Patent Publication Number: US-2017371987-A1

Title: Statistically Consistent Past, Present, and Forecast Weather Time-Series for Geographic Points

Description:
BACKGROUND 
     It may be useful to utilize weather information of multiple sources (e.g., observed and/or forecast weather information), such as to construct a more robust database of weather information for a particular location, and/or to predict or forecast future weather for the location. 
     Weather information of one source may, however, be inherently biased relative to weather information of another source due to differences in observation/measurement equipment, locations (latitude, longitude, and/or elevation of observation/measurement equipment), and/or computational algorithms (e.g., forecasting methodology), of the respective sources. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS/FIGURES 
         FIG. 1  is an example elevation map of geographically dispersed sources of weather information, which may have inherently biases (e.g., statistical differences), relative to one another. 
         FIG. 2  is a flowchart of a method of providing statistically consistent time-series of historical, real-time, and/or forecast weather information. 
         FIG. 3  is block diagram of an apparatus to provide statistically consistent time-series of historical, real-time, and/or forecast weather information. 
         FIG. 4  is a block diagram of a computer system configured to provide statistically consistent time-series of historical, real-time, and/or forecast weather information. 
         FIG. 5  is an illustration of example pseudo-code to process forecast/observation pairs. 
         FIG. 6  is a flowchart of a method of determining a model to render weather information of a secondary source statistically consistent with weather information of a primary source, for one of multiple time slots of a day of year. 
         FIG. 7  is an illustration of a weather information aggregation window DOY_W of n consecutive days, centered about a day of year (DOY). 
         FIG. 8  is an expanded view of the illustration of  FIG. 7 , in which the window DOY_W is illustrated as n=21 consecutive days, centered about the DOY. 
         FIG. 9  is an illustration of a set of aggregated weather information for a time-slot of a DOY (e.g., hour 1 of January 11). 
         FIG. 10  is an illustration aggregated weather information for a time-slot (e.g., from 1:00 AM through 6:00 AM, of January 11). 
         FIG. 11  is a block diagram of an apparatus/system to provide a weather model for each of multiple time-slots of one or more days of year based on m years of weather information from a primary source, and m corresponding years of weather information from a secondary source. 
         FIG. 12A  illustrates a statistical distribution of measurements of a weather parameter (e.g., temperature) of a primary data set. 
         FIG. 12B  illustrates a statistical distribution of measurements of the weather parameter of a secondary data set. 
         FIG. 12C  illustrates a statistical distribution of transformed measurements of the weather parameter of the secondary data set, which matches the statistical distribution of measurements of the weather parameter of the primary data set of  FIG. 12A . 
         FIG. 13  is a block diagram of an apparatus/system to supplement weather information of a primary source with transformed weather information of one or more secondary sources. 
         FIG. 14  is a block diagram of an apparatus/system to identify and compensate for missing and/or outlier weather information/data points of a primary source of weather information. 
     
    
    
     In the drawings, the leftmost digit(s) of a reference number identifies the drawing in which the reference number first appears. 
     DETAILED DESCRIPTION 
     For illustrative purposes, example uses of weather information are described below. Methods and systems disclosed herein are not, however, limited to the examples below. 
     Historic weather information for a locale may be used to construct a weather forecast model to predict future weather for the locale based on more recent weather information. If the source of the historic weather information and the source of the more recent weather information differ in any respect (e.g., different observation/measurement equipment and/or different locations of observation/measurement equipment), however, there may be a bias, or difference between the predicted future weather and the actual future weather. 
     A correlation between historic business performance information, such as sales numbers, and corresponding historic weather information may be used to construct a model to predict future business performance information based on predicted future weather (e.g., using a weather forecast model). The predicted future business performance information may be used for business/financial decisions regarding inventory, prices/discounts, investments, and/or risk mitigation. If the source of the historic weather information and the source of the current weather information differ in any respect, however, a bias may be introduced between the predicted future business performance information and actual (future) business performance information. 
     Weather information from multiple sources may be combined, such as to supplement weather information of a first source with weather information of a second source. Weather information of the second source may, however, be inherently biased relative to weather information of the first source due to differences in observation/measurement equipment, locations (latitude, longitude, and/or elevation), and/or computational algorithms of the respective sources. 
       FIG. 1  is an example elevation map  100  of locations  102  through  112 , which are geographically dispersed relative to one another (longitudinally and/or laterally). 
     Locations  102 ,  104 ,  106 , and  108 , are at a first elevation  120 . Elevation  120  may be, for example and without limitation, sea level. Location  110  is at a second elevation  122 , and location  112  is at a third elevation  124 . Elevation  110  may be higher than elevation  120 , and elevation  124  may be higher than elevation  122 . Alternatively, elevation  122  may be lower than elevation  120 , and elevation  124  may be lower than elevation  122 . 
     Table 1 below lists sources of weather information, A through F, for respective locations  102 - 112 . One or more of the sources may include and/or provide weather information that has been observed or measured at or proximate to the respective location, and/or may include or provide forecast/predicted weather information for the location. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Source 
                 Location 
               
