Insuring crops from space: the potential of satellite-retrieved soil moisture to reduce farmers’ drought risk exposure

Crop producers face significant and increasing drought risks. We evaluate whether insurances based on globally and freely available satellite-retrieved soil moisture data can reduce farms’ financial drought risk exposure. We design farm individual soil moisture index insurances for wheat, maize and rapeseed production using a case study for Eastern Germany. We find that the satellite-retrieved soil moisture index insurances significantly decrease risk exposure for these crops compared to the situation where production is not insured. The satellite-retrieved index also outperforms one based on soil moisture estimates derived from meteorological measurements at ground stations. Important implications for insurers and policy makers are that they could and should develop better suited insurances. Available satellite-retrieved data can be used to increase farmers’ resilience in a changing climate.


Introduction
Droughts put agricultural production and thus farmers' incomes at risk. Systemic drought events are expected to become more frequent and severe in Central Europe due to climate change (e.g. Grillakis, 2019;Kahiluoto et al., 2019;Seneviratne et al., 2010Seneviratne et al., , 2012Trnka et al., 2014). This is leading to an increasing demand for advanced agricultural drought risk management, also through insurance schemes (e.g. Bjerge and Trifkovic, 2018;Finger and El Benni, 2020;Meuwissen, Mey and van Asseldonk, 2018). Index insurances are viable solutions to insure agricultural production, especially for drought risks which can hit an entire region simultaneously and for which there are hardly any insurances in place.
In this paper, we investigate the potential of index insurances based on globally and freely available satellite-retrieved soil moisture data to cope with drought risks. Additionally, we compare index insurances based on satelliteretrieved information with insurance based on spatially interpolated, gridded soil moisture estimates derived from meteorological measurements at ground stations. We quantify the reduction of farmers' financial drought risk exposure in a case study on winter wheat, rapeseed and maize in Eastern Germany.
Systemic droughts affect regions, countries or even larger areas over a long period (Grillakis, 2019) and are a major risk to farmers' income security. With associated yield losses occurring simultaneously, a large amount of loss adjustment-related administration has to be done within a limited assessment window.
The human and economic resources to conduct physical inspections at every farm in a drought-affected region are not available. Therefore, reducing damage assessment time is particularly interesting for systemic risks. Index insurances are cost efficient, reduce the problem of asymmetric information, allow efficient and fast determination of payouts (Barnett and Mahul, 2007) and are thus rapidly being developed in both developing and developed countries (e.g. Jensen, Barrett and Mude, 2015;Leblois and Quirion, 2013;Vroege, Dalhaus and Finger, 2019). We expect that indices based on soil moisture estimates perform well in an insurance setting (Kellner and Musshoff, 2011) because moisture represents the site-specific water deficits resulting from prevalent meteorological conditions, topography and soil properties as well as the crops' physiology (Seneviratne et al., 2010;West, Quinn and Horswell, 2019). Measuring soil moisture in situ is however difficult and expensive, and spatial coverage is scarce . Weather-station measurements alone might be an insufficient proxy for soil moisture distant to these stations. Consequently, research interest in the retrieval of soil moisture information by satellites is large (e.g. Albergel et al., 2013;Brocca et al., 2017;de Jeu and Dorigo, 2016;Dorigo and de Jeu, 2016;Dorigo et al., 2017;Hirschi et al., 2014;Martínez-Fernández et al., 2016;Nicolai-Shaw, 2016;Peng and Loew, 2017;Sönegard, 2017). The potential of satellite-retrieved soil moisture measurements in the index design has to our knowledge only been explored without assessing the financial risk-reducing capacity of such insurance schemes at the farm level (Enenkel et al., 2018). Moreover, research and practice on the use of satellite-retrieved data in drought index insurances also considered sensing of the health status of the plant, precipitation and evapotranspiration (see for example Black et al. (2016), , Enenkel et al. (2018), Jensen et al. (2019), de Leeuw et al. (2014, Roumiguié et al. (2017), Vrieling et al. (2014) and Vroege, Dalhaus and Finger (2019)).
We extend this literature by quantifying the economic benefits of satelliteretrieved soil moisture measurements in an index insurance scheme for single farms. More specifically, we assess whether a satellite-based index insurance (based on the European Space Agency Climate Change Initiative (ESA CCI) satellite soil moisture product) reduces farmers' financial risk exposure (i.e. farmers risk premium) compared to (i) a situation without insurance and (ii) to an index insurance based on gridded soil moisture estimates derived from meteorological measurements at ground stations (taken from the German Meteorological Service, DWD). We also compare the two insurance options in terms of data availability and quality, spatial resolution and the recognition of individual farming practices (e.g. irrigation). We base our analysis on a case study with unique data from 89 large-scale farms from 1995 to 2015 which produce winter wheat, rapeseed and silage maize in Eastern Germany. This important grain production region is highly susceptible to droughts (Trnka et al., 2014).
