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Marin County Drought Analysis

The document presents a drought analysis for the Marin Municipal Water District, detailing historic rainfall data and drought occurrences from 1880 to 2021. It highlights significant differences between wet years (1880-1916) and dry years (1917-1950), with an emphasis on recent drought trends and water flows. The report concludes with a review of fiscal year 2021, noting a record low reservoir level primarily due to low rainfall.

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Marin Municipal Water District Marin County Drought Analysis Gaetan Lion, July 28, 2021
Content • Section 1. Rainfall annual (FY) data • Section 2. Droughts, monthly data • Section 3. Explaining FY 2021 2
Section 1. Rainfall Annual (FY) data 3
0 20 40 60 80 100 120 1880 1882 1884 1886 1888 1890 1892 1894 1896 1898 1900 1902 1904 1906 1908 1910 1912 1914 1916 1918 1920 1922 1924 1926 1928 1930 1932 1934 1936 1938 1940 1942 1944 1946 1948 1950 1952 1954 1956 1958 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 Fiscal Year, annual rainfall in inches On the next slide, we will observe large differences between the Wet Years from 1880 – 1916 and the Dry Years from 1917 – 1950. 4
0 20 40 60 80 100 120 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 Wet Year, annual rainfall in inches FY 1880 - 1916 0 20 40 60 80 100 120 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 Dry Year, annual rainfall in inches FY 1917 - 1950 Very large difference in annual rainfall between the Wet Years and the Dry Years. 5
0 20 40 60 80 100 120 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Ranked year from highest to lowest from Left to Right Wet Years vs. Dry Years. Ranked from Highest to Lowest Wet Dry Another look at the very large difference between the Wet Years and the Dry Years. 6
30 35 40 45 50 55 60 65 70 75 80 1889 1893 1897 1901 1905 1909 1913 1917 1921 1925 1929 1933 1937 1941 1945 1949 1953 1957 1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 2001 2005 2009 2013 2017 2021 10 Year AverageYearly Rainfall in inches Wet Year Dry Year Baseline Year Rainfall inchesper year Percentile Wet Dry Baseline 95% 100.3 68.9 86.7 75% 73.5 46.7 66.3 50% 60.4 39.2 47.4 25% 48.9 29.9 36.8 5% 34.2 22.5 28.7 The Wet Years and Dry Years are most divergent (divergence is somewhat attenuated by the 10 year averaging lagging effect) as shown on the graph. The long Baseline Year period is pretty much in between the two. That is true whether we look at 10 year average yearly rainfall on the graph or various percentiles in annual rainfall in the right hand table. 7
Count ofDrought Years Percentile 20% 10% 5% Inch per year 35 30 25 1880 -1916 3 0 0 1917 -1950 12 9 5 1951 -2021 14 6 3 % ofDrought Years Percentile 20% 10% 5% Inch per year 35 30 25 1880 -1916 8% 0% 0% 1917 -1950 35% 26% 15% 1951 -2021 20% 8% 4% The green area defines different Drought thresholds ranging from the 20th percentile at 35 inches per year down to the 5th percentile at 25 inches per year. These percentiles are based on the entire data set from 1880 – 2021. This table simply counts the number of Drought years falling within each category thresholds from 35 inches down to 25 inches per year. This table is actually much more informative because it discloses the percentage of years that fell into the respective Drought categories. And, if a period disclosed percentages are close to the overall percentile levels defining the Drought thresholds (20%/10%/5%), then this period’s Drought frequency is similar to the entire history of the data. And, we can see that this is the case for our Baseline period from 1951 – 2021 (20%/8%/4%). 8
9 This table shows the number of times a Drought has lasted at least two consecutive years or more. Keep in mind that the Dry Period (1917 – 1950) is less than half as long as the current Baseline Period (1951 – 2021). Given that, the Dry Period distinguishes itself as having more frequent long Droughts. This table is similar to the above, but identifies the periods when at least 50% of the years were in Drought conditions.