               
                   
                   
               
             
            
               
                   
                 A 
                 102 
               
               
                   
                 B 
                 104 
               
               
                   
                 C 
                 106 
               
               
                   
                 D 
                 108 
               
               
                   
                 E 
                 110 
               
               
                   
                 F 
                 112 
               
               
                   
                   
               
            
           
         
       
     
     Due to proximity of locations  102  through  112 , relative to one another, weather information of sources A through F, for a given point in time and/or over a range of time, may be similar to one another, but may not necessarily be identical to, or statistically consistent with one another. There may be, for example, differences (i.e., a bias) in temperature, wind velocity (i.e., direction and/or speed), pressure, humidity, and/or other weather parameter(s). 
     As an example, where weather information regarding location  102  is of interest, source A may be designated a primary source of weather information and one or more of sources B through F may be designated a secondary source. Source A may be designated the primary source based on location  102  and/or contents of source A (e.g., quantity and/or quality of weather information available from source A). In this example, weather information of each of sources B through F (i.e., regarding locations  104  through  112 ), may be biased relative to weather information of source A (i.e., regarding location  102 ), due to differences in location (e.g., latitude, longitude, and/or elevation), equipment, and/or algorithms. 
     To compensate for (i.e., remove and/or eliminate) bias, models are generated to transform weather information of one source to be statistically consistent with weather information of another source, without necessarily having to determine or compute the actual or specific bias. 
     Unless indicated otherwise herein, the term “weather forecast data source” refers to weather forecast data provided by a specific weather forecasting system or source. Examples of a weather forecast data include numerical model forecasts produced by government forecasting centers, forecasts produced by government organizations such as the U.S National Weather Service (NWS), and/or forecasts produced by commercial weather forecasting companies. 
     Unless indicated otherwise herein, the term “weather forecast time-series” refers to a dataset representing a geographic point where weather forecast data is collected into a time-series such that the data in the time-series comes from the earliest portion of the forecast data source. For example, a forecast initialized from a point in time will typically provide predicted values for weather parameters on regular time-steps many hours or days in the future. Forecast weather values that are the closest to the initialization time of the forecast may be collected and saved. This may be referred to as zero-hour forecast, or zero-hour analysis. If a zero-hour analysis is not available, forecasted weather information for the forecast time-step closest to the forecast initialization time may be collected and saved. The forecast data collection process provides a time-series of forecast source data that naturally has the greatest correlation to weather that actually occurred. 
     A weather forecast time-series is associated with a specific geographic point. Numerous geographic points may be supported by a weather forecast data source. 
     Unless indicated otherwise herein, the term “weather observation data source” refers to a dataset provided by a specific source that measures and/or analyzes weather conditions and records values of the conditions. Weather measurement systems are one common source of weather observation data. Weather measurement systems may include, without limitation, weather monitoring stations such as NWS Automated Surface observing System (ASOS) stations, radar observations, satellite observations, wind profiler observations, and/or other system(s) that monitor and record weather values. 
     Another viable source of weather observations comes from weather analysis computer programs designed to produce a meteorological analysis of weather values over a spatial grid, given various weather observations as input. In the meteorological community these analysis models are often referred to as ‘reanalysis’ models to distinguish them from forecast models which also have an analysis component. Reanalysis models produce an analysis of weather conditions over a geographic region and over a period of time. 