We find that both satellite-based and the gridded meteorological stationbased soil moisture index insurances can significantly decrease the risk exposure of crop producers. We provide insights to opportunities and challenges of using satellite-retrieved and meteorological station-based soil moisture information. We highlight that the performance of an insurance depends on the location of the farm, the insured crop and the insurance design. Our results allow insurers to develop more efficient drought insurances and thus contribute to a better drought risk management in agriculture.
The remainder of this paper is organized as follows. First, we provide a conceptual framework to condition index insurance payouts to a single farms' risk exposure based on quantile regression and we elaborate on the context of soil moisture as an index variable. Based on this, we develop a testing strategy for the risk-reducing capacity of weather index insurances. After presenting the datasets, we present the results, including the attained risk premium reduction. Finally, we discuss crucial dataset characteristics and draw conclusions for policy makers, insurance practitioners and future research.

Conceptual framework
In index insurance designs, an insurance pays out solely based on an independent index containing one or multiple parameters. This index should correlate with crop yield losses. For an index insurance to be successful, it is important that the index is comprehensive, cannot be influenced by either the insurer or the insured and that data continuity is guaranteed both historically and in the future (Cole et al., 2013;Vrieling et al., 2014). A general advantage of index insurances is that there are no information asymmetries, which means that both the insurance and the crop grower have the same information about the index data. Hence, problems of moral hazard (a shift to riskier practices) and adverse selection (risk exposed farms buying insurances more often) of traditional insurances can be overcome with index insurances Downloaded from https://academic.oup.com/erae/article/48/2/266/6132278 by Wageningen University en Research -Library user on 15 March 2021 Insuring crops from space 269 (Turvey, 2001;Vedenov and Barnett, 2004). Moreover, weather index insurances can be fully tailored to farm or even field-individual yield and historical weather records. Index insurances' key drawback is that measurements independent of the yield cannot reflect yield losses perfectly. This problem is known as basis risk (Dalhaus, Musshoff and Finger, 2018;Woodard and Garcia, 2008) and can lead to damages without indemnity payments or viceversa. An often-named example of basis risk is that a rainfall event may occur at a weather station but not at a distant field, so even a dense network of weather stations might miss this kind of idiosyncratic events. This has important implications for farmers' index insurance uptake (Clarke, 2016) and for the legal basis of index insurances (Vroege, Dalhaus and Finger, 2019).
The goal of the insurances considered here is to reduce financial losses arising from droughts and thus reduce farmers' risk exposure. We focus on insuring changes in production levels while assuming constant price levels. 1 Therefore, farm i pays an annual insurance premium Pr i . If the severity of a drought in year t undercuts a pre-set threshold (strike level S i ) in terms of soil moisture, farm i receives an insurance payout PO i,t : where π i,t is the insured revenue of crop production, P is the crop price and Y i,t is the crop yield. We assume a fair premium so that the premium reflects the expected level of payouts made over time (equation (A1) in the appendix). If there is no indicated drought event, the magnitude of the payout is zero. In case of a drought, more specifically when the soil moisture is below the strike level, the magnitude of the payout is determined by the severity of the soil moisture deficiency and the monetary payout per missing index unit (the tick size): where PO i,t is the payout, S i is the individual strike level, T i the tick size and I i,t the index value (see equation (A2)-(A3)).
To evaluate insurance options and to compare the satellite-retrieved and meteorological station-based index insurances, we assess the reduction of the farm-individual risk premium (RP) in an expected utility maximization framework. This framework allows us to compare and evaluate different insurance options in terms of their ability to reduce basis risk. More specifically, the risk premium reflects the loss of utility a producer experiences through the presence of risk. The risk premium depends on the risk exposure, which where derivatives of the utility function are U q = ∂ q U/∂x q ; and moments M q of the revenue distribution are represented as follows: We test the superiority of having insurance over having no insurance 2 (as well as differences across insurance solutions) by comparing the respective risk premiums. More specifically, any improvement in the ability to reduce the financial exposure to drought risk, for example by using an insurance or substituting different data sources in the insurance design, would ceteris paribus result in a reduced risk premium. Under the assumption of fair premiums, this results in a higher expected utility for the farmer.

Soil moisture as the index variable
To represent droughts, we chose soil moisture as the index variable. Agricultural droughts are typically defined as the combined effect of shortage in precipitation and enhanced evapotranspiration (induced by enhanced radiation, wind speed, or a vapour pressure deficit), leading to a critical drop in soil moisture that negatively affects crop yields (Panu and Sharma, 2002). Soil moisture is the water content of the unsaturated part of the soil and typically expressed as m³ water per m³ of soil (volumetric soil moisture content). Depending on soil type, absolute levels and dynamic ranges of volumetric soil moisture differ between locations, even at shorter distances (Mittelbach and Seneviratne, 2012). Alternatively, soil moisture can also be defined in relation to the porosity of the soil as percentage (or degree) of saturation, indicating the fraction of pore volume that is filled with water (Seneviratne et al., 2010). This relative measure reduces the impact of static soil properties and can be derived by rescaling the volumetric soil moisture time series (Brocca et al., 2014). Soil moisture is crucial for agricultural production and is of key importance for various climate processes as it impacts the partitioning of the available energy at the earth surface into sensible and latent heat fluxes as well as the generation of runoff and groundwater recharge (Seneviratne et al., 2010). We favour soil moisture as our index variable because it integrates both effects from water in-and outflows and it allows to account for temporal autocorrelation, as it accounts for water in-and outflows from previous periods.
