1. INTRODUCTION
The ability to simulate historical and climate conditions by using a numerical model has been developed. Extensive research sponsored by the DOD has been conducted over the past three years to develop a method of using a deterministic limited-area high-resolution numerical model to generate local climate statistics around the globe. This method, as described by Zack et al. 1996, was developed to address the limitations of both the use of long-term observational datasets and the probabilistic methods based on statistical relationships.
The numerical model approach to generating local climate statistics involves determining local climate from a set of long period mesoscale simulations. The goal is to simulate the actual climate statistics for a particular period of time over a specified region. This technique has been given the name CLImate statistics by a dynamical MODel (CLIMOD)
The issues of the quality of results, impact of model resolution, historical data assimilation, convective parameterization schemes, planetary boundary layer formulation, observed surface and upper air data availability and "warm" versus "cold" model starts are discussed in previous papers (Van Knowe et al. 1999, 2000 Doggett 2000, and Doggett et al. 1999).
This paper examines a method developed to utilize the knowledge gained from available observations to remove model bias.
2. MODEL CONFIGURATION
The simulation model used in CLIMOD is based on a deterministic numerical atmospheric mesoscale model called the Mesoscale Atmospheric Simulation System (MASS) (Kaplan et al. 1982; MESO 1995; Manobianco et al. 1996). For this research, MASS version 5.11 was used. Hydrostatic formulations of MASS were utilized in the studies. Unless otherwise noted, all the experiments used a baseline configuration of the Blackadar PBL scheme, a modified Kuo cumulus parameterization and 24-hour discontinuous data assimilation. All the surface model values used in the experiments were reduced to the 2-meter model level. The specific features of the MASS model are described in the MASS Reference Manual (MESO 1995).
3.
METHODOLOGY OF BLENDING
It has been determined that a method to reduce the bias in the simulated surface climatological database was needed. In an attempt to achieve this aim, a post-simulation method has been developed to "blend" observations and model generated data. The objective is to develop a method that will yield a single seamless and consistent database in such a way that the simulated statistics surrounding sites where observed data is available closely reflect the observed data. The blending of the observed and simulated data may seem to be somewhat redundant since the intention is to assimilate all or most of the available observed data into the model simulations. Thus, the model-generated database will already be a type of blend between the observational data and the model physics. However, the model is capable of simulating only a portion of the variance of each parameter because it cannot simulate atmospheric features that are below the resolvable scale of the model grid.
The basic methodology of CLIMOD involves initialization of the model with large-scale gridded data fields. The model then uses the large-scale gridded data fields and lateral boundary conditions and periodically ingests the available observed data through one of several possible data assimilation techniques (Newtonian relaxation periodic reanalysis, etc.). Next, the model dynamically fuses the available observations with its knowledge of the surface characteristics of the earth and the basic principles of physics to generate estimates of local climate statistics at locations for which no observational data is available.
The evaluation
of CLIMOD results has shown considerable success, but there is always some
model bias introduced into the simulated climatologies. The technique for removing model biases
addressed in this paper involves the use of observed climatologies. From the biases identified between the model
and observed climatologies, a correction factor is calculated and employed
through a weighted interpolation technique.
The formulation of the blending method is based on the principle that the statistical database should be heavily influenced by the observational data near the actual observing sites and blend smoothly into the model statistics away from observational data sites.
The blending procedure uses a weighted average of model and observational data. The weights depend upon the spatial statistics of each variable. In complex terrain, the weights will be smaller than in more uniform terrain regions. In the areas of more uniform terrain, the extent of the area of high spatial correlation will be larger and therefore allow a greater impact of observational data on the simulated data.
The
formulation of the blending method is based on the principle that the final
simulated statistical database should be heavily influenced by the observational
data near the actual observing sites and blend smoothly into the model
statistics away from observational data sites.
The final composite climatology should also contain the full
distribution of data, not just means and variances, so that a large suite of
statistical parameters can be obtained.
The blending
procedure uses a weighted average of model and observational data. The weights depend upon the spatial
statistics of each variable. In some
regions, and in some directions, the extent of the region of high spatial
correlation will be larger. In these
cases the impact of the observational data will likewise reach further. The spatial correlation depends on a variety
of factors including the terrain, the atmospheric dynamics, and the time of
year. An estimate of the spatial
correlation is obtained by inter-comparing the large grid simulations, the
nested grid simulations and observational data where available.
3.1
Results of Method Investigation
Results from
Saint Louis University's (SLU) evaluation determined there are four distinct
methods to blend or composite the observed data. All are based fundamentally on some form of distant weighting
from the observed site. The difference
in the methods is in the way that the autocorrelation function relating the
distance and the weight is determined.
The four methods are:
(1) Imposed Autocorrelation. The distance autocorrelation is calculated
based on derived relationships and reasonable meteorological assumptions
associated with such factors as terrain, slope and proximity to water.
(2) Observation Derived Autocorrelation: The autocorrelation function is calculated
based upon the relationship found between observed sites. The major disadvantage is the lack of a
sufficient density of sites.
(2) Model Derived Autocorrelation: The autocorrelation function is calculated
based upon the relationship found between model grid points. The advantage is there is adequate grid
coverage. The disadvantage is the
method will increase computational requirements.
(4) A Composite Autocorrelation: This uses a blend of the three
methods. It is likely that this would
produce the best method, but will require more research beyond the scope of
this project.