Section 2. Droughts, monthly data 10
These are the 15 driest years in our historical data going back to 1880. Notice that 8 of the 15 did occur during the Dry Year period (1917 – 1950). None occurred during the Wet Year Period (1880 – 1916). Within the 15th driest years, 2021 was in the mid of the pack early on. But, it was unusually dry during the mid-Winter and early Spring. 11 Cumulative rainfall in inchesduring respective Fiscal Year Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun 1 1924 0.30 0.30 1.08 1.50 2.37 5.22 11.90 16.24 19.08 19.08 19.08 19.08 2 1918 0.00 0.00 0.12 0.12 1.90 4.12 4.83 13.00 19.25 20.65 20.65 20.65 3 2021 0.00 0.35 0.35 0.35 3.40 8.31 14.57 16.85 20.26 20.62 20.62 20.66 4 1976 0.36 0.41 0.41 8.33 9.68 11.17 11.48 14.71 18.06 22.13 22.13 22.13 5 1920 0.00 0.00 1.30 1.56 2.02 9.18 10.37 12.61 18.19 22.91 22.91 23.45 6 1931 0.00 0.00 0.61 1.71 4.20 5.54 15.65 17.60 21.37 21.82 23.17 23.65 7 1939 0.00 0.00 0.17 2.40 4.82 8.58 15.54 18.95 23.15 23.44 24.45 24.49 8 1977 0.00 1.73 3.06 3.85 6.20 10.38 14.94 17.69 22.65 23.16 24.95 24.97 9 1929 0.00 0.00 0.04 0.09 5.47 13.64 15.29 19.92 21.76 24.69 24.69 26.96 10 1959 0.00 0.00 0.10 0.25 1.23 4.12 14.61 25.49 27.25 28.25 28.25 28.25 11 1947 0.05 0.05 0.27 0.56 6.54 10.78 12.31 16.64 24.02 25.17 26.24 28.48 12 1934 0.00 0.00 0.08 3.23 3.23 13.62 16.21 25.56 25.96 26.76 28.08 29.10 13 1987 0.00 0.00 1.24 1.68 1.81 4.65 12.91 21.69 28.72 29.15 29.18 29.18 14 1933 0.05 0.05 0.05 0.05 2.09 7.40 17.57 19.86 26.63 26.78 29.74 29.74 15 1972 0.00 0.00 0.40 0.61 4.71 15.65 18.62 23.99 25.28 29.51 29.55 29.92 2021 ranking. Monthsreflect cumulative rainfall up to that month Nov Dec Jan Feb Mar Apr May June 8th 7th 7th 6th 5th 2nd 2nd 3d
Same data as on the previous slide, but in graphical form. Same graph, but eliminating 1918 and 1976. Notice now how the 13 Droughts look remarkably similar with most of the rain hitting in December through March. 12
Section 3. Explaining FY 2021 13
A Simple Water Flow Model Based on the data provided by the MMWD, we can construct a simple water flow model to disclose the reservoir capacity and disaggregate it in several components described below: 14 Beginning Reservoir level (July 1st, at beginning of fiscal year) - Potable water generation + Sonoma water imports (estimated at 25% of Potable water generation) + Other items Ending Reservoir level (June 30th, at end of fiscal year) The Sonoma water imports are just an estimate representing 25% of Potable water generation. “Other items” capture all other net water flows that make the sum of the mentioned flows generate the correct Ending Reservoir level. We suspect a good part of the “Other Items” are associated with rainfall that replenish the reservoirs.
