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A Value-Added Approach in Degree Day Calculation

A Value-Added Approach in Degree Day Calculation. John Goff NOAA/NWS Burlington, VT. Overview. Current NWS Methodology Is this the best way? A proposed alternative Data Comparison and Analysis Other Considerations / Limitations Application to Real-Time Climate Datasets.

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A Value-Added Approach in Degree Day Calculation

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  1. A Value-Added Approach in Degree Day Calculation John Goff NOAA/NWS Burlington, VT

  2. Overview • Current NWS Methodology • Is this the best way? • A proposed alternative • Data Comparison and Analysis • Other Considerations / Limitations • Application to Real-Time Climate Datasets

  3. NWS Methodology of Degree Day Calculation • NWS method uses mean temperature of the day using the average of the maximum and minimum 24-hour temperature. Tnws (°F) = (Tmax + Tmin) / 2 • Tnws is then compared to a base temperature to determine HDD and CDD values. • Historically, 65° F has been established as the base temperature. • Thus: HDD = 65 – Tnws CDD = Tnws - 65

  4. NWS Methodology Contd. • This measure is accurate assuming daily temperatures are normally distributed.

  5. NWS Methodology • For longer time scales (≥ 1 yr) or over broad geographic areas this is generally a good approximation. • However, several studies discount this on a monthly or daily basis. • We know this as well!

  6. Here’s an Example • November 15, 2008 (@ KBTV) This is not a normal distribution!

  7. Determining Degree of Normality • Degree of normality can be calculated via Skew (γ1), or alternatively Kurtosis. γ1 = E [((X – μ) / σ) 3] = μ3 / σ3 = E [(X – μ) 3] / (E [(X – μ) 2]) 3/2 = κ3 / κ23/2 where -∞ ≤ γ1 ≤ ∞ γ1 < 0 γ1 > 0

  8. Determining Degree of Normality • Reliable references ( i.e. Bulmer, M.G., Principles of Statistics (Dover, 1979) suggest this rule of thumb: - If -0.50 < γ1 < 0.50 the distribution is approximately symmetric (or near normal). - If -1.0 < γ1 ≤ -0.50 or 0.50 ≤ γ1 < 1.0 the distribution is moderately skewed (or somewhat non-normal). - If -1.0 > γ1 > 1.0 the distribution is highly skewed (or strongly non-normal).

  9. So What Percentage of Days at Burlington, VT (BTV) Exhibit a Non-Normal Distribution Pattern? • Calculated daily, monthly and annual Skew at BTV for the period 2001-2010 using hourly temperatures. • 87,000+ hourly observations - 99.1% data availability (via NCDC )

  10. Example • Monthly decadal averages are fairly normal. However, averages can be misleading! - Similar to averaging bias -> wide variations can be masked

  11. Example Contd.

  12. Example Contd.Looking at it in a Different Way 38% of all days are moderately to highly skewed

  13. Looking at it Differently • So if we use the methodology in the pie slice example noted in the last slide…

  14. Alternative Methods • This suggests we could use an alternative method than Tnws to better approximate HDD and CDD values. • Historically, some have addressed this problem, so it is not unknown. - Guttman et al., 1992 - Dubin and Camponia, 2007 • Literature suggests use of daily degree hours or the average temperature of the day are better approximations than current NWS method.

  15. An Alternative Method • Our method will be to use the average temperature of the day (Ta) as opposed to Tnws at KBTV. Where • Statistically, Ta is a better approximation than Tnws in skewed distributions since it is not as affected by very large or small values.

  16. Differences Between Ta and Tnws • So let’s get a perspective on the daily differences between Ta and Tnws to see if they’re statistically significant.

  17. Definitions • To take it a step further, let’s define a variable Tdif, such that: Tdif = |Tnws – Ta|, where Tdif is rounded to the nearest integer. • What does the variability of Tdif show us in various time frames?

  18. Tdif Graphically So Tdif is the difference between the two points here. In this case Tdif is ~ 4 deg F.

  19. Daily Tdif Variability for a Sample Month Total Tdif sum difference is 50.

  20. Tdif Variability for All Months * Monthly Tdif sums range from 21 to 56.

  21. Decadal Tdif Distribution * Positively skewed distribution

  22. Determining a Low, Moderate and High Tdif Day • Use of the 3-sigma rule, otherwise known as the 68, 95, 99.7 rule**: • Applying this to our Tdif distribution plot on the prior slide, we establish that: * Tdif < 2 is defined as low (~ 70% of dataset). * 2 ≤ Tdif < 4 is defined as moderate (~ 26% of dataset). * Tdif ≥ 4 is defined as high (~ 4% of dataset).

