Cotton lint yield was significantly correlated to soil water (r = 0.53) measured in both transects (Fig. 3a). Yield increased linearly with an increase in soil water, and 80% of high yield (³ 800 kg ha^-1) was produced in soil containing soil water ³ 0.2 m³ m^-3 (0.0 - 1.5 m). However, 90% of high lint yields (³ 800 kg ha^-1) were obtained in soil with low soil P₂O₅ content (3-15 kg ha^-1), and only 10% of these high lint yields was linked to the higher P₂O₅ content (³ 16 kg ha^-1). Therefore correlations of cotton lint yield to soil P₂O₅ gave small r values (Fig. 3b). We know that an adequate soil water supply should lead to a higher lint yield; thus, the difference of water distribution could cause the variability in yield. Within transects, varying soil water contents can be interpreted as spatial differences in transport and infiltration of water within very short distances.

Cotton Lint Yield State-Space Models. Field topography is a parameter related to soil water, cotton lint yield, and their variability. There was a cyclic feedback relationship between cotton lint yield, total soil water, and elevation. This is shown in the scatter diagram (Fig. 4), where the cross-correlation functions of cotton lint yield vs. total soil water and elevation showed that soil water content was cross-correlated with cotton lint yield across a lag distance of ± 10 m (Fig. 4a), and elevation was cyclically cross-correlated with cotton lint yield across a lag distance of ± 25 m (Fig. 4b). State-space analysis is appropriate when soil or crop attributes are spatially cross-correlated since the behavior of correlated soil and a state-space model can describe crop parameters along one- and two-dimensions of the field.

Our state-space analysis demonstrated how cotton lint yield was related to soil water, P₂O₅ and elevation along the transect, and how strongly lint yield at position i was spatially based on previous measurement of lint yield, soil water, P₂O₅ and elevation at position i-1. The estimated 4 x 4 transition (coefficient) matrix (F) of the state-space equation corresponding to each irrigation level along 50% ET transect (F_50%ET) and 75% ET transect (F_75%ET) were given as shown in Table 3.

 

Fig. 3. Cotton lint yield as a function of soil water content (A) and P₂O₅ (B) for both irrigation levels.

 

This transition matrix showed the dynamic interaction among soil parameters. Estimates and forecasts for each variable of the state-space method were based on measurements of 4 variables. Cotton lint yield was positively related to soil water content and negatively correlated to elevation. For the 75% ET area, soil water content was negatively influenced by previous elevation, but not by previous cotton lint yield and P₂O₅ content. Field elevation is strongly related to previous elevation, which gave high t-values of 10.4 and 15.5 for the two models, respectively (Table 2).

The SE for the calculated parameter estimates of the transition matrix F is comparable for the two state-space models (Table 2). The t-statistics showed that cotton lint yield and soil water estimates were significant (t > 2) for both models, but elevation estimate is only significant for the 75% ET model (Table 4). Among these state-space variables, cotton lint yield was significantly and positively correlated to soil water content and negatively correlated to elevation (Table 2).

Fig. 4. Cross Correlation between cotton lint yield and total water content (A) and elevation (B) for the two irrigation levels.

State-space equations and 95% confident limits of estimates for lint yields at position i compared with measured lint yield values along the two transects are shown in Fig. 5. These equations describe how the state of cotton lint yield (yi) at location i was related to lint yield (yi-1), soil water (Wi-1), P₂O₅ content (Pi-1), and elevation (Ei-1) at the previous location i-1 via the state coefficient F. Both multivariate state-space equations demonstrate that cotton lint yield at location i, as a function of those state variables at previous position i-1 along two transects, is positively weighted on previous lint yield, especially previous soil water. However, the 50% ET cotton lint yield is more positively weighted on previous lint yield and soil water content than the 75% ET area.