     Unless indicated otherwise herein, the term “weather observation time-series” refers to weather information collected over time from a specific weather information source and for a specific geographic point. 
       FIG. 2  is a flowchart of a method  200  of providing statistically consistent time-series of historical, real-time, and/or forecast weather information. 
       FIG. 3  is block diagram of an apparatus  300  to provide statistically consistent time-series of historical, real-time, and/or forecasted weather information. Apparatus  300  may include, without limitation, circuitry, a machine, a computer system, a processor and memory, a computer program encoded within a computer-readable medium, and/or combinations thereof. Circuitry may include discrete and/or integrated circuitry, application specific integrated circuitry (ASIC), a system-on-a-chip (SOC), and combinations thereof. 
       FIG. 4  is a block diagram of a computer system  400  to provide statistically consistent time-series of historical, real-time, and/or forecasted weather information. Computer system  400  includes one or more processors, illustrated here as a processor  402 , to execute instructions of a computer program  406  encoded within a computer readable medium  404 . Computer readable medium  404  may include a transitory or non-transitory computer-readable medium. Computer readable medium  404  includes data  408 , which may be used by processor  402  during execution of computer program  406 , and/or generated by processor  402  during execution of computer program  406 . 
       FIGS. 2-4  are described below with reference to an example in which a primary set of weather information includes historical weather information, and a secondary set of weather information includes forecast weather information.  FIGS. 2-4  are not, however, limited to this example. 
     One or more of the foregoing embodiments (i.e.,  FIGS. 2-4 ), may utilize weather information (e.g., historical/observed) from a primary source, covering a period of time of one year or more, and at least one year of weather information from a secondary source (e.g., forecast), that overlaps at least a one-year period of the weather information of the primary source. In practice, it may be useful to use numerous sets of weather information of the primary and secondary sources (e.g., historical and forecast datasets), over a period of several years. 
     Paring Weather Information/Points of Primary and Secondary Sources ( 202 ,  302 ,  412 ) 
     The geographic arrangement of forecast points and observation points may be assumed to be constant over time, however, the forecast points and observation points may or may not be spatially co-located such that there is a perfect one-to-one spatial overlapping of forecast and observation points. 
     To provide statistically consistent past, present, and forecast weather time-series for geographic points, forecast and observation points are paired such that the points are as meteorologically consistent with one another as possible. 
     If the forecast and observation points are co-located to a common set of geographic points, then the co-located forecast and observation points may be simply matched up as pairs ( 324 ,  424 ) for the computations in creating statistically consistent past, present, and forecast weather time-series. 
     If the forecast and observation points are not co-located, an exercise may be conducted to match up the forecast and observation points such that the paired points ( 324 ,  424 ) are as close to each other as possible while also being physically as consistent as possible (e.g., in terms of elevation, land, and/or water surface type). 
     Numeric Processing Framework ( 204 ,  304 ,  414 ) 
     A numeric processing framework processes each set of paired forecast and observation time-series that are time synchronized covering a period of one year or more. The time processing interval may be any consistent interval. Examples are provided herein with respect to sequential days and hours. A goal of the numeric processing framework is to collect subsets of weather information from time-series that are seasonally meteorologically consistent, and use the data subset to create numeric equations (e.g., construct/train/evaluate model(s)), to relate the observation data to the forecast data. 
       FIG. 5  is an illustration of example pseudo-code  500  to process forecast/observation pairs. 
     In  FIG. 5 , DOY (day-of-year), is an integer from 1 to 366, to account for the maximum number of days in a year including leap years. In processing each DOY, all available years are considered in the processing. For example, for DOY=1, January 1st from all available years are processed. The variable W defines a window around the DOY that will be processed. Window W may be an integer from 0 to 182. In some situations, W values of 7 to 14 days may provide suitable (e.g., better/best) results. 
