Abstract:
A system and method are disclosed for forecasting probability of precipitation values and most probable precipitation amount values for, preferably, three hour time period increments starting from the present hour through approximately hour 96 (i.e., four days) or beyond. The values are recalculated at the beginning of each hour, based upon existing forecasting information and meteorological data. The values are communicated to end users through a communications channel such as the Internet.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of Invention 
   The present invention relates to systems for forecasting and communicating meteorological information, and in particular, to systems for producing multi-period probability of precipitation (POP) forecasts and disseminating the same through communications channels including, but not limited to the Internet, wireless devices, and broadcast systems. 
   2. Description of the Prior Art 
   The present invention was developed primarily in response to the need for enhanced weather information based on probability forecasts, a need recognized by members of The American Meteorological Society (AMS) in a 2002 Statement. 
   According to the AMS, weather forecasts have improved dramatically over the past two decades. In fact, forecasts produced by operational forecasters using meteorological observation data and forecasts produced by numerical models have become more accurate for nearly all weather elements and for most time and space scales of interest. Those forecasts contribute important information to decision makers and are valuable to a multitude of users, including the general public, the military, aircraft operators, businesses, and emergency managers, to name a few. 
   Progress has also been observed in developing accurate probability forecasts, which have a significant economic benefit because a sizable portion of the U.S. economy is weather sensitive. That progress has been important because POP forecasts (the percentage chance that a measurable amount of precipitation (at least 0.01 inches of rain or ice or 0.1 inches of snow) will fall at a specific location during a specific time period) are well accepted by many end users, including the general public. 
   Probability forecasts also have several benefits over categorical forecasts. One benefit is that they contain more information: the uncertainty in the forecast is expressed as part of the forecast. Thus, the end user is made aware of the uncertainty in the forecast and can use that additional information in making decisions. However, not all end users understand the information provided by probability forecasts or the meteorological event being represented by the forecasts. In its simplest terms, most people understand what is meant by the probability of an event occurring, such as the probability of obtaining “heads” when flipping a coin. What is significantly less intuitive to end users of POP forecasts is what is meant by a forecast that says “there is a 30% POP for State College, Pa., tomorrow.” Often, that forecast is interpreted ostensibly as meaning that it will rain over 30% of the State College, Pa., area tomorrow or there is a 30% chance it will rain somewhere in the immediate region tomorrow. Other combinations of those and other interpretations are also likely. Thus, while quantitative precipitation forecasts have become more accurate, have advantages over categorical forecasts, are generally accepted by the general public, and are relatively simple in terms of the information provided, they are, by their very nature, rather complex. 
   To simplify the complexity, according to the AMS, a POP forecast should provide a probability of any desired amount, say 0.5 to 1.0 inches of precipitation, for any desired time interval. Until the present invention, POP forecasts have been issued for periods of 24, 12 or six hours, starting at a preset, fixed time, such as 7 am, and this time would not change dynamically. Those intervals are too long to provide sufficient detail as to when precipitation might occur and when it is most likely to occur. Shorter intervals, such as three hours, would be significantly better in terms of accuracy. The problem with shorter intervals, however, is that simply dividing the longer period into shorter intervals can result in inaccurate or even meaningless forecasts. For example, given a probability of precipitation for a 6-hour period (POP-6) of 60%, simply dividing the POP-6 hours into two three-hour intervals and calculating POP-3 values based on the data for those hours may not accurately represent the probability of forecast for the two intervals. In fact, as the time interval for the POP gets shorter, eventually it becomes physically impossible to have enough precipitation fall to qualify under the definition of a measurable amount. A more robust computational method is needed to generate accurate probability of precipitation values for periods shorter than 6 hours. 
   Another problem with current systems is that once the preset starting time for a period has passed (i.e., the starting time for the POP for the two 12-hour periods beginning at 7 am-7 pm), the POP time periods would not move with the clock. That means that at, for example, 9 am, the POP forecast available would be for the 7 am-7 pm period (or possibly the remainder of that period) and for 7 pm-7 am, rather than 9 am-9 pm and 9 pm-9 am time periods. Further, once 0.01 inch of precipitation has fallen, the probability of precipitation would by definition be 100% for the period. Thus, a probability of precipitation that does not reset every hour during precipitation would tell the user nothing about the future weather, and would therefore be of no value. In addition, a probability of precipitation that is less than 100% and does not reset during precipitation, would be inconsistent with the weather that has occurred and the definition of POP, and therefore inaccurate and confusing. Accordingly, probability of precipitation forecasts that reset to the present time would also be better in terms of accuracy and usefulness. 
   U.S. Pat. No. 6,424,917, for example, discloses a system and method for spatial synoptic classification using “sliding seed days” as model inputs rather than fixed time periods. That method is disclosed as being advantageous in terms of forecasting synoptic conditions. 