  23. Relationship of High Tdif Days to Skew * Suggests Skew is not the perfect predictor of high Tdif days but does suggest that when |γ1| > 0.5 higher variations in hourly temperatures are more likely.

  24. Let’s Take it a Step Further • OK, but remember that Tdif only expresses the difference in Ta and Tnws, it doesn’t represent true Heating and Cooling Degree Days. • As an example, let’s compare the differences in heating degree days on a random day with a high Tdif value, then calculate the corresponding monthly and seasonal differences.

  25. Data Comparison • December 8, 2002: Tdif = 8 (Ta = 27, Tnws = 19) - Ta HDD = 38 - Tnws HDD = 46 • Month of December 2002: - Ta HDD = 1208 - Tnws HDD = 1221 • Heating Year July 2002 – June 2003: - Ta HDD = 7860 - Tnws HDD = 7946 17.4% decrease in HDD with Ta 1.1% decrease in HDD with Ta 1.1% decrease in HDD with Ta

  26. Comparison of Annual Heating and Cooling Degree Data • In longer time frames, diurnal temperatures approach normality with small Ta/Tnws diff. Tavg Ta Tavg Ta

  27. Further Discussion • It would seem plausible that use of Ta to determine HDD and CDD data has the most immediate value on the daily to perhaps monthly time scale. • In this way significant value could be added on the days in which moderate or high Tdifvalues are observed.

  28. But Wait! • However, in longer time scales the cumulative value of small gains in accuracy each day could potentially lead to bigger long term monthly or yearly savings for utilities. • Also potentially applicable for agriculture-based decision-making (when to spray).

  29. Potential Real World Value • Dubin and Gamponia calculated potential revenue adjustments of a standard utility company serving 1 million customers. • Complex analysis involving terms I don’t fully understand… - normalized load adjustments - energy demand equations - sensitivity coefficients

  30. Potential Real World Value • Found that for each additional HDD per annum revenues rose by $50,000 ($0.05 per customer per degree day). • For a test year, potential revenue adjustments could run in the millions - $1,500,000 dollars in cited example with annum difference of 25 HDD!

  31. Operational Value • What signals are evident in the data on high Tdif days? - Warm Season? - Cool Season? • NARR analysis

  32. Cool Season Signatures on High Tdif Days Clearing at dawn with snow cover. South wind event Arctic frontal passage at local midnight Strong CAA behind departing low

  33. Warm Season Signatures on High Tdif Days Morning frontal passage T-storm Hmmm. Weak front? Shower

  34. Warm Season Plots Contd. What on Earth is this?

  35. NARR Analysis • Given stark variability in patterns, full NARR analysis probably of limited value. • Still some signatures worthy to look at. - warm & cold advective regimes in the cold season - frontal passages - radiative effects -> clouds, or lack thereof - precipitation effects -> storms in the warm season

  36. NARR AnalysisCool Season (80 events)

  37. NARR AnalysisWarm Season (58 events)

  38. How Can we Display this Data? • So we’ve established that various weather regimes can occasionally lead to a non-normal distribution in hourly temperatures. • These distributions warrant a different, more accurate approach could be taken in the calculation of daily degree days. • The use of Ta is one such approach. So how can we display the differences shown via Tdif?

  39. The Next Step • We have hourly T grids (observed) in GFE. • Wrote a small script that calculates Ta, compares it with Tnws, and calculates daily Tdif values. • Data posted as an addendum on our climate web page at: http://www.nws.noaa.gov/climate/local_data.php?wfo=btv

  40. Web Page

  41. Notes on Web Maps • Differences of up to 1 degree day possible on Tnws and Tdif due to: - rounding errors - off-hour max/min temperatures - background mapping techniques (Serp) • Statistical rounding methods used in Serp responsible for “herringbone” appearance in Tdif maps.

  42. Limitations & Other Considerations • We didn’t address rounding, either in the current or proposed methods. This does introduce additional small error (up to 1% cited in the literature). • We didn’t discuss the re-normalization of historical climate data (i.e. can’t realistically compare to traditional HDD/CDD data).

  43. Acknowledgements • Nicole Hannon (NWS BTV/AJK)  data retrieval and entry • Conor Lahiff (NWS BTV)  web interface & design • Paul Sisson (NWS BTV)  oversight/review The author would like to thank the following for their support in this project:

  44. References • Dubin, J. A., and V. Gamponia, 2007: Mid-Range, Average, and Hourly Estimates of Heating Degree Days: Implications for Weather Normalization of Energy Demand. The Energy Journal, April 2007. • Guttman, N. B., and R. L. Lehman, 1992: Estimation of Daily Degree Hours. J. Appl. Meteor.,31, 797-810.

  45. Questions?

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