quiet and moderate ionospheres are fairly consistent with zero, but the CPS with active ionosphere is not. Thus, the ionosphere might affect the CPS, but there are only a few samples observed in the same group of pointings. Furthermore, same as Fig. \[fig:IonoA\], the dependency on sets of pointings can be found in the top right panel of Fig. \[fig:IonoX\]. This shows the contamination of leaked foreground on the error of CPS. Before moving to the next analysis, it is worth noting that the CPS oscillates around zero in Fig. \[fig:IonoX\]. This indicates that the CPS is dominated by the error including thermal noise and foreground. ]{}

[Systematics due to the ionosphere should be more important at smaller scales. However, we also do not find any correlation at $l$=1000 (not shown in this work) just as for $l$=100 and $l$=500. We note that only two of our samples have an active ionosphere, and an analysis with a more representative sample of ionospheric conditions will be required to more fully investigate these effects. We leave this for future work. ]{}

![image](./Fig_paper/Hist_A_167.675_1.eps){width="7cm"} ![image](./Fig_paper/Hist_A_197.115_1.eps){width="7cm"} ![image](./Fig_paper/Hist_A_167.675_2.eps){width="7cm"} ![image](./Fig_paper/Hist_A_197.115_2.eps){width="7cm"}

![image](./Fig_paper/Hist_X_167.675_1.eps){width="7cm"} ![image](./Fig_paper/Hist_X_197.115_1.eps){width="7cm"} ![image](./Fig_paper/Hist_X_167.675_2.eps){width="7cm"} ![image](./Fig_paper/Hist_X_197.115_2.eps){width="7cm"}

Frequency Dependence
--------------------

[The APS and CPS are expected to be dominated by 