   To also simplify the complexity of probability forecasts, according to the AMS, there should be new ways for displaying and communicating the probabilistic information compared to those presently available. The National Weather Service (NWS), operating under the auspices of the National Oceanic and Atmospheric Administration (NOAA), has recently been experimenting with communicating probability forecast information to various interested parties. Called a graphical forecast, the NWS chose a graphical (map) approach for displaying information on its web site that may be accessed over the Internet. The information available for displaying is generated and maintained in NOAA&#39;s National Digital Forecast Database, and includes POP-12 data (the percentage chance that a measurable amount of precipitation (at least 0.01 inches of rain or ice or 0.1 inches of snow) will fall at a specific location during a 12-hour time period). However, even on the NWS&#39;s “Experimental Products” web site, they do not offer any POP forecasts for less than 6 hours nor do they offer any POP forecasts that are not for pre-set, non-rolling time periods. 
   Commercial companies also use their web pages for providing weather-related information, but other communication channels have also been used, such as electronic mail over the Internet and facsimile, as in the case of “E-Weather,” which is provided to users by SkyBit, Inc. The “E-Weather” data may be in the form of a table array (3-hour time period increments along the top of the table and weather parameters (e.g., temperature, humidity, POP-6, etc.) along the left edge of the table). It is significant to note that even in this table array, although most data is presented in 3-hour increments, the POP forecasts are presented in 6 hour increments. U.S. Pat. No. 6,654,689 discloses methods of providing meteorological data (storm warnings) that include using a server connected to the Internet (or another network) for providing web-based text and images to a client&#39;s computer, uploading the same information directly to a third party&#39;s web site, sending the data via a pager or phone, and communicating the data and other information through broadcast systems (television or satellite). As discussed in U.S. Pat. No. 6,498,987, advances in computer connectivity technology available in most locations have allowed advances in communicating weather information to end users via the Internet by using web pages maintained on servers connected to the Internet and operated by various communications companies, such as local television and radio companies. 
   Before any information may be communicated to an end user, however, the appropriate probability forecast information must be determined. Systems and methods for generating the information are well known in the art. U.S. Patent Application Serial No. 2002/0114517A1, for example, discloses a short-term storm predictor system whereby meteorological image data from satellites or other sources is computer-processed to generate a 10- to 120-minute severe thunderstorm forecast (the raw data may be available, for example, from NOAA&#39;s NEXRAD network of radar systems). The results are communicated by a graphical representation of the event centered on the graph. Each pixel represents a location within a region and can be assessed a numerical value that represents, for example, the rate of precipitation. U.S. Pat. No. 6,128,578 also analyzes time-series changes in real-time radar images to forecast precipitation, the output being a graphical display having contoured and colored probability rings superimposed over a spatial region. 
   Although many features of the present invention are described in the prior art, none of the prior art patents are directed to a system specifically for providing location-specific, time-sliding (less than six-hour) probability of precipitation forecasts via the Internet. Moreover, the prior art do not contain any suggestion or motivation to calculate probability of precipitation values for time periods less than six hours or on a rolling time basis. There remains, therefore, the need for such a system to provide more accurate forecasts that may be used by decision makers planning activities that are weather sensitive. 
   SUMMARY OF THE INVENTION 
   A POP forecast provides the percentage chance that a measurable amount of precipitation (at least 0.01 inches of rain or ice or 0.1 inches of snow) will fall at a specific location during a specific time period. A “Trace” of precipitation is defined as a finite, non-zero amount of precipitation that falls, that is less than a measurable amount. A low POP means that there is a small chance of measurable precipitation; conversely, a high POP means the chance is greater. Once the forecast period has occurred, the actual POP will always be either 0% or 100%, i.e. either there was or was not a measurable amount of precipitation. However, this eventual outcome is not known with certainty in advance, which is why POP forecasts are typically a percentage between 0% and 100%. Although a POP forecast is the chance that measurable precipitation will occur, it does not indicate how light or heavy the precipitation might be. A POP-T forecast is a POP forecast where the time period interval is T hours (i.e., POP-3 is a three-hour POP forecast, a POP-4 is a four-hour forecast, etc.). 
   The preferred embodiment of the present invention is a multi-period POP-3 forecast that includes a prediction of the most probable amount of precipitation that may fall during each time period. The POP-3 values are based on POP-6 values that have already been computed. 
