Background

Introduction

Numerous surface and upper-air instruments deployed during wintertime field studies appear to provide good coverage of the atmospheric phenomena such as eddies, low-level jets, upslope/downslope flows, etc., often observed in the San Joaquin Valley (SJV).  However, because some of these meteorological measurements were made at sites within complex terrain, they may not be representative of conditions away from the monitoring sites.  To evaluate whether the meteorological network resolved atmospheric phenomena, we developed a method for estimating the spatial “representativeness” of the surface and aloft meteorological measurements.

Representativeness

Representativeness has been defined in many ways.  Nappo defined representativeness as “the extent to which a set of measurements taken in a given space-time domain reflect the actual conditions in the same or different space-time domain taken on a scale appropriate for a specific application”  (Nappo et al., 1982).  The Glossary of Meteorology defines representativeness as “the property of an air mass that is typical of the air mass as a whole and thus may be used in air mass analysis.”   The Glossary of Meteorology further defines a representative meteorological observation as an observation considered valid for a more or less extended area around a point (station) where an observation is made  (American Meteorological Society, 2000).  These definitions are not objective.

For this study, we started with the Glossary of Meteorology’s definition for a representative meteorological observation.  We were interested in determining the area around an observation of wind speed and direction for which the observation was still valid. To find this area we made the following assumptions:

·                    Representativeness will be greater when terrain is uniform.

·                    Wind direction is expected to influence horizontal representativeness by stretching the horizontal influence based on the predominant wind direction.

·                    Wind speed is expected to influence horizontal representativeness by stretching the horizontal influence at large wind speeds.  Higher winds represent larger scale forcing and probably a larger zone of representativeness.

·                     Horizontal representativeness will generally increase with increasing height above the ground because the effects of surface friction and diurnal variations decrease with increasing height.

Approach

The zone of representativeness for a particular measurement depends on many factors.  We incorporated several factors into our determinations, including distance, elevation, slope of elevation, time of day, season, height above ground, average wind speed, and average wind direction.  After grouping the data by time, height, and season, we applied spatial analysis methods using Geographical Information Systems (GIS) software to calculate zones of representativeness.

Details

Data Preparation

Wind data were downloaded from the CCAQS database for the winter 2000-2001 season.  The wind data consisted of Level 1.0 2-m and 10-m surface data and radar wind profiler data for all sites within the SJV.  The wind data were averaged over the course of a season for each hour of the day. For aloft measurements, we further averaged the data into several atmospheric layers.  We produced a separate representativeness map for four layers, including the surface, at three different times of day for wintertime data. The layers are determined by looking at seasonal average diurnal wind profiles for each upper-air site.  The layers were determined based on diurnal changes in wind speed and wind direction, and significant changes in wind speed and wind direction with altitude.  Once the layers were selected, all sites were compared to determine if the layers were similar at each site.  In the first layer, from about 100 m up to about 800 m, differences in wind speed and direction were found to be due to mesoscale flows such as the sea breeze.  In general, above about 800 m, the wind speed and direction were found to be similar, with some diurnal variations.  Above about 1600 m, wind speed and direction were found to be similar at all sites, reflecting the synoptic-scale influence.

Spatial Analysis

To create a map of representativeness we used a GIS analysis method called cost weighted distance (CWD), or parameter-weighted distance (PWD).  This method relies on the assumption that confidence in the validity of a particular meteorological measurement decreases as one moves further away from the point of the measurement. 

If distance were the only factor to determine representativeness, we could use a simple straight line distance calculation. However, we included several other parameters that contribute to the "cost" in confidence of traveling away from the data source.  These parameters included terrain slope, wind direction, and wind speed.

Slope is a measure of elevation change.  The greater the slope between two points, the more likely they are to have dissimilar wind characteristics.  Slope can detect both changes in elevation and intervening topography between two points.

Wind direction plays a role.  Points directly downwind and upwind of the measurement site tend to be more similar than points perpendicular to the predominant wind direction.

Wind speed is important because high wind speeds are more likely to be valid a greater distance away from the measurement point than low wind speeds.

These parameters were taken into account by creating a "factor surface" for each.  For example, we calculated the terrain slope for each grid cell in the domain.  These slopes were classified into discrete values, ranging from 1 to 10.  A cell with near zero slope would have a slope factor of 1.  A factor surface was created for each of the three parameters.  See the methodology page for details.

The three parameters were then combined to form an overall factor surface.  This result was used to create the final PWD map that gives a measure of "representativeness."  At each point, the "distance" to the nearest site was calculated, where "distance" was not the actual geographic distance but the cumulative PWD to traverse from the measured data to the current point.  Thus, the value increased as the point moved away from the measurement site, increasing faster where the slope was high and not along the average wind direction, for example.

The lower the PWD value at any location, the greater the confidence we have that the values measured at a nearby meteorological site is representative of the current location.

Tuning Parameter Weights

All parameters were combined to form the overall “factor surface.”  Each parameter was weighted differently.  In order to select the best combination of weights, a program was written that cycles through many combinations of different parameters and calculates the PWD. At each site where wind data were available, these data were withheld and the PWD was calculated to the nearest available site along with the differences in wind speed and wind direction between the withheld data and the nearest site data. 

With properly tuned parameter weights, site pairs with a low PWD should have similar wind speeds and directions.   The best parameter weight combination was defined as the combination that minimized the wind speed and wind direction differences at the lowest PWD.

Theoretically, at a PWD of zero, the difference between two wind measurements should be zero because the locations are identical.  As the factor-weighted distance increases, the difference in wind measurements can also increase.  Finally, after some distance, there is no relationship between two measurements.  For our test data set, there was spatial correlation for the closest 33% of data pairs and no relationship afterwards. The algorithm for determining the best fit parameters is described on the methodology page.  The best fit parameters maximized the chances that cells assigned a low PWD had wind characteristics similar to the observed values they were allocated to, i.e. the lower the PWD, the more representative the nearby site was of the actual unknown value at the location of interest.

Representativeness Index

Once the best fit parameters for a particular data set (season, time of day, layer height) were found, the final PWD was calculated.  We classified all PWD values into a “Representativeness Index” to make the results understandable and useful.  The criteria used to perform this classification are described on the methodology page.

References