Trip Length

Trip length data were examined for potential insights to relationships between embarkation probabilities and destination selection. While trip length was not explicitly used in the calibration of the simulation, it yields some potentially useful insights for selection of boat destinations. If a boat is only likely to embark for a few hours, it would be limited to destinations that are reachable in a few hours travel time. If there is a relationship between boat class or embarkation rate and duration of trip, that would be justification to limit a boat's choice of possible destinations to those that are within a reachable distance given its travel time.

A summary of trip lengths by boat class is given in table 4.6. A superficial observation of the summary shows that while average trip times are not very different between classes, there is significant variation at the extremes. Most notably, none of the speed, row, or commercial fishing categories reported traveling for more than a day. There are in fact very few boats that venture out for more than a few hours, and the ones that do are most likely to be power cabin or sail boats.

**Table 4.6:** Summary statistics of trip durations in hours for boat types.
\|t:=====:t\| Class	Count	1cmean
Row	6	1.75
Sail	70	9.8
Speed	47	2.37
Comm. Fish	76	3.87
Power Cabin	62	7.87
Comm. Fish	5	5.3
Other Comm.	3	37
\|b:=====:b\|

speed:	boat speed
triplength:	duration of trip in hours
dayfreqsum:	daily trip frequency in summer
dayfreqwin:	daily trip frequency in winter
monthfreqsum:	monthly trip frequency in summer
monthfreqwin:	monthly trip frequency in wither
summertrips:	total trips in summer
wintertrips:	total trips in winter
yeartrips:	total yearly trips

Another feature that becomes obvious is that there is very little correlation between the likely length of the trip and the frequency that the boat is taken out. When a correlation matrix is calculated on the interview data, one sees that trip length and number of yearly trips at which the boat travels have a correlation of .14, which is effectively no identifiable correlation (table 4.7). When a regression is run between trip time and number of yearly trips, an R ² of .02 and a model slope of .02 is obtained, emphatically rejecting any relationship between these two variables (table 4.8).

**Table 4.8:** Regression of trip times of boats against total yearly trips
$\begin{table} \small \centering \begin{verbatim} OLS Univariate Multiple Regress... ...39 0.02101 Error 72307.49 254 284.68 Total 73842.70 255\end{verbatim}\end{table}$

The relationship between trip times and frequency is illustrated in figure 4.4. The axes have been placed in log scale to decrease the effect of the wide range of data values. The great majority of boaters interviewed tend to take their boats out between 10 and 100 times a year, and stay out from two to six hours. Sail boats are the most likely to be taken out a few times a year for extended trips, while power cabin boats show all kinds of variety in their trip patterns. Recreational fishing and speed boats tend to be taken out more frequently for shorter periods of time.

**Figure 4.4:** Trip duration plotted against yearly total trips of various boat classes.
$\begin{figure} \centering \mbox{ \epsfig {file=figures/freq-by-yearly.eps, width=.8\linewidth} }\end{figure}$

**Table 4.9:** Loadings of trip data to components
$\begin{rotate} {20}speed\end{rotate}$
\|t:==========:t\| 0.101
-0.009
0.676
-0.725
-0.072
0.034
0.009
0.024
-0.000
\|b:==========:b\|

See table 4.7 for descriptions of variable names

**Figure 4.5:** Prinicipal components of trip data
$\begin{figure} \centering \mbox{A \epsfig {file=figures/pcat1.ps, width=.5\line... ...} } \mbox{C \epsfig {file=figures/pcat3.ps, width=.5\linewidth} }\end{figure}$

**Figure 4.6:** Trip length compared to cruising speed
$\begin{figure} \centering \mbox{ \epsfig {file=figures/LengthBySpeed.eps, width=.8\linewidth} }\end{figure}$

The trip information presented in table 4.7 are problematic as there are trivial correlations between some variables (monthly and daily probabilities of embarkation during the summer and total trips taken in the summer, for example), and unknown correlations between other variables. The relationships between the various trip summary statistics are better illustrated when a principal components analysis (PCA) is conducted on the correlation matrix. The fit indices, which are summarized in tabular form in table 4.9, show that more than half of the variation in the table is accounted for by the first component, and that 97% of the variation is captured by the first five components. The component scores are presented in table

and a graphic description of the components and their relationship to the variables is presented in figure 4.5.

The illustrations in figure 4.5 show the individual observations (boat owners) represented as dots, and variables in the original matrix represented as vectors that emanate from the center of the n-dimensional graph (the intersection of the various orthogonal components). The angle and length of the vector in relation to a particular component indicates the loading, or amount by which that variable is described by that component (a vector that is parallel to a component is in perfect agreement with that component).

**Table 4.10:** Regression of trip times of boats against speed
$\begin{table} \small \centering \begin{verbatim} OLS Univariate Multiple Regress... ...20 0.65811 Error 30519.84 254 120.16 Total 30543.43 255\end{verbatim}\end{table}$

The first component, which explains about half of the total variation, corresponds to how often boats are taken out (figure 4.5A). The variable that most closely corresponds to this component is the boat's yearly total trips. All the other variables that describe the frequency of boat trips are also loaded onto the first component (PC0), but divided by season along PC1. These are trivial relationships, as the variables that line up with each other are simply different expressions of the same field (number of trips). Figure 4.5B shows the same data plotted along components 2 and 3 (PC1 and PC2). The difference between summer and winter trip frequencies are shown very well along PC1, and an inverse relationship between speed and trip length are expressed along PC2. When these two variables alone are plotted against each other (figure 4.6, plotted in log scale), the negative correlation is almost undetectable, and not at all significant statistically. Figure 4.5C shows the same data plotted along the fourth and fifth components, which together explain about 15% of the variation in the dataset. The fourth component (PC3) shows that trip length and speed is different from trip frequency data (already illustrates in PC2), and the fifth component (PC4) shows that daily embarkation probabilities are distinct from all other trip summary data.

Sarasota Bay is about 25km in length. At the cruising speeds and durations of trips reported in table 4.6 and figure 4.6, it is feasible for the boats of the four numerically greatest categories (sail, speed, power cabin, recreational fish) to reach any destination in the study area.

Interpretation of the PCA in figure 4.5 supports the following assumptions in modeling boat traffic:

One additional aspect of figure 4.6 bears mentioning at this point. The cruising speed shows a clear separation between sailboats, which rarely reported cruising speeds above 8 knots, and all other power boats, which rarely report cruising speeds below 8 knots. In terms of duration, another division become apparent in the range of reported trip times. While all classes show roughly equal average trip times, speed boats show a much more limited range of trip times than the other boat types. While all boats in this sample show a preference for trips of two to eight hours, none of the speed boats in this sample went on trips for more than a day. When assigning cruising speeds for boats, it will be necessary to consider sail boats separately from power boats, and when assigning duration of trips, it will be necessary to consider speed boats separately from all other boats.