   The resulting POP-3 estimates are presented in alpha-numeric and graphical means and communicated via a web page maintained on and generated by a server connected to the Internet. In the preferred embodiment, the presentation of forecast information is as follows. For each of selected time periods (e.g., the next three hours, the next six hours, the next 12 hours, the next 24 hours, the next 48 hours and the next 96 hours (i.e., four days)), a POP value, expressed in percent ranging from 0% to 100%, is provided along with a graphic in the form of a bar, the length of which conveys the probability value (i.e., the longer the bar, the higher the POP value). Next to the POP value and bar is a numerical value representing the most probable amount of precipitation that may fall during the time period, expressed in equivalent inches of water (i.e., rain, melted snow and ice combined). Information for the specific types of precipitation is also calculated and may be communicated in the same manner. This includes probability of precipitation, as well as probability of snow, probability of ice, probability of rain, probability of thunderstorms and probability of other events. Other information and indicia may also be presented in various other forms. 
   In the preferred embodiment, each of the selected time periods starts with the current hour, so a high POP-3 value in the next few hours will carry over into all the longer time periods. For example, if the POP-3 in the next three hours time period is 90, then the POP in the next 96-hour time period will be at least 90, even if there is no chance of precipitation after the first three hours of the period. To provide a better understanding of this, a time-series graph depicting when the precipitation will likely occur is also provided (by three-hour intervals). For each time period on the x-axis, a vertical bar is used to represent the POP value. Thus, the height of the bars visually conveys when the precipitation event is forecast to occur. Each POP-3 value is reset at the start of the next hour, so the forecast is provided on a rolling basis. 
   In one embodiment of the invention, POP-3 forecast values are calculated using algorithm models that combine POP-6 forecasts for multiple periods and the most probable forecast hourly precipitation amounts. In those algorithms, POP-6 values are compared, and based upon their relationship to each other and the time period in question of less than 6 hours, a value “A” is assigned. Next, the most probable precipitation amount for each hour in the time period in question and in the hours surrounding that time period are examined, and based upon their relationship, a value of “B” is assigned. Then, a POP for the time period in question is determined based upon the relationship between the “A” and the “B” values. The “A” and the “B” values may be calculated utilizing the output from computerized numerical forecast models and may be modified based upon current data from manual or sensor observations of current conditions, as well as data from radar and satellite systems. The values may also be calculated and modified manually. 
   Accordingly, it is a principal object of the present invention to provide location-specific short-term POP forecasts for less than six-hour time periods and preferably for three-hour time periods. 
   It is another object of the present invention to provide location-specific short-term POP forecasts that are calculated for the current time period and on a rolling time-period basis thereafter. 
   It is still another object of the present invention to provide forecasts to end users via a communications channel, including, but not limited to wired, wireless and hardcopy channels such as a web page or e-mail on the Internet, a pager, telephony (voice and/or data), broadcast, printed page, and personal data organizer, each of which may include a voice-activated interface. 
   It is another object of the present invention to provide a system for forecasting and providing POP information to interested persons who may be interested in monitoring POP forecasts via the Internet by logging onto a server through a client station and entering user-specific inputs such as location or region to obtain the desired information. 
   It is still another object of the present invention to provide most probable precipitation amount forecasts for each hour in the time period in question. 
   It is another object of the present invention to provide probability forecasts for each different type of precipitation, including rain, snow, ice and thunderstorms. 
   It is still another object of the present invention to provide most probable precipitation amounts for each different type of precipitation. 
   These and other objects and features of the present invention are accomplished as embodied and fully described herein by a system involving a network server; a database populated with meteorological data and forecast information contained on the network server or another computer system operatively connected to the network server; a forecast model that executes algorithms (which input the meteorological data and forecast information from the database and output probability forecast information); and a communications system that generates information for end users, and is preferably a web-page generating software device, such as a hypertext mark-up language (HTML) or other proprietary page generator for generating a user. 
   Other objects, features and advantages of the present invention will become evident to one skilled in the art from the following detailed description of the invention in conjunction with the referenced drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic diagram of one embodiment of the system of the present invention; 
       FIG. 2   a  is a process flow diagram of the invention; 
       FIG. 2   b  is a continuation of the process flow diagram of  FIG. 2   a;    
       FIG. 2   c  is a continuation of the process flow diagram of  FIG. 2   b;    
       FIG. 2   d  is a continuation of the process flow diagram of  FIG. 2   c;    
       FIG. 2   e  is a continuation of the process flow diagram of  FIG. 2   d;    
       FIG. 2   f  is a continuation of the process flow diagram of  FIG. 2   e;    
       FIG. 2   g  is a continuation of the process flow diagram of  FIG. 2   f;    
       FIG. 2   h  is a continuation of the process flow diagram of  FIG. 2   g;    
       FIG. 2   i  is a continuation of the process flow diagram of  FIG. 2   h;    
       FIG. 2   j  is a continuation of the process flow diagram of  FIG. 2   i;    
       FIG. 2   k  is a continuation of the process flow diagram of  FIG. 2   j ; and 
       FIG. 2   l  is a continuation of the process flow diagram of  FIG. 2   k.    
   