Measuring soil moisture on ground is difficult and costly and, accordingly, coverage with in situ soil moisture data is scarce Panu and Sharma, 2002;Seneviratne et al., 2010). As a consequence, scientific interest in the retrieval of global soil moisture estimates from satellite sensors has grown in recent years Dorigo and de Jeu, 2016). Multiple satellite sensors are available that can be used to retrieve soil moisture data globally . Soil moisture remote sensing is mostly based on micro-wave techniques which can provide information on moisture conditions in the upper few centimetres of the soil. Due to the large contrast between the dielectric properties of dry soil and water, the microwave radiance emitted or reflected by the surface soil volume is almost linearly dependent on the soil-water mixing ratio (Ulaby, Moore and Fung, 1982). Both active and passive microwave instruments can be used to retrieve soil moisture information. Active instruments emit microwave radiation themselves and measure variations in the reflected backscatter. Passive instruments measure the natural emissions from reflected (sun)light. Both options can provide observations under nearly any weather conditions and independent of daylight . Retrievals are however impossible under snow and ice or when the soil is frozen, and complex topography, surface water, and urban structures have negative impacts on the retrieval quality. In addition, dense vegetation attenuates the microwave emission and backscatter from the soil surface and may mask the soil moisture signal. Altogether, these limitations may result in spatio-temporal data gaps of remote-sensing based soil moisture estimates.
In addition, global and regional soil moisture estimates can be derived by means of modelling (e.g. with a land surface or agrometeorological model (AMBAV)) using observed meteorological variables as input (e.g. Seneviratne et al., 2010). The meteorological forcing therefore can be either based on gridded measurements from meteorological stations (e.g. Balsamo et al., 2015;Orth and Seneviratne, 2015) or directly based on meteorological measurements at the stations with a subsequent gridding of the calculated soil moisture data (e.g. Deutscher Wetterdienst, 2018, further described in Section 4.3 DWD station-based soil moisture product). In both cases, the resulting soil moisture estimates are dependent on the quality of the applied physical model as well as the quality of the meteorological input data and gridding procedures.
Droughts affect crops differently. This can be due to differences in physiology, their root architecture (Walter, Silk and Schurr, 2009), and due to temporal differences of their phenological phases (Estrella, Sparks and Menzel, 2007) across crops. For insurance purposes, it is meaningful to focus on drought occurrence during crops' generative (and vegetative) phase, in which crops are most vulnerable to drought (Dalhaus, Musshoff and Finger, 2018). A drought during the generative phase leads for example to a reduced number of grains (wheat), reduced filling of the pods (rapeseed) or concurrence during the female and male reproductive organs (silage maize). Droughts during the vegetative phase of crops lead to less developed rooting systems and reduced leaf areas, numbers and lifetime. However, when still in the vegetative phase, crops can recover relatively well when water is again available and yield reductions are often lower (e.g. Daryanto, Wang and Jacinthe, 2017;Farooq, Hussain and Siddique, 2014;Hlavinka et al., 2009;Qaderi, Kurepin and Reid, 2006).

Empirical implementation
We compare the risk-reducing capacity of index insurances based on different index specifications to each other and to scenarios without insurance. Following Dalhaus, Musshoff and Finger (2018), we focus on the critical phenological phases of each crop and restrict the index measurement to this time frame. The indices are the median 3 of farm-individual satellite-retrieved soil moisture estimates (I sat ) and the median of the meteorological station-based soil moisture estimates (I station ) at the farm-level within different critical phenological phases. More specifically, we use two definitions of the critical phenological phase per crop to avoid biased inference due to potential imprecisions in the phenology reporting. We use a 'short phase', which includes the crop's generative phase. Moreover, we consider an extended phase, which additionally includes a preceding (wheat and maize) or a subsequent (rapeseed) phase. In total, we test 12 different insurances based on two methods, in two phenological phases for three crops and six scenarios without insurance (two phenological phases for three crops).
We detrend the yield data to account for technological progress. More specifically, we use Germany-wide yield data provided by the German statistical office Destatis (Statistisches Bundesamt (Destatis), 2019) to find a common linear time trend for all farms using the robust, i.e. outlier resistant, M-estimator following Finger (2013). 4 We first estimate the impact of the respective index variable I on farmspecific yields 5 using quantile regression. Then, we use these estimates to design the insurance contract parameters, i.e. strike levels and tick sizes, and simulate historical insurance payouts and derive respective insurance premiums. From this, we obtain simulated revenue observations per farm, per crop, per year and per index specification. Eventually, we test for differences in the risk premiums between these different scenarios.
