Reference evapotranspiration (ET_ref) is a key parameter of hydro-meteorological studies as well as water resource planning. In this study, we adopted the Penman–Monteith FAO 56 model to estimate ET_ref and through the differential equation and detrending method to determine sensitivities and the contributions of four meteorological parameters to ET_ref based on daily weather data from 60 stations of Jiangsu province during 1961–2015. Results reveal that ET_ref and its trends in the three sub-regions of the Jiangsu province had a significant spatial heterogeneity. A significant decreasing tendency of ET_ref (p < 0.001) was observed in the Huaibei region, while a slightly increasing tendency was identified in the Jianghuai and Sunan regions. These changes of ET_ref were caused by a significant increasing trend in air temperature (TA) and significant decreasing trends in wind speed (WS), sunshine duration (SD) as well as a non-significant change trend in actual vapor pressure (VP). However, the VP was the meteorological parameter to which ET_ref was most sensitive, whereas ET_ref was more sensitive to TA and SD in the summer but less so in the winter; the least sensitive factor, WS, had the opposite trend. Across the whole region, WS contributed most to ET_ref, followed by SD, while the positive contribution of TA to ET_ref could not offset the negative contributions of WS and SD. Although the effect of VP on changes in ET_ref is small, it could not be ignored, especially in the winter. The reverse relationship between increasing TA and decreasing ET_ref, namely the “evaporation paradox,” occurred in Jiangsu province. Thus, the outcomes of this study will contribute to thorough insight into the response to changes in ET_ref to the provincial water planning and management in eastern China.

A sensitivity analysis of the responses of crops to the chosen production adaptation options under regional climate change was conducted in this study. Projections of winter wheat production for different sowing dates and cultivars were estimated for a major economic and agricultural province of China from 2021 to 2080 using the World Food Study model (WOFOST) under representative concentration pathways (RCPs) scenarios. A modeling chain was established and a correction method was proposed to reduce the bias of the resulting model-simulated climate data. The results indicated that adjusting the sowing dates and cultivars could mitigate the influences of climate change on winter wheat production in Jinagsu. The yield gains were projected from the chosen sowing date and cultivar. The following actions are recommended to ensure high and stable yields under future climate changes: (i) advance the latest sowing date in some areas of northern Jiangsu; and (ii) use heat-tolerant or heat-tolerant and drought-resistant varieties in most areas of Jiangsu rather than the currently used cultivar. Fewer of the common negative effects of using a single climate model occurred when using the sensitivity analysis because our bias correction method was effective for scenario data and because the WOFOST performed well for Jiangsu after calibration.

Understanding variations in rainfall in tropical regions is important due to its impacts on water resources, health and agriculture. This study assessed the dekadal rainfall patterns and rain days to determine intra-seasonal rainfall variability during the March–May season using the Mann–Kendall ( $MK$ ) trend test and simple linear regression ( $SLR$ ) over the period 2000–2015. Results showed an increasing trend of both dekadal rainfall amount and rain days (third and seventh dekads). The light rain days ( $SLR$ = 0.181; $MK$ = 0.350) and wet days ( $SLR$ = 0.092; $MK$ = 0.118) also depict an increasing trend. The rate of increase of light rain days and wet days during the third dekad (light rain days: $SLR$ = 0.020; $MK$ = 0.279 and wet days: $SLR$ = 0.146; $MK$ = 0.376) was slightly greater than during the seventh dekad (light rain days: $SLR$ = 0.014; $MK$ = 0.018 and wet days: $SLR$ = 0.061; $MK$ = 0.315) dekad. Seventy-four percent accounted for 2–4 consecutive dry days, but no significant trend was detected. The extreme rainfall was increasing over the third ( $MK$ = 0.363) and seventh ( $MK$ = 0.429) dekads. The rainfall amount and rain days were highly correlated (r: 0.43–0.72).

In the framework of variational adjoint system, the spectral conjugate gradient (SCG) method, coupled with adjoint method, is adopted in this study as the functional minimization tool to retrieve the variable coefficient for the nonlinear convection–diffusion equation. The main steps focus on the determination of the search step size and the search direction. The former is deduced and then achieved numerically by solving the given sensitivity equation. The latter is formulated by the spectral gradient. The effectiveness of this solution strategy is evaluated by comparing it with L-BFGS iterative descent algorithm using different data types (dense and sparse, noise-free and noisy data). The effects of different forms of initial guess distribution of variable coefficient, as well as various levels of noise, on the retrieval results are also covered. The results indicate that (1) the performance of the SCG is superior to that of the L-BFGS in both the anti-noise ability within a suitable noise range and the enhancement of numerical accuracy. This is mainly due to the fact: first, the SCG adopts optimal step length calculated via the sensitivity problem at each iteration, and second, the SCG itself belongs to the iterative regularisation class; (2) it is demonstrated in our numerical test examples that the effects on the retrieval results caused by the changes of different initial guesses for the variable coefficient are much less in the SCG than in the L-BFGS.