2.2.2. Processing of Climate Data and Set-Up of the LARS Weather Generator

Historical weather observations, including daily maximum temperature, daily minimum temperature, daily rainfall, daily wind speed, daily minimum humidity, and daily maximum humidity were obtained from the nearest meteorological station to the study site—courtesy of the National Weather Service of Togo. These daily weather data available at the station range from 1983 to 2011. In addition, the observed monthly rainfall and maximum and minimum temperatures data from 1980 to 2016 were provided. These monthly data were utilized to characterize the climate of northern Togo with the climate diagram of Walter and Lieth [55]. The Dapaong meteorological station is located at latitude 10◦51 44.10 N, longitude 0◦12 27.43 E, and altitude 330 m above sea level (Figure 1). The solar radiation data, as well as sunshine hours data, were not available at Dapaong weather station. As a substitute, the uncorrected gridded incident solar radiation from the Prediction of Worldwide Energy Resource dataset from the National Aeronautics and Space Administration project NASA-POWER [58] was utilized. Van Wart et al. [59] showed that NASA-POWER is a good source of climate data for crop yields simulation studies. It is publicly accessible, shows acceptable general agreement with ground data for incident solar radiation, and has been used by similar previous studies (See Section 2.2.4).

**Figure 3.** General framework for generating stochastic crop water production functions (adapted from Schütze and Schmitz [36]).

Since the 29-year period (1983–2011) of weather data is not long enough to be used in the assessment of climate variability effect on crop yield, the Long Ashton Research Station Weather Generator version 4.0 (LARS-WG)—a stochastic weather generator—was used to generate a 100-year period of near future climate data. In this study, out of the existing weather generators, LARS-WG was used for two reasons. Firstly, it uses more complex distributions for weather variables and has been tested for diverse climates and found to be better than some other weather generators such as WGEN [60] (Appendix A). Secondly, Semenov [61] recently tested LARS-WG at different locations across the world and revealed its ability to model rainfall extremes with acceptable performance. Similarly, Mehan et al. [62] provided insights into the suitability of LARS-WG for use with water resource applications. Guo et al. [63] suggested performing more than a single realization when generating weather data using LARS-WG for hydrologic and environmental applications. We assessed the performance of the LARS-WG in simulating weather data of Dapaong by comparing the observed and the simulated data with the Kolmogorov–Smirnov test (KS-test). We used the KS-test for the comparison of the probability distributions for each month. The KS-test is a non-parametric and distribution-free test that tries to determine if two datasets are extensively different and come from different distributions. It is an alternative to the Chi-square goodness of fit test. The KS-test compares the two empirical distribution functions as in Equation (1) [64].

$$\mathbf{D} = |\mathbf{E}\_1(\mathbf{i}) - \mathbf{E}\_2(\mathbf{i})|\tag{1}$$

where E1 and E2 represent the empirical distribution functions of the two distributions, and D is the absolute difference between them.

The KS-test examines for changes in distributions coming from the generated and observed weather. The KS-test calculates a test statistic and an equivalent *p*-value [65]. It shows how likely it is that the generated and observed data originate from the same distribution. If the *p*-value is very low and below the significance level, set to 0.01 or 0.05, the simulated climate is unlikely to be the same as the "true" climate. Although a *p*-value of 0.05 is the standard significance level employed in most statistics, the authors of the LARS-WG model recommended that a *p*-value of 0.01 should be considered as the satisfactory significance level.

The calibrated LARS-WG for Dapaong was then used to forecast the 100-year daily rainfall and temperature data mentioned above for a near future. For this, the outputs of the General Circulation Models (GCMs) HADCM3 (Hadley Centre Coupled Model version 3) of the IPCC Special Report on Emission Scenarios (SRES) A2 were inputted into LARS-WG. The HADCM3 is the product of the UK Meteorological Office, gridded as 2.5◦ × 3.75◦. These long-term data were used to run the AquaCrop model to assess the five irrigation management strategies.