     In an example, where 5 years of overlapping forecast and observation data are processed, with W=10 (i.e., for a total window of 21 days), a subset collection may have 105 sets of paired forecast and observation weather values. 
     To increase the sample size, an additional loop may be provided (e.g., within an hour-processing loop  502  of pseudo-code  500 ), to add an N hours of data before and after the target hour (i.e., before and after each respective hour of loop  502 ). Setting N to 1 may triple the sample size. Values of N greater than 6 may have a negative impact (e.g., where there may exist significant diurnal variation). 
     The collected paired values from all available weather parameters are then processed via a suite of curve fitting tests to determine the best numerical relationship between the forecast and observation data for each day of the year and hour of the day. 
     The numeric processing may include curve fitting tests and curve selection. 
     For example, various weather elements from the collected forecast and observation subsets ( 324 ,  424 ), may be processed with a suite of curve fitting tests to determine the most accurate numeric relationship between the forecast and observation data. The suite of tests may include, without limitation, linear regression models, quadratic regression models, and/or b-spline models. The observation data is processed through the models to produce estimates for what the forecast data should be. These estimates are then compared to the actual forecast data and tested via ‘goodness of fit’ tests such as R-squared and root mean squared error (RMSE). The simplest model with the best goodness of fit is selected as the model to relate observation data to forecast data. 
     Application/Usage of Model(s) ( 206 ,  308 ,  418 ) 
     Models constructed as disclosed herein may be used/applied in one or more of a variety of applications. A model constructed as described in the example above may, for example, be used to adjusting past observations to be statistically consistent with forecast data. In this example, using the numerical models ( 326 ,  426 ) produced in the numeric processing/curve fitting ( 204 ,  326 ,  426 ), the full history (e.g., years or decades) of observations ( 328 ,  428 ), may be processed through the selected models ( 326 ,  426 ) to produce a time-series of weather values ( 330 ,  430 ), that are statistically consistent with the forecast data with which the observations were paired. 
     Real-time values from the paired observation dataset may also be processed via the models ( 326 ,  426 ), to produce a continuous source of updated data ( 330 ,  430 ). The resulting dataset can reach much further back in time than the original forecast data source. Because the resulting dataset is now statistically consistent with the forecast data, users can then build weather business models tuned precisely to be driven by the forecasts. 
     Further Data Aggregation and Model Generation Examples 
       FIG. 6  is a flowchart of a method  600  of determining a model to render weather information of a secondary source statistically consistent with weather information of a primary source, for one of multiple time slots of a day of year. Method  600  may be performed with respect to each of multiple time slots of each of multiple days of year. 
     Method  600  is described below with reference to  FIGS. 7-9 . Method  600  is not, however, limited to the example of any of  FIGS. 7-9 . 
     At  602 , a primary set and a secondary set of weather information is constructed from respective primary and secondary sources of weather information. This includes, for each of the primary set and the secondary set of weather information, aggregating weather information of the time slot over n consecutive days of each of m years to provide nxm time slots of weather information, where each of n and m is an integer greater than 1. 
       FIG. 7  is an illustration  700  of a weather information aggregation window DOY_W  702  of n consecutive days, centered about a day of year (DOY)  704 . Illustration  700  further includes m years of weather information  706  of a source q. Source q may represent a primary or a secondary source of weather information. 
       FIG. 8  is an expanded view  800  of illustration  700 , in which window  702  DOY_W  702 , illustrated here as n=21 consecutive days, is centered about DOY  704 , illustrated here as January 11. 
     In the example of  FIG. 8 , source q includes multiple time slots of weather information, illustrated here as twenty-four (24) one-hour time-slots of weather information  802 - 1  through  802 - 24 . Methods and systems disclosed herein are not, however, limited to hourly time slots. 
     Further in the example of  FIG. 8 , time slot of weather information  802 - 1  includes time slots  806 - 1  through  806 - 21  of year 1, and time slots  808 - 1  through  808 - 21  of year m. 