To find individual impacts of soil moisture deficits on yield losses, we use a regression framework to estimate equation (5): 3 We use the median soil moisture of all estimates within the insured timeframe to get a more robust estimate (compared to the mean) of the soil moisture average. 4 To transform yields into monetary units, we use the following crop prices: 15.1 €/dt for wheat, 35.9 €/dt for maize and 41 €/dt for rapeseed (Kuratorium für Technik und Bauwesen in der Landwirtschaft, 2019). 5 To address potential overfitting issues, we also use other approaches: one in which we use pooled yields of all other farms but exclude the farm's own yields and one in which we use farm-specific yields but exclude the year in which we specify insurance payouts. See also the discussion section as well as Tables A15 and A16. where Y i,t reflects the individual yield at farm i in year t, β 0 i,v and β 1 i,v farm individual regression coefficients (intercept and slope) for each index specification v (i.e. soil moisture from satellite observations or derived from meteorological measurements at ground stations), I i,t,v is the soil moisture index value at farm i in year t for the index specification v and the error term ε i,t,v reflects the farm, year and index-specific basis risk, i.e. the potential mismatch between the index value I i,t,v and the crop yield Y i,t (e.g. Woodard and Garcia, 2008). With this farm-specific regression framework, we assess the relationship between soil moisture and lower yields for each farm individually. These farm-fixed effects allow for control of farm-specific, time-invariant factors such as soil types. 6 Because we are particularly interested in the impact β 1i,v of I i,t,v for low levels of yield Y i,t , we follow Conradt, Finger and Bokusheva (2015) and use quantile regressions (equation (6)) to find the regression coefficients β 0i,v and β 1i,v , which we use to set individual strike levels S i,v and tick sizes T i,v . Quantile regression allows us to focus on the impact of the weather index I i,t,v in the lowest 30 per cent (τ = 0.3) of yield observations. More specifically, quantile regression minimizes the absolute distance sum between fitted values x T i,t,v * β 1 i,v and observed values Y i,t while weighting downside yield events by (1 − τ ) and upward residuals by Quantile regression is therefore more robust against outliers compared to Ordinary Least Squares (OLS) regression and allows us to condition the insurance to downside yield events.
We design insurance contracts when the impact β 1 i,v of the index variable I i,t,v on the yield Y i,t is positive following quantile regression. In other words, when we find a positive relation between the index and yields, while focussing on the lower tail of the yield distribution, we assume that farms voluntarily buy the index insurance contract in all years for which we know their yields. 7 Based on the positive quantile regression estimates, we simulate payouts PO i,t,v of farm i in year t and for index specification v. As in Dalhaus, Musshoff and Finger (2018), we expand the individual payout distributions 6 If farm-level data are not available and regional-level yields are used to design the insurance, the inclusion of additional information such as information on soil types has been shown to improve the insurance design (Du et al., 2017;Woodard and Verteramo-Chiu, 2017). 7 Note that when this relationship is negative, drought is not a major weather risk for the farm (quantile regression suggests that drier conditions imply higher yields). It is thus not possible to design a drought index insurance with fair premiums.
using a bootstrapping procedure with 1000 draws and take the average of these as farm individual premium Pr i,v and derive insured revenues R i,t,v according to equation (1). Note that for the scenarios without insurance (v = uninsured production), the insurance payouts and premiums in equation (1) are zero, i.e. the revenues of farm i are uninsured and thus solely depend on yields and prices.
To compare the satellite-retrieved and meteorological station-based index insurances and compare them to scenario's where farmers do not have insurance, we assess the reduction of the farm-individual risk premium RP i,v in an expected utility framework. We follow Di Falco and Chavas (2006) and define the risk premium RP i,v (see equation (3)-(5)) of farm i for each index specification v with respect to moments σ 2 π i,v (variance) and σ 3 π i,v (skewness) 8 (equation (A4)-(A5)) of the revenue distribution as follows: where −U ′′ /U ′ represents the Arrow-Pratt coefficient of risk aversion and −U ′′′ /U ′ reflects the aversion against downside risks (e.g. Chavas, 2004). We follow Leblois et al. (2014) and base the analysis on the power utility function: To test for differences in a farm's risk exposure across insurance options, we compare different vectors of individual risk premiums RP v with paired difference tests, i.e. the Wilcoxon−signed-rank test comparing the relative rank (Dalhaus, Musshoff and Finger, 2018). Because farmers' level of risk aversion α is highly diverse (Iyer et al., 2020), we compare the risk-reducing capacities of insurances for different levels of risk aversion α ∈ [0.5, 2, 3,4]. The chosen levels of risk aversion reflect recently elicited risk preferences of German farmers (see Iyer et al., 2020 for an overview).

