1) Mann-Kendall Test

The Mann-Kendall (MK) trend test is a non-parametric statistical method that is used to capture the trend in data over time. The test observes whether a random response variable monotonically rises or falls with time [29].

The Standardized Mann–Kendall test statistic is given as follows;

S = ∑ i = 1 n − 1 ∑ j = i + 1 n sgn ( x j − x i ) (1)

where S is a statistic, x_i, and x_j are the sequential data values, n is the distance of the time series, and sgn ( x j − x i ) is clarified as;

sgn ( x j − x i ) = { 1             if   x j > x i 0             if   x j = x i − 1         if   x j < x i (2)

In the monotonic trend test, we need to test the null hypothesis (H₀) of no trend or the alternative hypothesis, H₁ , where there is rise or fall monotonic trend [30]. Positive (+) values specify a rise over time while, negative (−) values indicate descend [29]. Since the data is independent and normally distributed, the variance of the S statistic (Var(S)) is identified by;

V a r ( S ) = n ( n − 1 ) ( 2 n + 5 ) 18 (3)

The values of S and Var(S) are used to compute the test statistic “Z” as follows:

Z = { S − 1 V a r ( S )       if   S > 0 0                               if   S = 0 S + 1 V a r ( S )       if   S < 0 (4)

The Z value is used to calculate the statistically significant trend. A positive or negative value of Z represents a rise or fall trend, respectively. The null hypothesis is excluded at the significance level of α if | Z | ≥ Z α / 2 , where Z_α/2 is the critical value of the standard normal distribution with a probability exceeding α/2, and it shows that the trend is significant. If | Z | < Z α / 2 , the null hypothesis is recognized, and the trend is not significant. A trend is examined to be statistically significant if α ≤ 0.05 or ≥95% level [31].

2) Sen’s Slope Estimator (SSE)

This method was used to find the magnitude of the considered trend in a certain time series [32]. It is usually applied when the assessed slope is measured to be linear. This is demonstrated exactly as;

S S E i = x k − x l k − l     for   i = 1 , ⋯ , n (5)

where i is the number of the time steps, x k and x l are the data points at point k and l respectively. In this case, k must be larger than l.

In the case of only one datum in each period, then n can be explained as n = n ( n − 1 ) / 2 .

When there are multiple data in one or more-time periods, then,

n < n ( n − 1 ) / 2 .

where n characterize the time steps. The n values of SSE are organized from lowest to highest and then the Sen’s slope estimator is defined as;

Q m e d = { S S E ( N + 1 ) / 2                                                     when   n   is an odd number S S E ( N / 2 ) + S S E ( N + 1 / 2 ) 2         when   n   is an even number (6)

The trend is specified by the sign of the Q m e d while its value portrays the degree of the slope. The confidence interval of the Q m e d at certain probability is then acquired to examine if the slope is statistically significant at zero. The confidence interval of the considered gradient is exposed in Equation (7) [33] [34].

C α = Z 1 − a 2 V a r S (7)

where, the variance of the S statistic (Var(S)) is demonstrated in Equation (3). Z 1 − a / 2 is the tabulated value obtained from the t-table. According to [33], the lower and upper limits levels of the significant bands, Q max and Q min , are M 1 t h largest and the ( M 2 + 1 ) t h largest of the N ordered slope estimates. In this case,

M 1 = N − C a 2 and M 2 = N + C a 2 . In this study, the slope will be measured statistically significant at ( α = 0.01 ) and if the two limits Q min and Q max have same sign.

In order to predict the expected yearly maize yield for future food secure country, a multiple linear regression model was built based on the seasonal climate indices of the growing period and regions which have significant influence on the annual maize yield. Indeed, Pearson correlation method and t-test at 95% significance level was used to classify the region where climate stress has significant impacts on maize yield. The correlation was amid climate indexes anomalies (rainfall, minimum, and maximum temperature) and the maize yield anomalies at each region represented by the synoptic station.

The climate indexes for building the multi linear regression model was obtained by averaging the climate indexes for all regions with statistically significant correlation coefficient (positive or negative). Mathematically, the multi linear -regression model can be expressed as:

Y ( t ) = β 0 + β 1 x 1 ( t ) + ⋯ + β n x n ( t ) + ε (8)

where y(t) is the maize yield in year t ( t = 1 , 2 , 3 , ⋯ , 20 ),

n = denotes the number of climate index used, x 1 , x 2 , ⋯ , x n represented the seasonal hydroclimate variables in region that has statistically significant correlations coefficient. β 0 = y-intercept and ε = Error term.

Notably, since multicollinearity inflates the explained variance, it was tested using variance Inflation Factor and all the variable considered did not significantly correlate with each other.

Variability of agriculture production is caused by occurrence of extremes in the distribution that leads to climate variability. The identification of high/low years were based on the standardized anomalies; i.e. +1 and −1, respectively. Results show that, four years of above average and two years of below average yield were observed. The wettest years (>1.0) were 1995, 1999, 2001 and 2002; worst drought was 2003 and 2005 (Figure 7). Remarkably, during the El Niño years 1997/1998, below mean climatological maize yield were recorded. This can be linked to damages caused by excessive rainfall during that extreme ENSO event.

Since climate variability has a significant influence on maize yield, it’s necessary to examine weather characteristics during extreme maize yield periods. Mean seasonal cycles of rainfall, maximum and minimum, temperature ranges were calculated during those years with respect to the climatological mean. Results show that, high yield years were characterized by increased rainfall during the two growing seasons but more pronounced during the long rains season (MAM) (Figure 8(a)). At the same time maximum temperature was below the climatological mean, while minimum temperature increased above the long-term mean. Additionally, temperature range was below the climatological mean in both seasons.

