream (and would not be easily covered through local weather data); pests and diseases may be associated with certain weather conditions but are not necessarily caused by them. Agriculture extension services/advisories could reduce certain risks which cannot easily be covered in an index. Losses against excess rainfall could be better accounted for with the inclusion of a drainage index based on certain non-climatic parameters, including topography (risk to water-logging), land use and soil type. We were unable to use a drainage index in the study of Bihar as the data were unavailable. Elevation modelling at low vertical gaps is one of the missing pieces of data and therefore a better reflection of the consequences of excess rainfall-induced risks is for the time being imperfect.

Conclusions
The CCC method offers a novel way to quantify farmers' economic risks that can be insured.
We have referred to all the main drivers of climate change parameters impacting the productivity of agricultural crops as identified by the World Bank, 66 namely changes in precipitation, temperature, CO 2 fertilisation (CO 2 -induced crop yield gain), climate variability and surface water runoff. We have shown that the nonlinear, multi-parameter CCC index, which incorporates both climatic and non-climatic parameters, reflects the financial risks of farmers more accurately than TII. The CCC index has a higher correlation to farm income losses, better risk reduction properties and much lower pure risk premiums than TII. The CCC index also provides a method to calculate the percentage of the pure risk premium which can be attributed to climate change, thus providing the needed tool to deal with this issue at a policy level, rather than continuing the unfair practice of charging it to farmers. The CCC thus contains several novelties: one that provides better modelling of agricultural droughts (influenced in post-rainy season notably by rain in the previous rainy season) and a 66 World Bank (2007).
The Geneva Papers on Risk and Insurance-Issues and Practice 300 new design of an index that is easily contextualised to crop-season-location specificities, both climatic and non-climatic ones. Researchers, practitioners and policymakers can apply this CCC method for a wide range of uses, be it the application of policy measures to apply the "polluter pays" principle, or reducing farmers' basis risk, or making crop index insurance more attractive for farmers.