Yield and phenology data
We use unique crop yield data from 1995 to 2015 on 89 farms in Eastern Germany ( Figure A1 and Table A1), collected by a local agricultural insurance agency. These data are from large-scale farms (i.e. farms representative for Eastern Germany, where farms are on average about 400 ha (Bokusheva and Kimura, 2016;Hartvigsen, 2014;Huettel et al., 2013)) and yield records 8 Higher moments of the revenue distribution such as Kurtosis and decision maker's preference with respect to these higher moments may also influence farmers' decisions. Yet, previous research has shown little relevance of these higher moments in empirical research (e.g. Chavas, 2004;Groom et al., 2008). Indeed, including kurtosis (and higher moments) in our analysis did not change our results. Until 2015, there were no drought insurance options available to farmers in this region. Recently, a German insurance company (Vereinigte Hagel) started offering a double trigger drought index insurance. This insurance pays out when both regional soil moisture estimates from the German meteorological service (DWD) and regional yield levels are below a certain threshold (Vereingte Hagel, 2019). Also the payout size is determined based on the regional level yield losses. Due to the double trigger and because also the size of the payout is determined based on the regional yield level, this product suffers from a considerable amount of basis risk. Also, governmental ad hoc disaster aid payments are still paid to the most drought affected farms, for example in 2018 (Bundesministerium für Ernährung und Landwirtschaft, 2018), setting incentives for more risky production practices. As a result, there is currently still a low drought insurance uptake.
To define the insurance period, we follow Dalhaus and Finger (2016) and Dalhaus, Musshoff and Finger (2018) and chose the insurance start and end date based on phenology observations. We extend the approach of Dalhaus, Musshoff and Finger (2018) by using site-and crop-specific phenology estimations of plant growth stages taken from the phase model (Gerstmann et al., 2016). This interpolation model is developed specifically to interpolate a German phenology point database that is provided by the German Weather Service and based on real phenology reports of voluntary observers from over 1200 active stations (Deutscher Wetterdienst, 2019a;Gerstmann et al., 2016). The model uses daily mean temperatures as well as a free elevation data product to interpolate the phenological observations (Gerstmann et al., 2016) to 1 km × 1 km gridded phenology estimates for crops in Germany. This model thus provides Germany-wide gridded data on 'day of the year' (DOY) of the start of crop-specific growth phases. In the case of wheat, the generative phase (here: 'short' phase) lasts from heading until milk ripeness and the extended time frame starts with the earlier stem elongation (see Table 1). The generative phase of rapeseed goes from bud formation until flowering and as extension, we used a timeframe lasting until full ripeness of the rapeseed. For maize, we use the generative phase going from the visibility of the tip of the tassel until flowering. We also consider an 'extended' phase in which the insured timeframe already starts with the vegetative growth in height. See Table 1 for an overview and Figures A2-A4 for more details. The definition of the phases is based on the manual on the phenology data (Deutscher Wetterdienst, 2014).

ESA CCI satellite-retrieved soil moisture product
The ESA CCI data (version 04.4) offer a global harmonized surface soil moisture product based on satellite-retrieved information covering more than 40 years Gruber et al., 2017). Three products are available: one from active and one from passive microwave sensors, as well as a product based on a combination of both data sources based on their error characteristics (Liu et al., 2012(Liu et al., , 2011 Soil moisture content is given in unit of m³m −3 for the passive and combined (active and passive) product and in degree [per cent] of saturation for the active product. We use version v04.4 of the combined product, which has increased coverage due to the optimal combination of both retrieval techniques. In the production process, the ESA CCI soil moisture product is validated with in situ measurements from the International Soil Moisture Network . The ESA CCI product provides information on moisture conditions in the upper few centimetres of the soil. This layer is highly correlated with soil moisture of deeper soil layers, except under very dry conditions when the surface layer may dry out completely and thus exhibit a reduction in temporal variation (Hirschi et al., 2014). For our study region however, such behaviour is less relevant as complete dryness is not encountered.
We rescale the volumetric soil moisture content (in m³m −3 ) to percentage (or degree) of saturation following Brocca et al. (2014) to correct the soil moisture index for spatially varying soil porosities. The rescaling is done relative to the observed minimum and maximum soil moisture values within the analysed 1995 to 2015 time period (Table 2, Table A2 and Figure A5).
The spatio-temporal coverage of the ESA CCI product increases over time due to the increasing number of available satellites, reaching 80 per cent to full temporal coverage for recent years in most parts of the case study region . Nevertheless, full coverage cannot be achieved for specific grid cells and due to the limitations outlined in Section 2.2.

DWD station-based soil moisture product
We compare the index insurance based on satellite-retrieved soil moisture to a gridded meteorological station-based soil moisture product  (Löpmeier, 1994) using meteorological measurements as inputs. The soil moisture unit is in percentage of plant available water capacity assuming a wilting point of 13 volume per cent and a field capacity of 37 volume per cent. Subsequently, the DWD interpolates the calculated soil moisture values into a publicly available gridded dataset with a spatial resolution of 1 km × 1 km by using regionalised multiple linear regression and triangulation with respect to orographic parameters ( Table 2, Table A3 and Figure A6) (Deutscher Wetterdienst, 2018). The interpolation does not adjust the soil moisture values to soil and vegetation type and thus uncertainties arise from model design, parameterization and interpolation (Gerstmann et al., 2016). Publication of the latest data is done at the end of the penultimate month, which allows an indemnification in near time. Summary statistics of the yield, index values and phenology observations are provided in Table 3.