   DETAILED DESCRIPTION OF THE INVENTION 
   In the present invention, several preferred embodiments are described for illustrative purposes. Referring first to  FIG. 1 , which is a schematic diagram of the preferred embodiment of the system of the present invention, there is shown a computer-assisted probability forecast and report generator  105  that generates POP-T forecasts. In the preferred embodiment of the invention, time period interval, T, is less than 6 hours. In the most preferred embodiment of the invention, T=3 hours. The probability forecast information is provided for the current time through a pre-set time period, t=12, 24, 48 and/or 96 hours. For each time period, a POP is calculated for each successive time period interval (i.e., for T=3, values for POP-3 (0−3) , POP-3 (3−6) , POP-3 (6−9) ), . . . POP-3 (t−3 to t)  are calculated). 
   The forecast generator  105  preferably receives inputs from database server  115 , which contains a forecast database and which receives data and information from various external sources. Those sources may include, but are not limited to, current observational data source  110 ; historical and climatological database source  120 ; numerical model forecast source  122 ; and direct input  125  from operational forecast meteorologists. 
   The current observational data source  110  may be satellite, radar, automated and manual surface observation systems or any other systems that provide real-time or near real-time data and information. For example, NEXRAD radar data may be accessed and downloaded or telemetry from geosynchronous weather satellites may be collected and stored. The historical and climatological database source  120  includes data for various meteorological parameters and it may or may not be connected to a network. That is, the data may be input to database server  115  from a digital source, such as a magnetic tape, or entered manually from hard copy printouts. The numerical model forecast source  122  includes computer-generated forecasts created by atmospheric forecast models run by U.S. and/or foreign governments, as well as those run by private entities and universities, and it may or may not be connected to the network. 
   The forecast generator  105  produces POP forecast information and makes it available through a network server  130 , which is connected to a network like the Internet and may create a web page. An end user may access the forecast information by logging onto the network server  130  through a client computer  135  connected to the Internet, or may receive the information via a pager or telephony system  140  or a broadcast system  145 . Other channels of communication not expressly shown in  FIG. 1  are also contemplated, including, but not limited to wired, wireless and hardcopy channels such as a web page or e-mail on the Internet, a pager, telephony (voice and/or data), broadcast, printed page, and personal data organizer, each of which may include a voice-activated interface. 
   The forecast generator  105  computes the POP values and the most probable precipitation amount values corresponding to each hour of the selected time period of interest, utilizing the artificial intelligence technique known as an expert system, which is designed to simulate the thought processes and the procedure that might be followed by an expert in determining these predictions, based upon the best available data. In this process, the expert might base the POP values on existing POP-6 values and forecast hourly precipitation amounts, which those having ordinary skill in the art will be familiar with and know how to estimate. 
   In the case of the preferred embodiment of the invention, a POP-6 is a six-hour POP that already exists in a digital forecast database that may reside in the same computer as the forecast generator  105  or it may reside in the database server  115  that is connected to the forecast generator  105 . The POP-6 C  is the six-hour POP that contains at least the earliest part of POP-6 that already exists in the database (i.e., the current POP-6). POP-6 (C+1)  is the six-hour POP from the database for the six-hour period that immediately follows POP-6 C . POP-6 (C−1)  is the six-hour POP from the database that immediately precedes the POP-6 C . 
   Referring now to  FIG. 2   a , which is a process flow diagram of the present invention, the forecast generator  105  performs several basic steps as shown. First, in process step  205 , a value for POP-T X  for a particular time period is determined based upon the forecast precipitation amount for each hour in the period. In process step  210 , a value for POP-T Y  for a particular time period is computed based on the POPs for longer time periods using computations executed in module “A” or “B.” Next, in process step  220 , POP-T C , the POP forecast value for this period, is set to the average of the POP-T X  and POP-T Y  values and then adjusted, as needed (as described later). Each successive POP-T value is also calculated (i.e., POP-T (C+1) , POP-T (C+2) , etc.). Then, based on the POP-T values for each interval, the six, 12, 24, 48 and 96 POP values are calculated in process step  225 . Finally, the results are communicated to an end user in process step  230 . This process can be used for precipitation or for any individual form of precipitation, such as rain, snow, ice or thunderstorms. 
   In the preferred embodiment of the invention, T=3 hours, so POP-3 values are computed. A POP-3 is the percentage chance that a measurable amount of precipitation (at least 0.01 inches of rain or ice or 0.1 inches of snow) will fall at a specific location during a three hour time period. In process step  205 , an appropriate POP-3 X  value is obtained from the following table (where Tr=trace): 
   
