The primary processes driving soil moisture dynamics in the
Vacant to Vibrant parcels are rainfall events that act as sources (both direct
rainfall and runoff) and losses due to infiltration, evaporation, and plant
mediated evapotranspiration. In the
previous blog post (here), I presented evidence that the patterns of diurnal
variation in soil moisture were driven by variation in soil temperature and did
not reflect the effects of the primary drivers.
The regularity of the diurnal variability and its low amplitude allows
use of smoothing functions to characterizing longer term declines in soil
moisture associated with the loss processes (infiltration, evaporation, and
evapotranspiration). Figure 1 shows the
application a simple linear regression to a time series between rainfall
events. Using the linear fit to the time
series, Figure 2 shows the that the removal of the longer-term trend emphasizes
the diurnal variability, and Figure 3 shows that the variation in the residuals
are correlated with observed soil temperature.

Figure 1. Semi logarithmic plot of decline of soil moisture over the period May 25 to June 6, 2016 for the Gary E1 parcel at 3 cm. The blue line is a linear regression. |

Figure 2. Plot of the residuals for the regression in Figure 1. |

Figure 3. Plot of the residuals from Figure 2 showing association with measured soil temperature at 3 cm depth. The blue line is a regression between the two variables (r= 0.80, p <0.0001). |

The advantage of the linear regression in Figure 1 is that
the slope is a first order (i.e. an exponential decay rate) estimate of the
rate of change of soil moisture between rainfall events. The estimated rate for the Gary E1 parcel at
3 cm soil depth is -1.68e-07 (1/s). This
method can be applied to trends at other depths or for the weighted average
soil moisture and provides data for comparison of experimental and control
parcels in the different soil types of the neighborhoods of the three cities in
the project.

The remaining decline pattern (presented in the previous
blog post) is the transient associated with a rainfall event. Figure 4, presents the observed relation
between increment of soil moisture and the subsequent first order rate of
decline.

Figure 4. Relation between soil moisture increment and subsequent rate of decline in soil moisture at 3 cm depth in the Gary E1 rain garden. |

The slope of the relation in Figure 5 is -1.488e-05
(r=-0.5408624, p=0.1663, NS). The hint
of an inverse relation between the increment of soil moisture following a
rainfall event exists, but is not statistically significant. The average rate of decline, however, is
1.02e-6 (1/s). An outlier occurs on
April 30, 2016. On 4/29 and 4/30 (see
Figure 6), there was a double increase.
The identification of extrema near this interval is a problem and it is
reasonable to regard the April 30 point as anomalous. Figure 7 shows the result of eliminating this
point. The estimate of the decline rate
is a statistically significant -1.90e-5, which is nearly two orders of
magnitude greater than the rate of decline of the inter-event interval in
Figure 1. Clearly, more data are needed
to explore this relationship and its drivers, but it seems reasonable to expect
that the rate of decline following a rainfall event is a function of the soil
moisture gradient and the permeability of the soil.

Figure 6. Pattern of variation in soil moisture (m3/m3) at 3 cm soil depth in the Gary E1 rain garden. |

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