     In accordance with  602  of method  600 , for each of time slots  802 - 1  through  802 - 24  of DOY  704 , weather information of source q (i.e., source q as a primary or as a secondary source of weather information), is aggregated over n=21 consecutive days of years  704 - 1  through  704 - m , to provide nxm time slots of weather information (e.g., 21×m time slots of weather information). 
       FIG. 9  is an illustration of a set of aggregated weather information (set)  900  for time-slot  802 - 1  of DOY  704  (i.e., hour 1 of January 11). Set  900  includes time slots  806 - 1  through  806 - 21  of January 1 through January 21, for each of years 1 through m. Set  900  may represent a primary set of weather information or a secondary set of weather information of the time-slot. 
     In an embodiment, the aggregating at  602  includes aggregating weather information of the time slot and of one or more additional/adjacent time slots (e.g., a time slot ±i adjacent time-slots), to provide (2j+1)×m time slots of weather information. This is illustrated below with reference to  FIG. 10 . 
       FIG. 10  is an illustration of an example of aggregated weather information  1000  for a time-slot  802 - 3 . Time-slot  802 - 3  may represent, for example, a one-hour time slot from 3:00 AM to 4:00 AM, of January 11. 
     In the example of  FIG. 10 , aggregated weather information  1000  includes n=21 subsets of weather information  1006 - 1  through  1006 - 21  for year 1, and n=21 subsets of weather information  1008 - 1  through  1008 - 21  for year m. Each subset of weather information  1006 - 1  through  1006 - 21 , and  1008 - 1  through  1008 - 21  includes five (5) time slots of weather information (i.e., hours 1 through 5), which may be centered about time-slot  802 - 3 . Where time slot  802 - 3  corresponds to 3:00 AM to 4:00 AM, each subset of weather information  1006  and  1008  may include weather information for 2 hours preceding time-slot  802 - 3 , and weather information for 2 hours subsequent to time-slot  802 - 3 . 
     Returning to method  600  in  FIG. 6 , at  604 , multiple models are constructed, each to correlate between the primary set and the secondary set of weather information based on a respective one of multiple correlation techniques, such as described in one or more examples herein. 
     At  606 , at least a portion of the secondary set of weather information is transformed with each of the models to provide multiple respective transformed sets of weather data. With reference to  FIG. 9 , where set  900  represents a secondary set of weather information, at least a portion of set  900  is transformed with each of multiple models to provide multiple respective transformed sets of weather data. 
     At  608 , one of the transformed sets of weather information is identified as statistically consistent with the primary set of weather information based on a comparison of a statistical measure of the primary set of weather information to statistical measures of the respective transformed sets of weather information, such as described in one or more examples herein. 
     At  610 , the model associated with the statistically consistent transformed set of weather information is selected as a weather information conversion model for the respective time slot of the respective day of the secondary source. 
     In an embodiment, method  600  may be used to provide 24 hourly models for each day of year. 
       FIG. 11  is a block diagram of a system  1100  to provide a weather model for each of multiple time-slots of one or more days of year based on m years of weather information  1102  from a primary source  1103 , and m corresponding years of weather information  1104  from a secondary source  1105 . 
     System  1100  includes a pairing engine  1106  to construct a primary set of weather information  1108  and a secondary set of weather information  1110  for each time-slot of each day of year, such as described above with reference to  602  in  FIG. 6 . 
     System  1100  further includes multiple correlator/model generators  1112 , each to construct a model to correlate between each primary set of weather information  1108  and corresponding secondary set of weather information  1110 , based on a respective one of multiple correlation techniques, such as described above with reference to  604  in  FIG. 6 . Each correlator/model generator  1112  may be configured to generate a model for each time-slot of each day of year. 
     Each correlator/model generator  1112  may be further configured to transform at least a portion of the respective secondary set of weather information  1110  to provide a respective transformed set of weather data  1114 , such as described above with reference to  606  in  FIG. 6 . 
     System  1100  further includes a statistical distribution comparison, adjustment, and model selection engine  1116  to identify one of the transformed sets of weather information  1114 , for each time-slot of each day of year, as statistically consistent with the respective primary set of weather information  1108  based on a comparison of a statistical measure of the primary set of weather information  1108  to statistical measures of the respective transformed sets of weather information  1114 , such as described above with reference to  608  in  FIG. 6   