     
       
             
             
           
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
                 
                 
             
             
                 
               Number of hours in the time period 
             
             
                 
               with a trace of precipitation 
             
           
        
         
             
               POP-3 x   
               0 
               1 
               2 
               3 
             
             
                 
             
           
        
         
             
               Number of hours 
               0 
               10 
               40 
               45 
               50 
             
             
               in the time period 
               1 
               50 
               60 
               65 
               — 
             
             
               where precipitation 
               2 
               70 
               80 
               — 
               — 
             
             
               is at least 0.01 inches 
               3 
               90 
               — 
               — 
               — 
             
             
                 
             
           
        
       
     
   
   The following example explains the concept of using the above table to select an appropriate POP-3 X  value. If there are no hours in the next three hours that have an hourly precipitation forecast of a trace amount and there are two hours in the next three hours where the hourly precipitation forecast is at least 0.01 inches, then, reading down column “0” to row “2” gives a value of 0.70 (i.e., 70%) for POP-3 X . 
   Still referring to  FIG. 2   a , values for POP-3 Y  are determined using one of two modules “A” or “B” that execute depending upon the answer to query step  215 . Modules “A” and “B” are designed to simulate an intuitive analysis using artificial intelligence embodied in the algorithms of those modules. The problem that must be addressed is that a POP-6 represents a value for a six-hour time period (hours 1-6) and we are interested in obtaining a three-hour time period sub-set within those six hours (or a three-hour time period that straddles two POP-6 six hour time periods). For example, in its simplest terms, if POP-6 is 60% for hours 0-6, what is the POP-3 for the three-hour interval for hours 0-3 and the three-hour interval for hours 3-6. The POP-3 Y  values are determined by looking at the POP-6 values and the hourly precipitation amounts for the six-hour time period. If, for example, POP-6 (C−1)  is 90% and POP-6 (C+1)  is zero, then POP-3 C  is logically somewhere between zero and 90%. If the precipitation forecasts suggest that measurable precipitation will occur during the first three hours of the POP-6 (C+1)  time period, the value for POP-3 C  may be closer to the 90% value. The specific method for estimating the POP-3 Y  values from POP-6 data are illustrated below by reference to the accompanying figures. 
   Still referring to  FIG. 2   a , query step  215  requires a determination of whether all the hours in POP-3 are in the same POP-6 time period. The answer to that query would be “No” if hour 1 of POP-3, for example, corresponds to hour 6 of POP-6 C  but hours 2-3 of POP-3 correspond to hours 1 and 2, respectively, of POP-6 (C+1) . POP-6 and hourly precipitation forecast values for the location of interest are stored in database server  115  ( FIG. 1 ) and are previously calculated by methods well known in the art. 
   Referring now to  FIG. 2   b , which represents computation module “A,” query step  235  requires a determination of whether the amount of precipitation for each hour of POP-3 is equal to zero. Query step  240  requires a determination of whether the amount of precipitation for each hour in POP-3 is less than or equal to T. Query step  245  requires a determination of whether there is any amount of precipitation for any hour in POP-6 C , other than the hours for the POP-3 time period, that is greater than or equal to 0.01. Query step  250  requires a determination of whether the amount of precipitation for all the hours in POP-6 C  is equal to zero. Query step  255  requires a determination of whether the amount of precipitation for all the hours in POP-6 C  is less than or equal to a trace amount. Query step  260  requires a determination of whether the amount of precipitation for at least one of the two hours before and at least one of the two hours after POP-3 is greater than or equal to 0.01 inches. Depending on the answers to those queries, as shown in  FIG. 2   b , different modules of the forecast generator  105  will be executed as discussed below. 