This climate characteristic made the environment more favorable for maize growth as compared to a normal year, hence anomalous high maize yield.

Anomalous or declined low maize yield years were characterized by a decrease in rainfall throughout the year, coupled with high maximum temperature from March to the rest of growing season, though there were no differences from May-September. The minimum temperature was below climatological mean before the beginning of long rains which indicates a false start of the growing season, and was above climatological mean during the short rains. In high/low yield years, the temperature range differs from the climatology. This coupled impact of the hydroclimate leads to harsh weather that was not conducive for maize growth, hence the reported anomalously or declined low maize. Low yields result from a decrease in rainfall accompanied by high temperature leading to both water and moisture stress to the crop. Conclusively, years with high/low maize yield was associated with rainfall, maximum, minimum, and temperature range that marginally positively deviates from the climatological mean.

Region scale climate change and variability consequences are the main factor that alters maize yield variability in Tanzania. Rainfall amounts and its distribution are very important in the rain-fed agriculture system in Tanzania, since different parts of the country have different rainy seasons. For instance, studies by [36] [37] have reported that increasing temperature and decrease rainfall in East Africa regions affect water availability, food security, and human health. To quantify which climate indexes in which regions in Tanzania has a significant influence on the maize yield, Pearson correlation was performed between the hydroclimate at each synoptic station and national maize yield.

The results of the Pearson correlation between maize yields and hydroclimate parameters indicate that, significant relationship between national maize yield and main maize growing regions have presented in Figure 9. Figure 9 reveals that a stronger relationship indicates that the station is the main contributor to the maize production, and its precipitation/temperature anomalies have a significant influence on maize yield. Moreover, the results indicate that the regions near the coast exhibit significant positive relationship with rainfall, while many other maize growing regions are not significantly impacted by changes in rainfall. This could be due to the fact that, maize is very sensitive to water availability during the growing period, so sufficient rainfall will increase yield. For example, Musoma, Morogoro, Dar es Salaam, and Handeni stations (Figure 9(a)) are major contributors to the maize yield but are extremely hit by rainfall variability. Therefore, adaption techniques including the use of irrigation schemes are very advocated for in those regions.

Indeed, results revealed that MAM seasonal variation in maximum temperature exhibited a significantly strong negative relationship with maize yield, which had significant negative consequences on yield, as evinced by the correlation

factor of r = −0.49, at p < 0.1 (Figure 9(b)). This could also due to the fact that an increase of soil evaporation, which lessens the soil moisture availability for crop growth, and its effects differ from one area to another. For instance, the regions around Lake Victoria basin (Musoma), northeastern part of Tanzania (Arusha and Moshi), central part (Dodoma) and the coastal region (Tanga and Dar es salaam) depicted an anomalous increase of maximum temperature, which resulted in higher stress on maize in the major zones as shown in (Figure 9(b)).

During the short rains season maximum temperature anomalies had significant negative impactions to Tanzania. For example, at Musoma station located in the northern part of the country (Figure 9(c)) had no significant correlation among minimum temperature and maize yield in both seasons.

The results of the fitted multiple linear regression models between the maize yields and climate indices presented in Figure 9 shows that there are three seasonally altering areas that had a significant correlation. The fitted model (Equation (11)) used three climate indices namely, OND maximum temperature (OND_tm) for Musoma station, MAM maximum temperature (MAM_tm) considered in ten stations of Musoma, Arusha, Moshi, Tanga, Dodoma, Morogoro, Dares salaam, Sumbawanga, Mbeya, and Songea, respectively. Finally, the model used the MAM rainfall (MAM_rain) averaged at four stations Musoma, Handeni, Morogoro, and Dar es Salaam, respectively. In both seasons, there was no significant correlation between maize yield and minimum temperature at any station, so it was not used in model construction. Also, in fitting the statistical model four assumptions were taken in consideration: 1) the errors are assumed to be independent, 2) the residual is normally distribution, and 3) equal spread of variance, 4) the dependent variable average response is a linear function of each set of predictor values. To evaluate the validity of these assumptions’ quantile plots and observation of the residual plot were made and all were adhered on.

The regression model is:

Y = 10.582 + 0.011 M A M r a i n − 0.159 M A M t m − 0.213 O N D t m (11)

y = Predicted maize yield, tm = Maximum temperature.

If the climate variable remains constant on the period mean, the constant term in the equation computes the yield variance. It also accounts for other factors like land management practices, such as fertilization, tillage technique, and technological advances which have not been considered in the study. The remaining terms of Equation (11) evaluate the influences of climate changes on maize yield. The specific yield was produced by the interaction between rainfall and temperature during the growing period, so both could account for 58.78% of maize yield variability. The model’s p-value is 3.257 × 10⁻⁵ 5 at p < 0.05. Residual standard error was 0.3714 on 26 degrees of freedom, Multiple R-squared: 0.5878, Adjusted R-squared: 0.5403 and F-statistic: 12.36 on 3 and 26 degrees of freedom.

Factors that affect maize yield variability were evaluated to determine which parameter is the most important in determining maize output. MAM seasonal rainfall index accounts for 44.1%, while MAM seasonal maximum temperature accounts for 3.1%, and OND seasonal maximum temperature 7.3% of maize yield variance. Therefore, maize yield variability was highly attributed to MAM seasonal rainfall than temperature. Notably, maize yield is very sensitive to climate change, particularly the effects of changes in rainfall. These results concur with reference [38], who observed that agriculture is becoming more sensitive to climate change/variability.

The results of the model performance using the Taylor diagram Figure 10 under statistical measures of correlation coefficient (r), unbiased root mean square, and standard deviation (amplitude) shows a standard deviation of no more than one, unbiased root mean square of 0.64 and a correlation coefficient of 0.78 at p < 0.05 indicating the level of the goodness of fit of the model.