VIEWS: 4 PAGES: 5 POSTED ON: 12/12/2011 Public Domain
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-