   In  FIG. 2   c , which represents module “B,” query step  265  requires a determination of whether the amount of precipitation for all of the hours in POP-3 is equal to zero. Query step  270  requires a determination of whether the amount of precipitation for all the hours in POP-3 is less than or equal to a trace amount. Query step  275  requires a determination of whether the amount of precipitation for any hour in POP-6 C  or POP-6 (C+1) , that is also not an hour in POP-3, that is greater than or equal to 0.01 inches. Query step  280  requires a determination of whether the amount of precipitation for all the hours in POP-6 C  and POP-6 (C+1)  is equal to zero. Query step  285  requires a determination of whether the amount of precipitation for all the hours in POP-6 C  and POP-6 (C+1)  is less than or equal to a trace amount. Query step  290  requires a determination of whether the amount of precipitation for any hour in both POP-6 C  and POP-6 (C+1) , that is not an hour in POP-3, that is greater than or equal to 0.01 inches. Depending on the answers to those queries, as shown in  FIG. 2   c , different modules of the forecast generator  105  will be executed as discussed below. 
   Next, in  FIG. 2   d , which represents module “C,” query step  295  requires a determination of whether the amount of precipitation for POP-6 C  is less than or equal to a trace amount. Query step  300  requires a determination of whether the amount of precipitation for all of the hours in POP-6 that is greater than or equal to 0.01 inches is for the hours before the hours for POP-3. Query step  305  requires a determination of whether the amount of precipitation for all the hours in POP-6 that is greater than or equal to 0.01 inches is for the hours after the hours for POP-3. Depending on the answers to those queries, as shown in  FIG. 2   d , different modules of the forecast generator  105  will be executed as discussed below. 
   Next, in  FIG. 2   e , which represents module “D,” query step  310  requires a determination of whether the amount of precipitation for any of the three hours before POP-3 is greater than or equal to 0.01 inches. Query step  315  requires a determination of whether the amount of precipitation for any of the three hours after POP-3 is greater than 0.01 inches. Depending on the answers to those queries, as shown in  FIG. 2   e , different modules of the forecast generator  105  will be executed as discussed below. 
   In  FIG. 2   f , which represents module “E,” query step  320  requires a determination of whether the amount of precipitation for all the hours in POP-6 that is greater than or equal to 0.01 inches are for hours before the hours for POP-3. Query step  325  requires a determination of whether the amount of precipitation for all the hours in POP-6 that is greater than or equal to 0.01 inches is for hours that are after the hours for POP-3. Depending on the answers to those queries, as shown in  FIG. 2   f , different modules of the forecast generator  105  will be executed as discussed below. 
   Next, in  FIG. 2   g , which represents module “F,” query step  330  requires a determination of whether the amount of precipitation in any hours in POP-6, other than the hours for POP-3, are equal to a trace amount. Query step  335  requires a determination of whether the amount of precipitation for all the hours in POP-6 that is equal to a trace amount are for hours before the hours for POP-3. Query step  340  requires a determination of whether the amount of precipitation for all the hours in POP-6 that is equal to a trace amount is for hours that are after the hours for POP-3. Depending on the answers to those queries, as shown in  FIG. 2   g , different modules of the forecast generator  105  will be executed as discussed below. 
   In  FIG. 2   h  and  FIG. 2   i , which represents modules “L” and “M,” respectively, query step  345  requires a determination of whether the amount of precipitation in any of the last three hours of POP-6 (C−1)  is greater than or equal to 0.01 inches. Query step  350  requires a determination of whether the amount of precipitation for any of the first three hours of POP-6 (C+1)  is greater than or equal to 0.01 inches. Depending on the answers to those queries, different modules of the forecast generator  105  will be executed as discussed below. 
   Next, in  FIG. 2   j , which represents module “Q,” query step  355  requires a determination of whether the amount of precipitation for all the hours in POP-6 C  is equal to zero. Query step  360  requires a determination of whether the amount of precipitation for all the hours in POP-6 (C+1)  is equal to zero. Depending on the answers to those queries, different modules of the forecast generator  105  will be executed as discussed below. 
   In  FIG. 2   k , which represents module “S,” query step  365  requires a determination of whether the amount of precipitation for all the hours in POP-6 C  is less than or equal to a trace amount. Query step  370  requires a determination of whether the amount of precipitation for all of the hours in POP-6 (C+1)  is less than or equal to a trace amount. Depending on the answers to those queries, different modules of the forecast generator  105  will be executed as discussed below. 
   Referring to  FIGS. 2   a - 2   k , the following table lists the values assigned to the variable POP-3 Y  after executing one or more of the previous modules. 
   
