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					                                     PRISM Single-Cell Operation
                                                                        and
                                       Message Box Interpretation



When PRISM is clicked on a cell, the message box displays a detailed account of the functions and
decisions that lead up to the final prediction. The following discussion of this account is filled with links to
the online manual.

Note: Where applicable, numerical values are given in PRISM internal units


                                                               Table of Contents

Preliminary Information .............................................................................................................................. 2
Time-Independent Station Weighting ....................................................................................................... 2
Regression Situation .................................................................................................................................. 2
Monthly Messages ...................................................................................................................................... 2
  Time-Dependent Station Weighting .......................................................................................................... 2
     Initial Facet Weighting ........................................................................................................................... 3
     Initial Layer Weighting ........................................................................................................................... 3
     Final Facet Weighting............................................................................................................................ 3
     Final Layer Weighting............................................................................................................................ 4
  Station Information .................................................................................................................................... 4
  Regression Calculations ........................................................................................................................... 5
  Prediction Messages ................................................................................................................................. 5




Current as of: 12/12/11
Preliminary Information
    At the top of the message box, PRISM displays the location of the cell in map and cell units, and
    its elevation. Also shown are the Radius of Influence, Maximum Facet Barrier, the cell's inversion
    height (either from the Mask/Inversion Ht Grid or the Domain - Wide Inversion Height), and its
    vertical layer (1 = below inversion height, 2 = above inversion height).

    The next two lines describe the results of PRISM's search for the Minimum Number of Stations
    on Facet. The facet level at which the station accumulation stopped (see Facet Smoothing Levels
    Used), and the cell orientation at this level, are given. This is followed by the actual number of
    stations accrued on the cell's facet, the Minimum Number of Stations on Facet sought by the user,
    and the total number in the regression.

Time-Independent Station Weighting
    PRISM performs time-independent station weighting functions before entering into the monthly
    loop. These include cluster, distance, and elevation weighting. Cluster Weighting seeks to
    compensate for inhomogeneities in the spatial distribution of stations across the modeling domain.
    Those grouped with other stations within the minimum cluster radius specified here are
    downweighted severely; those grouped within the maximum radius specified are downweighted
    less severely. These cluster radius limits are scale-dependent, based on percentages of the
    distance at which the furthest station lies (usually slightly less than the radius of influence).
    Distance Weighting and Elevation Weighting are then performed on the cluster-weighted stations
    using the listed exponents. Applying the respective weighting importance factors, distance and
    elevation weights are then combined and normalized to unity (see Station Weighting Exponents
    for equation). The end result is a station dataset weighted for the time-independent factors of
    clustering, distance, and elevation.

Regression Situation
    PRISM now considers the number of stations in layers 1 and 2 to determine how the regression
    should be run. The regression situation is coded as a case number with an absolute value
    between 1 and 5; negative cases indicate that the grid cell falls into layer 1, the case is positive
    for cells in layer 2. The case is followed by a brief description of the action that will be taken.
    Further explanations of regression cases are located in Regression Case Descriptions.

Monthly Messages
    Messages written from here to the end of the PRISM report are repeated for each of the Months
    to Model. PRISM does time-dependent weighting, displays station information, runs regression
    statistics, and reports the prediction after any final adjustments.

    Time-Dependent Station Weighting
            Time-dependent weighting consists of facet and layer weighting. Unlike cluster, distance,
            and elevation weighting, which have fixed exponents, the user may allow PRISM to vary
            the facet and layer weighting exponents based on an assessment of the station
            observations in that month. In this case, the weighting exponent set by the user becomes
            the maximum that can be invoked. For example, if the facet exponent is set to a relatively
            high maximum value, but PRISM determines that there is relatively little difference in
            climatic regime among facets near the grid cell that month, the facet weighting exponent
            is reduced significantly. Note that PRISM does not determine the actual value of the
            exponent, just a reduction factor on the maximum value set by the user. This value is the
            greatest weighting exponent the user feels is necessary to reproduce the sharpest
            climatic gradients in the modeling domain.