Results and discussion
By assessing the individual risk premium change for all farms, we find that both the satellite-based and the meteorological station-based soil moisture index insurance products significantly decrease farmers' risk exposure. More specifically, they reduce the sample average risk premium of crop production for each crop and timeframe (Table 4). Regarding the meteorological stationbased insurances, these findings are in line with previous findings of Kellner and Musshoff (2011). We find some differences in the performance of the two insurance options for different crops and timeframes, but there is no clear best insurance option regarding the soil moisture estimation method. The satellite product significantly outperforms the meteorological station-based product in the extended insured time frame of maize and the meteorological stationbased product performs better in the shorter insured time frame of rapeseed H0: The sample mean of the risk premium in the tested scenario (in rows) is larger or equal than in the comparison scenario (in columns).
and maize (see also Table A4). The duration of the short phase of rapeseed (16 days) and maize (7 days) is short compared to the short phase of wheat (on average 30 days). A reason for this could be that the satellite-retrieved data appears to have larger gaps in the first years of our sample . Therefore, the satellite-retrieved soil moisture averages in shorter timeframes that are only based on a small number of observations, which might be a reason for the better performance of the meteorological station-estimated soil moisture insurances with the shorter insurance timeframes. This effect might be amplified because the temporal auto-correlation of the satellite-retrieved soil moisture appears lower than the one of the meteorological station-based data, likely due to the applied normalization step in the production of latter (see Figure A7). We identify that a drought risk can be identified at between 63 per cent (extended phase, meteorological station-based insurance for rapeseed) and 86 per cent (short phase, meteorological station-based insurance for maize) of the farms in our sample (Table A5). For two of the farms we were not able to retrieve reliable satellite-derived soil moisture information (and thus not able to create a satellite-retrieved index insurance) due to their location close to the Baltic Sea. To avoid potential bias in our results, we did not design any insurance contract for these two farms. By assuming fair insurance premiums, overall revenues are equal for the uninsured and the insured scenarios. The index insurance premium costs, depending on the index, on average around 2-4 per cent of the average revenues (Table A6). Note that we assess the risk premium change for all farms, i.e. including both those with and without insurance (so the change is zero for the latter). For detailed results, see Table A4-A11. Moreover, we here also use a quantile approach to select the strike level (see equation (A3)). Earlier research mostly used yield averages to define the strike level of the insurance (e.g. Conradt, Finger and Bokusheva, 2015;Dalhaus and Finger, 2016) and Table A12 shows that we find larger differences between the insurance designs with that approach. Furthermore, when we select the insured time frame for each crop based on the largest individual risk reduction potential, we achieve a larger on average risk reduction (Table A13). Additionally, we have also used a split sample with observations only from 2005 onwards to assess the influence of missing satellite data in earlier years. We find that including less observations in general decreases the performance of the insurances, which highlights the importance of long historical records, even when data gaps appear (Table A14).
Important advantages of both soil moisture data sets in the design of index insurances are the length of the consistent data record, which are needed to design meaningful insurances . This, as well as the consistency and the short data latency (10 days for version 3.03), makes the ESA CCI a unique satellite-based soil moisture product. Compared to the DWD soil moisture data, an important advantage of the satellite-retrieved data set is the data validation process. Moreover, its global data availability can reduce transaction costs for multinational insurance companies because the information is not restricted to national borders, as is the case for data from national weather services. Another important advantage of the satellite-retrieved data is that the retrieved soil moisture value is informative for the area of the sampled pixel. More specifically, while the nominal spatial resolution of the meteorological station-based data is much higher, it relies on a spatial interpolation of a limited number of stations. Therefore, soil moisture anomalies in between the weather stations could be missed or averaged out. In contrast, the satellite measured soil moisture is representative for the pixel area, resulting in spatially more distinct and localized information (Figures A2 and A3). Furthermore, soil type and vegetation affect absolute soil moisture availability. The consideration of relative soil moisture estimates (i.e. per cent of plant water capacity and per cent of saturation) reduces the impact of spatially varying soil properties and vegetation type (Mittelbach and Seneviratne, 2012). The meteorological station-based approach directly provides relative soil moisture estimates based on an AMBAV. These, however, are only estimated for sandy loam soils covered with grasslands. Therefore, these soil moisture estimates might not well reflect droughts where soil types and vegetation are different. In contrast, the satellite information initially provided as absolute values is rescaled to relative soil moisture estimates based on the pixel-specific minima and maxima, which corrects for the impact of location-specific soil and vegetation characteristics (Brocca et al., 2014).