     
       
             
             
           
         
             
                 
             
             
               Module 
               POP-3 Y   
             
             
                 
             
           
           
             
               G 
               0.9 * POP-6 C   
             
             
               H 
               0.8 * POP-6 C   
             
             
               I 
               (0.5 * POP-6 C ) + (0.4 * POP-6 (C−1) ) 
             
             
               J 
               (0.5 * POP-6 C ) + (0.4 * POP-6 (C+1) ) 
             
             
               K 
               0.7 * POP-6 C   
             
             
               N 
               (0.6 * POP-6 C ) + (0.2 * POP-6 (C−1) ) 
             
             
               O 
               (0.6 * POP-6 C ) + (0.2 * POP-6 (C+1) ) 
             
             
               W 
               0.9 * max (POP-6 C , POP-6 (C+1) ) 
             
             
               V 
               0.8 * max (POP-6 C , POP-6 (C+1) ) 
             
             
               U 
               max (0.45 * (POP-6 C  +POP-6 (C+1) ), 
             
             
                 
               0.8 * max(POP-6 C  + POP-6 (C+1) )) 
             
             
               R 
               (0.4 * POP-6 C ) + (0.4 * POP-6 (C+1) ) 
             
             
               T 
               (0.3 * POP-6 C ) + (0.3 * POP-6 (C+1) ) 
             
             
                 
             
           
        
       
     
   
   As shown in the table above, the generalized formula for POP-3 Y  is as follows, for modules G, H, J, K,  0 , R and T:
 
POP-3 Y   =a *(POP-6 C )+ b *(POP-6 (C+1) )  (I)
 
Where: 0≦a≦1 and 0≦b≦1. For modules I and N, the generalized formula for POP-3 Y  is as follows:
 
POP-3 Y   =a *(POP-6 C )+ b *(POP-6 (C−1) )  (II)
 
Where: 0≦a≦1 and 0≦b≦1. For modules W and V, the generalized formula for POP-3 Y  is as follows:
 
POP-3 Y   =a *max(POP-6 C ,POP-6 (C−1) )  (III)
 
Where: 0≦a≦1.
 