     Engine  1116  may be configured to output a model selection  1118  for each time slot of each day of year, such as described above with reference to  610  in  FIG. 6 . 
     Engine  1116  may be configured to adjust a statistical distribution of a transformed set of weather information  1114  to more closely match a statistical distribution a respective primary set of weather information  1108 . This is described below with reference to  FIG. 12 . 
       FIG. 12A  illustrates a statistical distribution  1200  of measurements of a weather parameter (e.g., temperature) of a primary data set. 
       FIG. 12B  illustrates a statistical distribution  1202  of measurements of the weather parameter of a secondary data set. 
     Where, as in this example, statistical distribution  1202  differs from statistical distribution  1200  (e.g., in terms of mean and/or standard deviation), the measurements of the secondary data set may be transformed with a model(s) as described herein such that a statistical distribution  1204  ( FIG. 12C ) of the transformed measurements matches statistical distribution  1200  ( FIG. 12A ). In other words, the measurements of the secondary data set are transformed to be statistically consistent with the measurements of the primary data set. 
     Further Model Usage Examples 
     Further model usage examples are provided below for illustrative purposes. 
     Methods and systems disclosed herein are not, however, limited to the examples below. 
       FIG. 13  is a block diagram of a system  1300  to supplement weather information of primary source  1103  with transformed weather information of one or more secondary sources  1105 - 1  through  1105 - y.    
     System  1300  includes a set of models  1118  for each of one or more secondary sources  1105 , such as described above with reference to  FIG. 11 . 
     Each set of models  1304  may include multiple time-slot specific models for each of multiple days of year, such as described in one or more examples herein. Each set of models  1304  may further include multiple parameter-specific models for each time-slot (e.g., separate models for temperature, pressure, humidity, wind velocity and/or other objective and/or subjective (e.g., wind chill factor) parameters). 
     Each set of selected models  1118  may be used to transform additional weather information  1302  of the respective secondary source  1105  into transformed weather information  1306  that is statistically consistent with weather information of primary source  1103 . 
     At  1308 , transformed weather information  1306 , or a portion thereof, is added to and/or combined with weather information  1102  of primary source  1103  to provide a database of modified weather information  1310 . 
       FIG. 14  is a block diagram of a system  1400  to identify and compensate for missing and/or outlier weather information/data points of primary source  1103 . 
     System  1400  includes an engine  1402  to evaluate weather information of primary source  1103  relative to transformed additional weather information  1306 , to detect/identify missing and/or anomalous/outlier weather information of primary source  1103 , and to modify primary source  1103  with suitable weather information of transformed additional weather information  1306 , to provide modified weather information  1404 . 
     Engine  1402  may, for example, be configured to identify a time slot of a day of year for which weather information is absent from primary source  1103 , and to supplement primary source  1103  with transformed additional weather information  1306  of the time slot of the day of year. 
     Alternatively, or additionally, engine  1402  may be configured to compare weather information of primary source  1302  with transformed additional weather information  1306 , for a time slot of a day of year, to detect weather information of primary source  1103  that differs relatively significantly from transformed additional weather information  1306 , for the time slot of the day of year. In this example, engine  1402  may be further configured to replace or substitute weather information of primary source  1103  with transformed additional weather information  1306 , for the time slot of the day of year. 
     Methods and systems are disclosed herein with the aid of functional building blocks illustrating functions, features, and relationships thereof. At least some of the boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries may be defined so long as the specified functions and relationships thereof are appropriately performed. While various embodiments are disclosed herein, it should be understood that they are presented as examples. The scope of the claims should not be limited by any of the example embodiments disclosed herein.