Generally, the systemic nature of drought risk reduces the importance of data with high spatial resolution, which might be another reason why the low-resolution satellite product works comparably well. This fits to our case study region, as Eastern Germany is characterized by large farms (on average about 400 ha) (Bokusheva and Kimura, 2016;Hartvigsen, 2014;Huettel et al., 2013). Here, idiosyncratic risks often affect only a small share of the overall production, which can be either averaged out or managed by savings. Largescale systemic risks, however, can threaten the complete farming system of the region. This makes the availability of insurance against systemic risks particularly important in this area. Thus, the approach we take here is particularly viable for farming systems with large-scale farms. However, the newer Sentinel satellites have since 2015 been collecting data at much higher resolutions. A soil moisture product with a resolution of 1 km × 1 km is already freely available for Europe (Bauer-Marschallinger et al., 2019). Thus, opportunities to use similar approaches also for smaller scale farming are emerging. Future research could evaluate an insurance scheme, where the historical record is specified based on the ESA CCI (and possibly also on the newer data product), while the payout could be determined with the newer product (Setiyono et al., 2018;Vroege, Dalhaus and Finger, 2019). Yet, at this moment, the quality of the ESA CCI product is better validated.
Satellite information from the drought summer of 2003 misses systematically in some areas, particularly in the Northern area of our case study region (close to the Baltic Sea). This is due to spatial gaps in the retrieval from the passive sensor (mostly due to vegetation cover) used as replacement for the temporary failure of the active sensor in this specific time period . Because it is crucial in insurance practice to have a continuous information flow, the possibility of sensor failure might be perceived a disadvantage for satellite-based insurances (while the probability for an extensive failure of the meteorological station measurements is likely lower). Yet, this problem has been reduced substantially in recent years, strengthening the reliability of satellite-retrieved soil moisture index insurance. Moreover, this problem can be greatly reduced by relying on data from multiple active and passive sensors, as is nowadays the case for the ESA CCI product .
Moreover, an important difference between the two products is that farming practices like irrigation and tillage and its effects on soil moisture is not observed with the meteorological station-based soil moisture estimation (Ding, Schoengold and Tadesse, 2009), since it is calculated from meteorological observations. In contrast, satellite measurements are able to capture these effects, most importantly reflect the signal of large-scale irrigation (Qiu et al., 2016). Yet, this is not an important constraint of our case study because irrigation is not widespread (e.g. Siebert et al., 2015). Nevertheless, this is more general an important consideration to make in the design of satellite index insurances in the future, because farmers might have an incentive to change the riskiness of the production and face problems of moral hazard. Yet, this is limited as farm practices at a single farm only have a restricted impact on the estimated soil moisture in the coarse-scale pixel of the applied low-resolution product.
By comparing the performance of satellite-retrieved and meteorological station-based soil moisture estimates, this research puts the usefulness of earth observation approaches for insurance applications into a perspective. Still, other drought indicators can be observed from space and associated global data sets are available (AghaKouchak et al., 2015;West, Quinn and Horswell, 2019). Satellite-retrieved spectral vegetation indices as well as precipitation and evapotranspiration estimates also deliver information that can well be used in index insurance designs (e.g. Black et al., 2016;Enenkel et al., 2018;Jensen et al., 2019). Nicolai-Shaw et al. (2017) show that the drought indicators (soil moisture, precipitation, evapotranspiration and vegetation activity) co-vary but that temporal delays occur. For example, missing rainfall, which is a key element of drought development, precedes soil moisture droughts in most regions and increased evapotranspiration is often followed by a response in vegetation activity West, Quinn and Horswell, 2019). Which (satellite-retrieved) drought indicator performs best to insure farmers against drought risks is an empirical question and the answer may differ for each individual farm (Bucheli, Dalhaus and Finger, 2020), for different insurance timeframe settings and for different crops. Nevertheless, soil moisture is in general more informative to agricultural droughts than precipitation or evapotranspiration anomalies alone (Seneviratne et al., 2010;West, Quinn and Horswell, 2019). Vegetation spectral reflectance indices, such as the Normalized Difference Vegetation Index, which reflect the impact of a drought on the vegetation, could relate even more directly to farmer's yield losses. Yet, management practices and other risks, such as pests and diseases as well Insuring crops from space 283 as heat and frost, have similar impacts on yields (e.g. Webber et al., 2020) and the vegetation's spectral reflection as droughts. Therefore, identifying if a drought was the cause of the yield loss may be a challenge with spectral indices (AghaKouchak et al., 2015).
In the future, further data integration could improve both investigated products. For the meteorological station-based product, integrating localized data on soil type and vegetation activity into the AMBAV could improve the product. For the satellite product, integrating sub-daily information could increase the product accuracy . Moreover, satellite microwave remote sensing may deliver drought indicators that combine soil moisture and vegetation water content assessments (AghaKouchak et al., 2015). In addition to these developments of gridded products, in-situ soil moisture sensors can deliver point-scale information on drought status. However, installation of large-scale in situ soil moisture networks is difficult and expensive, and spatial coverage of in situ soil moisture observations will barely reach the extent of the current meteorological station networks or the available satellite-based soil moisture products. Nevertheless, the expansion of in situ soil moisture networks is beneficial to validate gridded soil moisture products as used in this study and to reduce associated uncertainties.