The decision was made to proceed with the imposed autocorrelation method for several reasons. This method requires the least amount of computational power and produces acceptable results. The second method using the observed derived autocorrelation was also developed. This method follows an Optimal Interpolation (OI) framework and potentially has more flexibility than the first method. However, there are more difficulties with this method, which has lead to more uncertainties in the final blended products. This method is also much more computationally intensive than the first method. This is an area where further improvements could probably be made with additional research.
Analysis of model results indicates that the model statistics differ by only a small amount so that the blending should only make small adjustments. However, quantifying the differences in blending algorithms is an area where further improvements could probably be made to the method with additional research.
3.2 Description of the Methods
The first step
in formulating the blending algorithm is to determine the weights for the model
and blended observational data. The
blended value is related to the model and observations by
where i refers to the grid point, j refers to the station location, Ti represents the variable to be blended at the grid point i (in this case temperature, but any variable could be substituted), w is the weight given to the model and observations at each respective grid point, and the superscripts B, M, and Obs denote the blended, model and observational data respectively. The weights are obtained by solving the standard system of equations associated with a particular algorithm.
With the Imposed Autocorrelation the weights were determined by the variation in the terrain from the observing site to the center of the grid point under consideration. In particular, the weights are proportional to
where r is the distance from the observation point to the grid point, R and D0 are scale factors which act to “control” the reach of the observational data, and D is the variance of the terrain along the great circle path from the grid point to the observation. It is defined as:
where h is the height of the terrain and <h> is the average height along the path.
The weight for the model value (at the grid point) is determined by the condition
This method allows the weights to be determined once (same weights are used for each variable) and results indicate the improvement is mainly in the large-scale biases. As such, it was found to be best applied to the statistical quantities (i.e. means) rather than individual simulation times.
The second method used to blend the observations with the model makes use of
observational autocorrelations. This
optimal interpolation scheme determines weights from the following equation
where P(rij) is the error correlation between site i and site j (as determined by observations) and P(r0j) is the error correlation between site j and the model grid point. P(r0j) is determined by spatially interpolating the P(rij). This approach differs only slightly from tradition OI schemes in that long-term biases are not assumed to be zero (or removed).
This method is more suitable to blending the individual time periods rather than blending the averages as mentioned above. The OI framework acts to minimize variability between the model and observations and not simply remove biases. Several additional difficulties were found to occur when applying this method to spotty data. If, for example, the weights are determined based on the statistics of ten stations, but only seven reports are available at a particular time, the blending of those seven stations can be biased. Consequently, only stations with reliable records can be used.
Both of these blending algorithms were applied to one month of January simulations for upstate New York. The differences in the resulting statistics were quite small and the differences between the blended and original model statistics were also quite small. Most of the changes appeared to be bias corrections in the neighborhood of observational data.
4. RESULTS
The method is now being tested for operational use. Figures 1 and 2 show an example of pre-blended and post-blended temperature grid for Korea. Early results for the combined average temperature at three representative stations, Osan AB (47122), Hoengsong AB (47118) and Taegu AB (471420) Osan AB, Korea are shown in Table 1.
Fig. 1: Pre-blended surface temperature
Fig. 2. Blended Surface temperature
There are both positive and negative influences of blending. If observational point climatological data is available over a region of interest, blending observed climatologies into the simulated climatological grids can reduce model bias. However, this technique must be used with caution and should not be used if the point observation site is not representative of surrounding region.
Table 1. Comparison of observed, simulated, and blended temperature
statistics
|
Data Blending Experiments by Month Temperature (T) °F |
||||||
|
Data Source |
Avg T |
Avg Max T |
Avg Min T |
|||
|
Jan |
Jul |
Jan |
Jul |
Jan |
Jul |
|
|
Observed |
25.6 |
74.2 |
33.1 |
79.2 |
18.9 |
70.1 |
|
A |
24.9 |
76.3 |
31.1 |
82.3 |
18.8 |
71.8 |
|
Blended |
25.2 |
75.0 |
32.1 |
80.9 |
18.9 |
70.5 |
|
D |
18.2 |
80.3 |
23.7 |
91.2 |
10.0 |
73.9 |
In general the blending technique should not be used if point observation site is not representative of surrounding region. In such cases, the simulated climatologies are often more representative of the surrounding grid boxes than the observed location. In desert locations, observation sites are most often in urban areas that are more humid than the surrounding region because of human activities. Also it may be of limited use in complex terrain regions such as mountains and coastal regions. The AF Combat Climatology Center performed a limited desert temperature and dewpoint study comparing the model results with special data sets of urban and rural desert regions of Saudi Arabia, Egypt and Nevada (Thompson, 1999). The study found that the mean dewpoint difference between the Urban and Rural desert locations (Dewpoint Urban - Dewpoint Rural). was approximate 5.4 degrees F.
5. SUMMARY AND CONCLUSIONS
If observational point climatological data is available, blending of observed climatologies can effectively reduce the model bias surrounding the observed point if the point is representative of the surrounding regions surface type. However, the technique can actually decrease quality of climatologies if the surface characteristics at the observed stations are not representative of the region’s surface characteristics.
6. ACKNOWLEDGMENTS
This work has been supported by the Department of Defense Modeling and Simulation Organization's Air and Space Natural Environment Modeling and Simulation Executive Agency under Air Force Research Lab contract number F19628-97-C-0025.
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