                                             Messages
                                               -2-
Facet and layer weighting are done in an iterative fashion, because results from the
weighting calculations affect one another.

Initial Facet Weighting
        If the facet weighting exponent is allowed to vary, it is initially set to one half of
        the maximum value specified in the control file. This is done temporarily to allow
        an initial layer weighting calculation. If the facet weighting exponent is fixed, the
        exponent is left as-is.

Initial Layer Weighting
        If the layer weighting exponent is fixed, the exponent is left as-is. If it is allowed to
        vary, PRISM first checks to see if there are enough stations in each vertical layer
        to warrant the calculation of a modified layer weighting exponent. If there are less
        than three stations per layer, the layer weighting exponent is set to a default
        value of one half the maximum value specified in the control file.
        If at least three stations are available in each layer, PRISM determines by how
        much the maximum exponent should be reduced. PRISM runs a weighted
        parameter-elevation regression ONLY for stations in the present layer (the layer
        in which the grid cell resides). Stations are weighted by the time-independent
        factors, plus topographic facet, using the initial exponent value discussed above.
        If the P/E slope does not meet the validity criteria set out in the Layer 1 P/E
        Slopes or Layer 2 P/E Slopes (depending on the present layer), the layer
        weighting exponent is set to a default value of one half the maximum value
        specified in the control file and the routine exited.
        If the slope is valid, the standard deviation of the residuals around the regression
        line (termed factor1 in the message box) is calculated. PRISM then calculates
        the standard deviation of residuals for stations in the other layer around the
        present layer line (termed factor2 in the message box). If factor2 is much greater
        than factor1, stations in the other layer do not match the present layer P/E trends
        well, and are probably within a different climatic regime. If factor2 is less than or
        equal to factor1, the two layers probably represent the same regime and can be
        safely combined. The ratio 1 - (factor1/factor2) represents the factor by which the
        maximum layer weighting exponent is multiplied to obtain the new layer exponent.
        This exponent is used to obtain initial layer weights for each station, which are
        then combined with the time-independent weights.

Final Facet Weighting
        If the facet weighting exponent is fixed, the exponent is left as-is. If it is allowed to
        vary, PRISM first checks to see if there are enough stations off and on the facet
        to warrant the calculation of a modified facet weighting exponent. If there are not
        at least one station off the facet and one station on the facet, the facet weighting
        exponent is set to a default value of one half the maximum value specified in the
        control file.
        If the station criteria are met, PRISM determines how much the maximum
        exponent should be reduced. PRISM runs a weighted parameter-elevation
        regression ONLY for stations on-facet (the facet on which the grid cell resides).
        Stations are weighted by the time-independent factors, plus the initial layer
        weighting discussed above. If the P/E slope does not meet the validity criteria set
        out in the Layer 1 P/E Slopes or Layer 2 P/E Slopes (depending on the present
        layer), the P/E slope is set to the default slope and the process continues. The
        P/E slope is also set to the default when the number of stations on facet is less
        than the Minimum Number of Stations on Facet, which implies that an insufficient
        number of on-facet stations exist to produce a viable P/E regression.



                                 Messages
                                   -3-
             The range of residuals around the regression line is calculated and compared to
             the Max Facet Parameter Variability allowed. If the range of residuals exceeds
             the maximum, sub-facet grouping is invoked until the variability is reduced to
             below the maximum or the Minimum Number of Stations on Facet is reached.
             The P/E regression using on-facet stations is rerun to obtain new slope and
             residual statistics each time a station is moved off-facet during sub-facet
             grouping.