   Once POP-3 Y  is known, the forecast generator  105  executes the routine shown in  FIG. 21  (i.e., process step  220  shown in  FIG. 2   a ). In process step  375 , POP-3 C  is calculated using the following relationship:
 
POP-3 C =½(POP-3 X +POP-3 Y )
 
Where POP-3 C  is the three-hour POP for the current time period (i.e., hours 0-3) beginning with the current hour. Values for POP-3 C  are adjusted, as necessary, in order to make the resulting POPs consistent with the definition of POP. If, for example, the calculated value for POP-3 Y  using one of the modules from the table above is 30% but the hourly precipitation forecast data indicates there will be precipitation in one of the three hours of the time period, the probability of precipitation must be at least 50% for the POP time period.
 
   Query step  380  requires a determination of whether the amount of precipitation for any of the hours in POP-3 C  are greater than or equal to a trace amount. Query step  385  requires a determination of whether POP-3 C  is less than or equal to 40. Query step  400  requires a determination of whether the amount of precipitation for any hours in POP-3 C  is greater than or equal to 0.01 inches. Query step  405  requires a determination of whether POP-3 C  is less than or equal to 50. Query step  415  requires a determination of whether POP-3 C  is greater than or equal to 50. 
   Depending upon the answers to the above queries, process step  390  assigns a value of 40 to POP-3 C , process step  395  assigns the current value of POP-3 C  to the variable POP-3 C  and process step  410  assigns a value of 50 to POP-3 C . Thus, the value for POP-3 C  is equal to 40, 50 or the current calculated value for POP-3 C . 
   Referring back to  FIG. 2   a , when the routine is finished for the first time period T C , the calculations are repeated for each subsequent consecutive time periods. Thus, there will be 32 values for POP-3 X  and POP-3 Y  and POP-3 C  for a 96-hour period, which leads to 32 values for POP-3, one for each of the 32 three-hour periods. In process step  225 , POP values for each interval of interest are determined (i.e., POP-6, POP-12, POP-24, POP-48 and POP-96, or others). To do this, each consecutive pairs of POP values are combined (e.g., hours 0-3 and 3-6), which reduces the number of POP values from 32 to 16. Those values represent POP-6. Next, each consecutive pairs of POP-6 values are combined (e.g., hours 0-6 and 6-12.), which reduces the number of POP values to 8. This process is repeated to come up with a single POP-96 value. Combining two successive probability values is done according to the following formula:
 
If POP- T   C  is lower than POP- T   (C+1) , then POP-(2 T )=1−(1−0.4*POP- T   C )*(1−POP- T   (C+) )
 
Otherwise, POP-(2 T )=1−(1−POP- T   C )*(1−0.4*POP- T   (C+1) )
 
For example, where T=3 hours (so 2T=6 hours) and given values for POP-3 C =40 (i.e., hours 1-3) and POP-3 (C+1) =60 (i.e., hours 4-6):
 
POP-6=1−(1−0.4*0.4)*(1−0.6)
 
POP-6=0.664(i.e., 66%)
 
   In the preferred embodiment, once the values for probability of precipitation and most probable precipitation amount have been computed for each three-hour time period, the values are made available to end users via the network server  130 . That server generates and sends web page content through a network (i.e., the Internet) to a client computer where it is displayed on the client computer users&#39; monitor as a web page. The information is preferably shown numerically and graphically for each of six time periods: T through T+3 (i.e., the next three hour time period); T through T+6 (i.e., the next six hour time period); T through T+12 (12 hour time period); T through T+24 (one day time period); T through T+48 (two day time period) and T through T+96 (four day time period). It is preferably also shown for each consecutive three-hour period from hour 0 through hour 96. Methods for generating web page content and displaying data numerically and graphically are well known in the art, as are other methods for communicating the as identified herein. 
   Although this invention has been described in connection with specific embodiments, objects and purposes for the invention, it will be appreciated by one of skill in the art that various modifications of the invention, other than those discussed above, may be resorted to without departing from the nature and scope of the invention.