Methodology

 

·        Data Selection/Data Acquisition

·        Data Averaging

·        Analysis Grid Creation

·        Parameter-Weighted Distance Calculation

·        Parameter Preparation

·        Parameter Weight Tuning

·        Representativeness Index Calculation

 

Introduction

This page details the methodology used to create the representativeness maps.  Figure 1 is a schematic diagram of the process.

 

Figure 1.  Process flow diagram for representativeness calculation

 

Data Selection/Data Acquisition

Surface Meteorology

Wind speed and direction data were queried and downloaded from the Central California Air Quality Studies (CCAQS) database.  All hourly and hourly averaged data from 2-m and 10-m towers within the domain with valid QC flags (V2 – valid estimated value, VH – valid hourly data, V0 – valid value) were selected and imported into a local database.  For the few areas with both 10-m and 2-m data, only the 10-m data were used.  Site locations are shown in Figure 2.

Figure 2.  2-m and 10-m meteorological tower sites used in the analysis

           

Upper-air Meteorology

Aloft wind data were downloaded from the CCAQS database.  All hourly averaged data from radar wind profilers within the domain with valid QC flags were selected and imported into a database.  Figure 3 shows the locations of these profilers.  These data were grouped into 50-m bins.

Figure 3.  Wind profiler locations

Elevation

Elevation data were compiled for the domain from USGS digital elevation maps.

 

 

Data Averaging

Surface Data

Surface wind data were grouped and averaged by season and time of day.  For this study, we focused on winter, defined as November through February.   Three time-of-day averages were created, morning (6:00 a.m. to 11:00 a.m.) afternoon (12:00 p.m. to 5:00 p.m.) and night (6:00 p.m. to 6:00 a.m.).  All times were in Pacific Standard Time.

 

Upper-air Data

The binned upper-air wind data were averaged using the same scheme as the surface data.  This produced diurnal vertical profiles. Time-height cross sections of these profiles, such as that shown in Figure 4, were created for each site. Layers were subjectively determined by examining the time-height cross-sections.   Generally, three layers were identified:

1.      Boundary layer winds, characterized by diurnal fluctuations in wind speed and direction.

2.      Mid-boundary layer winds, characterized by a less dramatic diurnal shift in wind speed and direction.

3.      Synoptic layer winds, characterized by a more uniform wind speed and direction typical of synoptic scale high and low pressure systems.

 

Layer	Height (above ground level)
Layer 1	100 – 800 m
Layer 2	800 – 1600 m
Layer 3	> 1600 m

 

Figure 4.  Time-height cross-section of Richmond station with layer boundaries drawn

 

Elevation Data

USGS digital elevation maps were available at 30-m resolution.  Because this resolution was much higher than necessary for this analysis, we reduced the resolution to 300 m.

 

Analysis Grid Creation

An analysis grid was defined over the entire domain shown in Figure 5, with a nominal grid cell size of 2 km².  All spatial analysis was performed using ESRI’s ArcGIS® software.

Figure 5.  Domain used in the analysis (shown in blue)

 

Parameter-Weighted Distance Calculation

The likelihood that a particular grid cell a will have meteorology data similar to data from an observation site at grid cell b is dependant on the data parameter values in the grid cells between a and b.  In our analysis the parameters were wind speed, elevation, elevation slope, and wind direction difference angle.  The processing described below resulted in a grid of classified values for each parameter that ranged from 1 to 10.  These grids were combined to create a single factor at each grid cell.  We call this the overall factor grid.  This factor represents the “cost” in terms of representativeness of traveling across the cell, relative to other cells.  With the overall factor grid, we calculated the parameter-weighted distance (PWD) from each grid cell to the “nearest” meteorology observation site. This calculation also determines the site allocation boundaries.  The PWD is determined not by geographic distance but by calculating the cumulative representativeness cost to traverse from the grid cell to the observation site along the “least cost” path.  This is not necessarily a straight line.  A small PWD at a grid cell means that the wind speed and direction are more likely to be similar to the allocated observation data than a cell with a larger PWD.

 

Surface and Layer 1

For the Surface and Layer 1 data, three factor grids (classified slope, wind speed, and wind direction) were combined to create the overall factor grid, F.

 

 

Each of the three factors were weighted differently for each layer and averaging period.  The weights, a, were determined using a weight-tuning process described below.

           

Layer 2 and Layer 3

For these layers, the overall factor grid consisted of the classified elevation grid only.

 

 

Parameter Preparation

The PWD we used required a combination of different parameters together to create a single overall factor at each grid cell.  In order to combine our parameters, we gridded the data using the analysis grid and reclassified all values to integers from 1 to 10.  The four parameters we used were elevation slope, wind speed, wind direction difference angle, and elevation.