             The standard deviation of residuals around the on-facet regression line (termed
             factor1 in the message box) is calculated. PRISM then calculates the standard
             deviation of residuals for off-facet stations around the on-facet line (termed
             factor2 in the message box). If factor2 is much greater than factor1, off-facet
             stations do not match the on-facet P/E trends well, and are probably within a
             different climatic regime. If factor2 is less than or equal to factor1, the various
             facets probably represent the same regime and can be safely combined. The
             ratio 1 - (factor1/factor2) represents the factor by which the maximum facet
             weighting exponent is multiplied to obtain the new facet exponent. This exponent
             is used to obtain final facet weights for each station, which are then combined
             with the time-independent weights.

     Final Layer Weighting
             With final facet weighting in place, PRISM enters the layer weighting scheme for
             the final time. Calculation of a modified layer weighting exponent is repeated in
             exactly the same way as before. If the exponent is fixed, it is left as-is.

Station Information
     PRISM displays a table of diagnostic information about the stations used in the
     regression calculations. Due to space constraints, only the nearest twenty stations are
     listed. "Sta ID" is the station ID string as it appears in the station data file. "Mo n val" is
     the observed value of the climate parameter for month n (1-12; 13=annual). "Elev" is the
     elevation (m) used by PRISM in the regression calculations (see Max DEM-Station
     Elevation Diff for details and further links on elevation). "Inv ht" (inversion height) is the
     height of the boundary between layers 1 and 2 at the station location. "X-coor" and "y-
     coor" are the station coordinates in grid cell units. "Distance" is the distance between the
     station and the modeled grid cell in cell units. "Smth lvl" is the facet smoothing level at
     which the station was accepted into the regression data set. "Sta Orn" and "Cell Orn" are
     the station and cell facet orientations at the above smoothing level, respectively. 1=WNW,
     2=WSW, 3=SSW, 4=SSE, 5=ESE, 6=ENE, 7=NNE, 8=NNW, and 9=flat. "Fac diff" is the
     difference in orientation between the cell and the station, given in categories.

     Station weights are given next. "Clusterwt" is the weight given to account for station
     clustering. A value of 1.0 indicates the station was not perceived to be clustered with
     other stations. "Dist wt" and "Elev wt" are the distance and elevation weights, respectively,
     each normalized so that the weights sum to unity. "Facet wt" and "Layer wt" are the facet
     and layer weights, respectively. A station with a facet orientation difference of one
     category or less from the grid cell will have a facet weight of 1.0. Stations in the same
     vertical layer as the grid cell will have a layer weight of 1.0. "Total wt" is the final
     combined weight that enters into the regression calculations, normalized so that the
     weights sum to unity.




                                      Messages
                                        -4-
Regression Calculations
     The next section reports on the parameter-elevation regression calculations as they are
     performed. The slope of the P/E line is given, along with minimum and maximum
     allowable P/E slopes from the control file. If the slope does not fall between the minimum
     and maximum, the station deletion routine is invoked in an attempt to omit an outlier
     station that is producing the invalid slope. Starting with the station with the smallest total
     weight and moving towards progressively greater weights, PRISM omits stations one by
     one, recalculating the P/E regression line each time. Station deletion ceases when either
     (1) the P/E slope falls between the minimum and maximum P/E slopes, or (2) the number
     of stations left in the regression dataset reaches the Minimum Number of Stations in
     Regression. If the station limit is reached before the P/E slope becomes valid, the slope
     is set to the default slope.

     Regression statistics are listed, including the R2, y-intercept, slope, slope normalized by
     the mean parameter value in the regression dataset, the weighted mean x and y values,
     and the prediction variance. The prediction variance is valid only if the regression had a
     valid slope.

Prediction Messages
     PRISM then makes its predictions of the parameter value at the grid cell for that month.
     These predictions are referred to as "raw" or "unpolished" because they may be altered
     during post-processing in POLISH. If a Regression Type involving weighted residuals
     was chosen, the modification of the predicted value by the weighted residuals is shown if
     the regression had a valid slope. If a Diagnostic Grid parameter was chosen, the value is
     given. The prediction interval is valid only if the regression had a valid slope.




                                      Messages
                                        -5-

				
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posted:12/12/2011
language:English
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