Forecasting Future Crab Landings

One of the first observations we made that began our investigation of freshwater flow and blue crab landings was that years of rapidly decreasing freshwater discharge were correlated with years of rapidly declining commercial crab landings.  This correlation had the highest predictive power when flow from two years prior was used to predict the current year's crab landings (shown above).  This gives us an immediate back-of-the-envelope approximation for future blue crab landings by knowing the annual flow of the Edisto River two years earlier.  This relationship can be described by this simple linear equation:

Expected landings (in millions lbs) = 2.51 X log (Edisto annual flow in cu ft/s) - 2.78 (a constant)

So given that the Edisto annual flow for 2013 was 931 (cu ft/s) then the expect blue crab landings for 2015 should be:

2.51 X log(931) - 2.78 = 4.67 millions lbs.

So why choose the Edisto River freshwater discharge levels rather than some more integrated measuring involving all of the rivers in South Carolina?  First of all, SC river discharges are highly correlated with adjacent rivers such that one is likely to represent the trend of the whole set.  Second, the Edisto River is undammed and thus, shows normal seasonal cycles unimpacted by regulation for hydroelectricity production.  Third, the USGS gaging station at Givhans Ferry, SC (02175000) has one of the longest historical record of discharge records dating back to 1940.  Finally, the Edisto River was river used to parameterize the SCBCRABS IBM with the ACE Basin NERR field study.

This graph shows the historical record of Edisto River discharge (at USGS station 02175000) over the last 75 years (blue line).  At first glance it is easy to see that discharge levels vary a lot from year to year and that recent discharge levels are below the levels they were prior to 1990.  So if we want make a best guess what the river discharge levels will be in the future, we should consider both the slope of this decline in discharge levels and the periodicity of the interannual variation.  One mechanism to do this is to use a auto-regressive integrative moving average model (ARIMA).  This model assumes a sine-curve smoothing function with a period of twelve years.  I chose this period for it was the best period for a simple sine-curve function fit to the historical record and it also approximates the periodicity of larger global weather patterns that affect precipitation (ENSO, NAO).  The ARIMA model is fit to the historical record (red line) and then projected forward in time based on the predicted future flow levels.  Overall the slope of the flow decline is approximately 0.04 which is less than the rate of decline observed over the last 10 years.  Likewise the magnitude of the forecasted droughts (2026 and 2038) are of similar magnitude to the one observed in 2002.

To merge this ARIMA model of Edisto River flow with the SCBCRABS blue crab model, I chose to focus the simulation runs over a 50 year period from 1990 to 2040.  That means for the first 25 years of the model run, the flow input is the actual historical data of monthly river discharge from the Givhans Ferry USGS gage (blue line).  For the years from 2015-2040, the river flow is assumed to follow the predictions from the ARIMA flow model (red line).  Data for weekly flow levels were then read into the SCBCRABS model as an input file with 2600 time steps (52 weeks X 50 years).

To better visualize the cumulative impact of freshwater flow has over blue crab for multiple years, I constructed a heat map that captures the impact of droughts multiple years after the event.  I first selected a critical minimum annual flow level based on the annual flow level that seemed to have the greatest influence of future crab landings.  The critical minimum flow was 1250 cu ft/s flow (log 3.1).  In this heat map, each year is color coded by the number of years prior where the flow was above the critical minimum level.  For example, year 2000 is green because flow for 1998, 1999 and 2000 were all above the critical minimum flow whereas 2012 is orange because only flow for 2010 but not 2011 or 2012 was above the critical minimum flow. The impact of these hydrological drought events (annual levels below the critical min of 1250 cu ft/s) is presumed to impact blue crabs for a five year period and thus the green color assigned to 2000 extends through 2004 and the orange color for 2012 extends through 2016.  Thus, crabs should do well during the green years and should not do well during the red years.

Here we show the estimated annual commercial landings from the SCBCRABS ARIMA IBM.  The model output of crabs trapped were divided by a constant (50) to derive the approximation of the annual landings in millions of lbs.  The line connects the mean landings for 100 runs of the model and the error bars represent +/- 1 standard deviation.  The model predicts relatively high or increasing blue crab landings for periods of good water flow (green years).  When an isolated drought occurs (yellow years), crab landings usually remain stable without strong increases or decreases.  When droughts occur twice during a three year period (orange years), crab landings usually decline. When severe, prolonged drought occur (red years), crab landing decrease more rapidly and are less responsive to recovery when higher flows return. The forecast for the period of 2015 through 2023 suggests a gradual increase in landings as river flows continue to be above the critical minimum flow. However, the landings are expected to decrease with the arrival of next prolonged drought beginning in 2023.  By then river flows are expected to regularly be below the critical minimum flow, a condition where a sustainable blue crab population would be unlikely.

So is there anyway to test the validity of the model forecast?  We can compare how the model performed relative to the observed SC annual landings for blue crabs (black diamonds).  If the model is accurately predicting crab landings, the observed landings should fall within the range of values shown by the vertical error bars 67% of the time.  During the first ten years (1990-1999) the observed landings fell within this margin of error only 20% of the time with 80% of observed landings coming in higher than predicted.  This suggest that the model may be to harsh on crabs in elevated flow conditions which may not be as bad as low flow conditions.  During the second ten years (2000-2009) landings fell within the margin of error 90% of the time with observed landings coming in both higher and lower than predicted.  This suggests that the model may be more accurate when river flows are at or near the critical minimum flow.  Finally, in the most recent five years (2010-2014) the model failed to predict an unexpected dip followed by a three year rise in commercial landings that occurred during yellow and orange river flow conditions.  These results suggest that actual landings are much more variable year to year than the average of 100 runs of the model which minimizes severe changes from one year to the next.

Here are the entire range of model forecasts for 2015.

 

Mean forecast = 3.69

Median forecast = 3.67

67% range 2.90 - 4.48

95% range 2.11 - 5.28