Climate and landscape mediate patterns of low lentil productivity in Nepal

Dadeldhura (Far-western region). A total of 43 VDCs and 600 households were surveyed in 2015 using the same selection methodology as in the previous year. Data were collected through face-to-face interviews using a structured questionnaire, con- ducted following lentil harvest. The questionnaire includes sections to elicit information on household demographics, lentil production technologies, inputs, agronomic practices, yields, end uses for harvested lentil, and general perceptions towards lentil cultivation. Households that planted lentil but lost the crop due to biotic or abiotic stress were retained in our analysis. Weather data Daily minimum and maximum temperature (˚C), and rainfall (mm) data corresponding to the household survey periods were collected from the Department of Hydrology and Meteo- rology, Government of Nepal [54]. Rainfall (mm) along with maximum and minimum tem- peratures (˚C) were averaged for each weather station (n = 16 for temperature, n = 58 for precipitation) within our study area over the lentil season (October to March). An inverse dis- tance weighting (IDW) algorithm [55] in ArcGIS v10.3 was used to create gridded weather data at a 1 km resolution. Gridded data were then paired with survey locations. Furthermore, long-term (1985–2015) historic weather data for selected meteorological stations from differ- ent districts of the Nepal Terai were also obtained from the same sources [54], and a historical trend analysis has been carried out for seasonal precipitation. Station data from Banke district

was used to drive the Stempedia model simulations. Stochastic frontier model A production frontier represents the maximum output attainable for a given set of inputs and a given production technology [56]. Failure to attain the frontier output implies that produc- tion is technically inefficient. However, survey data on agricultural production may be heavily contaminated by statistical noise due to measurement errors, variability in climatic and edaphic conditions, or interactions with pests and diseases. In contrast to Data Envelopment Analysis (DEA) that attributes any deviation from the frontier output to inefficiency [57], sto- chastic frontier analysis accommodates statistical noise. We therefore chose this approach for our analysis. The stochastic production frontier was independently proposed by Aigner et al., [58] and Meeusen and van Den Broeck [59] and is defined as follows: Yi ¼ FðXi; bÞexpðVi UiÞ; i ¼ 1; 2; . . . ; N ð1Þ Where; Y = Quantity (or value) of output of the i-th firm F(�) = Suitable production function X = Vector of input quantities β = Vector of parameters to be estimated V = Random error term U = Non-negative error term representing technical inefficiency V is a random variable, assumed to be independently and identically distributed as N(0, σv). U, which captures systematic shortfalls from the frontier due to technical inefficiency, is assumed to follow a particular one-sided distribution. A number of different distributions have been proposed in the literature, namely the half-normal and exponential [58], the truncated normal

[60], and the two-parameter Gamma distribution [61]. The technical efficiency (TE) measure for the i-th household TE = exp(−Ui) 2 [0, 1] is the ratio of the observed output and the maxi- mum attainable output at the frontier. The maximum likelihood (ML) estimation of Eq (1) PLOS ONE Climate and landscape mediate low lentil productivity PLOS ONE | https://doi.org/10.1371/journal.pone.0231377 April 16, 2020 4 / 19