## 1 Introduction
### Theoretical Background  
The application of the Mann-Kendall test is widely applied with climate-related time series for trend detection. When a significant trend is detected, Sen's slope estimator can be used to estimate the rate of change [19]. The MK test and Sen's slope estimator were used by [20] for monthly rainfall data from 1989 to 2018 in Kerala (India), identifying a positive trend on the annual scale and in the monsoon season. [PERSON] and [PERSON] [21] applied these statistical procedures for temperature and rainfall trend detection in Pakistan between 2000 and 2020, detecting significant positive trends in rainfall, both in the monsoon and the non-monsoon seasons, and increasing temperature trends in summer and autumn. [PERSON] et al. [22] carried out similar analysis for the Dire Dawa region in Eastern Ethiopia for 1981-2021, identifying increasing temperature trends and decreasing rainfall trends. In [23] temperature time series were analyzed by these tools in Ghana, from 1986 to 2015, revealing significant increasing trends in minimum temperatures. In [24] a similar analysis was performed in the Amhara region, Ethiopia, for the period 1990-2020, detecting a positive trend in annual maximum temperatures and a negative one in the annual minimum temperatures. Beside rainfall and temperature series, the MK test is also widely applied for hydrological data, e.g., to analyze the total annual river flow time series for more than 50 rivers and 40 to 180 years of annual data [25]. Although there exist criticisms related to the power of the Mann-Kendall test [26; 27], its reliability and power increase with the length of the time series. Data series considerably longer than 10 measurement points tend to lead to reliable results [26; 27]. As [19] argue, a reasonable minimum length of time series for trend analysis should be 5 years of monthly data, i.e., 60 data points. This gives a solid foundation for applying the MK test and Sen's slope estimator for our 40-year time series of monthly or seasonal data. The multivariate probit (MVP), introduced by [PERSON] and [PERSON] in 1970 [28], is a class of models used when the dependent variable is multivariate, correlated, and discrete, while the explanatory variables are a mixture of continuous and discrete variables [29; 30]. Various applications of these models can be found in the biological, sociological, and economic literature, and they are particularly useful for evaluating which socioeconomic factors influence the choice between adopting or rejecting a specific strategy. The multivariate probit is popular for modeling correlated binary data, with an attractive balance of flexibility and simplicity [30]. The field of application is extensive: [PERSON] et al. [31] used an MVP model to assess the choice of market outlets by Ethiopian farmers, using age, gender, education, household size, size of livestock herd, access to market information, distance from roads, and access to credit as factors influencing the farmers' decisions. MVP is generally used for assessing the decisions related to adaptation to climate change. [PERSON] and [PERSON] [32] analyzed the climate adaptation strategies of cocoa farmers in Ghana, establishing that the main socioeconomic variables influencing the farmers' climate adaptation strategy choices were sex, age, education, farm size, quality of extension service delivery, access to credit, and membership in farmer groups. [PERSON] and [PERSON] [33] assessed the influential factors on climate change adaptation options by farmers in Nepal, also including age, gender, education, household size, size of livestock herd, access to information, distance, and access to credit among other factors influencing the farmers' adaptation strategy choices. [PERSON] et al. [34] used a similar model for assessing the climate adaptation strategies of smallholder farmers in Malawi, relying on very similar socioeconomic features of the analyzed farmer population.