In this study, we focus on insuring production risks in an expected utility framework. While we here compare the ability of different insurances to reduce basis risk, this might not fully explain farmers' actual insurance choice. To understand which insurance contract farmers might purchase also other factors play a role. These are captured in other decision making frameworks such as Cumulative Prospect Theory and especially state-dependent reference levels therein might be better able to explain farmers' insurance choice (Babcock, 2015;Bocquého, Jacquet and Reynaud, 2014;Du, Feng and Hennessy, 2016;Feng, Du and Hennessy, 2019). More specifically, Dalhaus, Barnett and Finger (2020) take up the current knowledge on behavioural factors in crop insurance decisions and propose a behavioural weather insurance that is particularly designed to better fit farmers' behavioural preferences.
Moreover, we are unable to come up with a single farm in-sample training out-of-sample testing procedure (as for example in Conradt, Finger and Bokusheva, 2015), which would require longer records of yield data at a single farm. We address potential overfitting issues by using pooled approaches as robustness checks (Tables A14 and Table A15). Differences in results displayed in Table 4, Tables A15 and A16 arise not solely from potential overfitting but also because the insurance contracts are no longer tailored to the specific drought risk at the insured farm. More specifically, while our farm-specific tailoring procedure (Table 4) captures farm-specific timeinvariant characteristics in the tick size and strike level, the pooled procedure (Tables A15 and Table A16) does not. The digitalization of agriculture will increase the availability of long-term and site-specific yield data (Walter et al., 2017), which can contribute to design better insurance solutions.

Conclusion
In this paper, we evaluate whether soil moisture insurance solutions can reduce farms' financial drought risk exposure using a case study for wheat, maize and rapeseed production in Eastern Germany. We find that soil moisture index insurances, both from gridded meteorological station-based and satellite-retrieved soil moisture, can reduce the financial exposure to drought risk-related yield losses and thus enlarge farmers' possibilities to cope with climate change. We show how both approaches can be used to reduce farmers' risk premium and argue that considerations for the design of satellite index insurances should include data availability, product quality and validation as well as location-specific farming practices.
Our findings have clear industry and policy implications. Insurance companies should use more, farm-specific information when offering insurance to farms. Moreover, we find performance differences between the satelliteretrieved soil moisture insurance and the meteorological station-based soil moisture insurance depending on the insured crop and growth stage. This heterogeneity calls for tailored, farm-and crop-specific, index insurance solutions.
For policy makers our results indicate that the resilience of the farming sector could be enlarged by improving data availability and accessibility for insurers. For example, our analysis highlights the value of high-quality satellite imagery, weather station, phenology and crop yield data that is freely available for the development of better insurance solutions. Better insurance solutions contribute to the resilience of agricultural systems by maintaining stable incomes and the economic viability of farms (Finger and El Benni, 2020). This helps to avoid costly collective drought-related governmental disaster payments (Meuwissen et al., 2019). Supporting the development of satellite data products that enable the development of better agricultural insurances could thus complement with and substitute for other forms of governmental support of agricultural insurances such as premium subsidies. Insurance solutions based on soil moisture retrieved from satellite imagery have clear advantages as these are cheap, efficient and applicable for various crops globally. Moreover, satellite based index insurance can ensure immediate compensation for a high number of farmers at the same time. In contrast, traditional insurances could not ensure cost-efficient on-farm damage assessments within a narrow timeframe of many farms within a short-time period. Here, satellite based index insurance can bring relief.
Future research should consider how other than drought events that can be measured from space could be integrated into index insurance design. Increasing the number of options to insure, will likely reduce basis risk and stimulate adoption of index insurance. Further considerations about farmers' preferences, beliefs and experiences with insurance based on satellite-retrieved weather data is needed as this can influence insurance uptake and thus performance of the insurance.
where Pr i,v is the farm-specific insurance premium based on the index specification v and PO i,t,v is the insurance payout to farm i in year t based on index specification v. N i,t is the total number of years from which we know farm i's yield.
where T i,v is the tick size in farm i's insurance contract that equals the slope of the quantile regression β 1 i,v (relation between farm i's yield and index values at the lower part of the yield distribution) multiplied by a constant price P to make this a monetary unit.
where S i,v is the strike level of the index insurance specified at farm i with index specification v. Y i are the yields at farm i. q 0.3 (Y i ) reflects that we focus on the 30 per cent percentile of the empirical yield distribution Y i . β 0i,v and β 1i,v are farm individual regression coefficients (intercept and slope) for each index specification v (i.e. soil moisture data from satellite observations or derived from meteorological measurements at ground stations).
πi,v is the third moment (the skewness) of the revenue distribution π i,v at farm i under index specification v.   Min.     Min.

Max
Max.
Max.      Note that farm revenues are largely the same in different scenario's (including the uninsured scenario) but slight difference may occur from the bootstrapping procedure.        b H0: The sample mean of the risk premium in the tested scenario (in rows) is larger or equal than in the comparison scenario (in columns).