6 Covering smallholder farmers’ weather perils – a crop model based insurance approach for
6.4 Conclusions
The combination of the statistical and process-based crop modeling increases the accuracy of assessing actual yield variability. In our approach, we capture the plant-physiological yield development within the process-based model and large amounts of the remaining, unexplained yield variability by using a statistical model. The improvement in accuracy and robustness makes our approach suitable for crop production risk assessments on a district scale. Among other constraints for a successful and sustaina-ble implementation, inadequate yield and yield impact information inhibit widespread implementation of index-based crop insurance schemes. We show that the suggested approach can contribute towards establishing a successful insurance scheme in Tanzania and other regions in SSA. This can reduce the vulnerability to severe yield losses for smallholder farmers and enhance farmers’ ability to cope with climate change and altering weather patterns. Furthermore, the suggested area-based yield insurance scheme can contribute to long-term food security by incentivizing higher investments into agricultural production techniques.
Materials and methods
126 6.5 Materials and methods
We apply a combined process-based (PM) and statistical (SM) modeling approach (PM-SM) to cap-ture weather-attributable and non-weather-related yield variability. The PM capcap-tures influences on yield variability directly attributable to weather. The residual, non-weather-related yield variability of the process-based model is then modeled by a SM (see also SI Fig. S.3).
Process-based modeling of the weather-attributable yield variability
As PM we use the Soil and Water Integrated Model (SWIM). SWIM is an eco-hydrological model to capture river discharge, land use, and agricultural crop yield development (Krysanova et al., 2015, 2000). The crop module of SWIM is a modified approach of the Erosion Productivity Impact Calcula-tor (EPIC) model (see also SI S.1.3 for further description). SWIM computes crop yields as a product of total above-ground biomass and the harvest index. Any divergence from the optimal growing condi-tions reduces biomass growth by stress factors within a minimum function. Considered stress factors are heat stress and water, nitrogen, and phosphorus scarcity. SWIM considers several agronomic man-agement measures like fertilization, planting and harvest dates, and crop variety selection by maturity groups.
Statistical modeling of the non-weather-related yield variability
For our statistical model, we use a similar statistical approach to the approach used by Gornott and Wechsung (2016). The SM captures spatial and temporal heterogeneity in the residual yield variability of the PM. The SM estimates district-specific yield influences within a logarithmic function (Eq. 1).
We use the statistical model with the residuals (𝜀𝜀𝑖𝑖𝑖𝑖) between the observed (𝑦𝑦𝑖𝑖𝑖𝑖) and the process-based modeled yields (𝑦𝑦𝑖𝑖𝑖𝑖𝑃𝑃𝑀𝑀) as the endogenous variable and a vector of 𝐽𝐽 exogenous variables (𝑥𝑥𝑗𝑗𝑖𝑖𝑖𝑖). The exogenous variables are maize acreage (in ha), paid subsidies on crop production (in US$), and urea application (in tons for entire Tanzania). Time-constant effects like land tenure security or market ac-cess (see SI S.1.4.3) are captured by the district-individual intercept (𝛽𝛽0𝑖𝑖).
𝜀𝜀𝑖𝑖𝑖𝑖= log𝛽𝛽0𝑖𝑖+� 𝛽𝛽𝑗𝑗𝑖𝑖log 𝑥𝑥𝑗𝑗𝑖𝑖𝑖𝑖
𝐽𝐽
𝑗𝑗=1
+ log𝐵𝐵𝑖𝑖𝑖𝑖, (1)
with 𝛽𝛽 as parameters and 𝐵𝐵𝑖𝑖𝑖𝑖 as error term for 𝑇𝑇 years (𝑡𝑡= 1, … ,𝑇𝑇) and 𝑁𝑁 spatial units (𝑖𝑖= 1, … ,𝑁𝑁).
Maize yield losses and insurance index
The mean weather and non-weather attributable yield loss (average yield anomaly below mean yield level) is calculated as semi-standard deviation (𝑆𝑆𝑆𝑆𝑉𝑉𝑖𝑖𝑆𝑆𝐿𝐿𝑏𝑏𝑁𝑁𝑏𝑏, Eq. 2) for each district:
𝑆𝑆𝑆𝑆𝑉𝑉𝑖𝑖𝑆𝑆𝐿𝐿𝑏𝑏𝑁𝑁𝑏𝑏=�(𝑇𝑇 −1)−1 �
𝑇𝑇
𝑖𝑖=1
min�(𝑦𝑦𝑖𝑖𝑖𝑖− 𝑦𝑦�𝑖𝑖), 0�2, (2)
with 𝑦𝑦� as arithmetic average yield across the T years.
The average indemnity claims are the product of 𝑆𝑆𝑆𝑆𝑉𝑉𝑆𝑆𝐿𝐿𝑏𝑏𝑁𝑁𝑏𝑏, maize acreage and maize price. In our case, the critical value for indemnity payments is the average yield. But other critical values, like the 25%-percentile and 10%-percentile, are also applied.
The maize yield insurance index (𝐼𝐼𝐼𝐼) is calculated by Eq. 3. As maize yield insurance index (𝐼𝐼𝐼𝐼), we use a weighted product of process-based modeled weather-related and observed yield variability. De-pending on the accuracy of the combined model approach to explain the total yield variability, we weigh the share of modeled weather-related and total observed yield variability by the model R².
Where the model is able to fully (R² = 1) explain total yield variability (by weather and non-weather-related impacts), only the weather-non-weather-related modeled yield variability is used as the index. With decreas-ing R², the share of observed yield variability increases in the index (Eq. 3). The insurance index is normalized with the average yield and the factor 100.
𝐼𝐼𝐼𝐼𝑖𝑖𝑖𝑖 = 100��𝑦𝑦𝑖𝑖𝑖𝑖𝑃𝑃𝑀𝑀
𝑦𝑦�𝑖𝑖𝑃𝑃𝑀𝑀�R2𝑖𝑖 +�𝑦𝑦𝑖𝑖𝑖𝑖
𝑦𝑦�𝑖𝑖� �1−R2𝑖𝑖�� (3)
To come to a claim payout, three steps are necessary: (1) Modeling of weather-attributable yield with (solely) weather data (2) calculation of the indemnity on bases of the historical weather-related yield distribution for each district, and (3) payout of the indemnity (see SI S.3.1.ii for details).
.
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Decomposing weather- and management-related impacts on crop yields
130