 

Elevation Slope

Slope calculations were performed on the 300-m elevation maps using ArcView Spatial Analyst.  The resulting slopes were then reclassified to a scale of 1 to 10 using “natural breaks,” an algorithm that groups values on the basis of least variance within class and maximum variance between the classes.  This method divides the data into natural clusters of values. The resulting classified slope grid is shown in Figure 6.

Figure 6.  Elevation Slope Classes

 

Wind Speed

Each cell in the analysis grid was assigned the average wind speed of the nearest measurement site. These values were then reclassified based on a scale of 1 to 10.  The highest wind speed was given a value of 1 and the lowest a value of 10.  All values in between were divided into equal-sized subranges.  The resulting classified wind speed grid is shown in Figure 7.

Figure 7.  Classified wind speed grid for the surface data winter afternoon averaging period

           

Wind Direction Difference Angle

For each cell in the analysis grid we calculated the smallest angle between the average wind direction at the nearest measurement site and the direction to that site (see Figure 8).  We called this the wind direction difference angle.  Note that this angle ranges from 0 – 90°.

 

Figure 8.  Wind direction difference angle

 

These values were then reclassified.  Ultimately, grid cells along the direction of the wind have a shorter PWD than those perpendicular to the average wind.  This is true especially in canyons, where the wind flow is restricted to channels.  Figure 9 shows an example of a classified wind direction difference angle grid.

                       

Difference Angle (degrees)	Class
0-10	1
11-20	2
21-40	3
41-60	4
61-80	5
81-90	6

Figure 9.  Classified wind direction difference angle for surface data winter afternoon averaging period

 

Elevation

For the upper two layers (Layer 2 and Layer 3), elevation was used as a parameter in place of slope. The elevation values were classified as shown in the table.

                       

Layer	Height (m)	Value
2 (800 – 1600 m)	-80 – 800	1
2	801 – 1600	10
2	> 1600	15
3 (> 1600 m)	-80 – 1700	1
3	1701 – 3400	10
3	> 3400	15

 

 

Parameter-Weight Tuning

For each time of day for the surface and first layer, the parameters were tuned so that station pairs with similar wind data had smaller PWDs than station pairs with relatively dissimilar data.  The optimum parameter weights, a, were calculated programmatically.  The program cycled through many different parameter-weight combinations and calculated PWDs.  For each station location, the PWD to the nearest station was calculated, along with the differences in wind speed and wind direction.  Example program output is shown in the table below.

 

Slope weight	Wind speed weight	Wind direction weight	Site 1	Site 2	Wind speed difference	Wind direction difference	PWD
0.2	0.2	0.6	ABU10MH	BRVA2MH	0.1495	29.51	276031
0.2	0.3	0.5	ABU10MH	BRVA2MH	0.1495	29.51	294410
0.2	0.4	0.4	ABU10MH	NIC2MH	0.4575	68.23	561002

 

With this information, the best parameter-weight combination was found by doing the following for each combination:

1.      Find the PWD value that encompasses 33 % of the site pairs.  This is defined as the cutoff value, CV.

2.      Define the error weight (EW) by the function:

 

 

3.      Calculate the total error as the sum of Diff*EW for all data pairs, where Diff is the difference between the two measurements.  Do this for both wind speed and wind direction.

 

The total error for each parameter-weight combination was then ranked from lowest to highest for both wind speed and wind direction.  The combination that produced the lowest total sum of the two ranks was chosen as the best fit.

 

Representativeness Index Calculation

Once the optimum parameter weights were found, the final PWD was calculated for each grid cell.  Each grid cell was allocated to the “nearest” tower site in terms of PWD.  This site was not necessarily the nearest in terms of geographic distance.  The grid cells were finally assigned an Index of Representativeness, which was determined by using the data collected from the parameter-weight tuning program.  Site pairs were ordered by increasing PWD.  Then we determined if the site pairs had “similar” meteorological data over the averaging period, where similar was defined as average wind speeds within 0.5 m/s and average wind direction within 90° of each other.  The cumulative fraction of “similar” site pairs was then plotted as a function of PWD.  Figure 10 shows that as the PWD increases, sites are less likely to be similar to each other.  We used this plot to set the boundaries of the Representativeness Indices.  All grid cells with PWD less than the value at which 50% of site pairs were similar were given a Representativeness Index (RI) of 1–“most representative.”  Grid cells with PWD greater than the first bin and less than the value at which 35% of site pairs were similar were given an RI of 2–“less representative.”  All grid cells with a greater PWD were assigned an RI of 3–“not representative.”

 

Figure 10.  Representativeness plot for surface data winter morning averaging period