Here is the relevant data from 1987 to 2021 FY. The data provided included: • Beginning reservoir level • Ending reservoir level • Potable water production The reason the Ending reservoir level was at a record low as of June 30, 2021 was due to the record negative Other Water Flow of – 8,319 acre feet. This figure is in good part due to the near record low rainfall during FY 2021. 15 Reservoir Flows in acre foot Beginning Reservoir level Potable Water Production Sonoma Water Imports (25%) Other Water Flow Ending Reservoir level Begin to end change Rainfall in inches 1987 69,179 -33,056 8,264 9,003 53,390 -15,789 29.18 1988 53,227 -32,845 8,211 20,120 48,713 -4,514 30.55 1989 48,580 -28,555 7,139 33,178 60,342 11,762 36.44 1990 60,197 -29,392 7,348 6,174 44,327 -15,870 31.01 1991 44,274 -25,210 6,303 25,038 50,404 6,130 35.38 1992 50,393 -23,078 5,770 33,250 66,334 15,941 39.41 1993 66,299 -23,459 5,865 26,398 75,103 8,804 61.09 1994 74,988 -26,951 6,738 5,955 60,730 -14,258 33.02 1995 60,590 -26,288 6,572 35,766 76,640 16,050 87.44 1996 76,548 -28,039 7,010 20,138 75,657 -891 66.53 1997 75,822 -29,423 7,356 12,765 66,520 -9,302 51.65 1998 66,414 -27,111 6,778 31,272 77,353 10,939 91.71 1999 77,262 -29,405 7,351 18,038 73,247 -4,015 53.10 2000 73,102 -30,125 7,531 22,599 73,107 5 49.17 2001 72,930 -31,343 7,836 10,429 59,852 -13,078 34.26 2002 59,742 -30,452 7,613 33,695 70,598 10,856 54.98 2003 70,439 -30,310 7,578 27,233 74,939 4,500 56.71 2004 74,753 -31,406 7,852 16,958 68,156 -6,597 47.39 2005 67,910 -28,636 7,159 31,110 77,543 9,633 66.05 2006 77,394 -28,963 7,241 18,570 74,242 -3,152 73.03 2007 74,080 -29,775 7,444 8,307 60,056 -14,024 36.31 2008 59,899 -29,365 7,341 25,676 63,551 3,652 41.24 2009 63,256 -27,474 6,869 17,430 60,080 -3,176 42.94 2010 59,944 -25,231 6,308 34,118 75,139 15,195 58.24 2011 74,992 -25,372 6,343 20,379 76,342 1,350 70.16 2012 76,250 -26,070 6,518 16,796 73,493 -2,757 40.51 2013 73,372 -27,060 6,765 11,384 64,461 -8,911 40.20 2014 64,319 -26,709 6,677 15,619 59,906 -4,413 33.40 2015 59,661 -22,454 5,613 24,391 67,212 7,551 39.82 2016 67,094 -29,007 7,252 27,646 72,985 5,891 49.74 2017 72,823 -23,006 5,752 19,825 75,393 2,570 95.95 2018 75,278 -25,175 6,294 16,258 72,655 -2,623 38.89 2019 72,539 -24,590 6,147 23,253 77,350 4,811 74.03 2020 77,243 -26,828 6,707 6,177 63,299 -13,944 34.99 2021 63,175 -26,196 6,549 -8,319 35,209 -27,966 20.66
16 -15,000 -10,000 -5,000 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 Other Water Flow in Acre Feet 0 20 40 60 80 100 120 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 Rainfall in Inches There is definitely a correspondence between Other Water Flow and Rainfall. The correlation coefficient between the two is 0.54, which is statistically significant given the number of data points. This corresponds to an R Square of close to 0.29 when using a linear regression to explain Other Water Flow, as the dependent variable Y, using Rainfall (as the causal X variable). However, on the next slide we present a polynomial regression that can dramatically increase the R Square of the model up to 0.42. In plain English, this second model using Rainfall as the X variable can explain 42% of the variance in Other Wate Flow, the Y variable.
17 y = -9.6299x2 + 1403.3x - 22858 R² = 0.424 -15,000 -10,000 -5,000 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 0 20 40 60 80 100 120 Other Water Flows in ACF Rainfall in Inches Rainfall vs. Other Water Flow Polynomial Model explaining Other Water flows with Rainfall As shown, there is close to a linear relationship between Rainfall and Other Water Flow when Rainfall ranges between 20 and 60 inches. Beyond that point, this relationship somewhat evaporates. This is probably due because when Rainfall exceeds 60 inches, depending on the beginning Reservoir Level, a portion of the Rainfall just overflows. Focusing on 2021, the actual Other Water Flow is negative – 8,319 ACF. Meanwhile, the model estimate comes in at + 2,025 ACF. Thus, in this case the model overestimates 2021 Other Water Flow by 10,344 ACFs. This represents the 2nd largest overestimation out of 35 data points.
Model Performance 18 That is what a model with an R Square of 0.42 looks like. It is far from perfect. But, it does capture some overall trends. (30,000) (20,000) (10,000) - 10,000 20,000 30,000 40,000 50,000 60,000 Other Water Flows in ACF Estimating Other Water Flow. Including 90% Confidence Interval Other Model Estimate Low High
Model Performance since 2009 with 90% C.I. 19 (30,000) (20,000) (10,000) - 10,000 20,000 30,000 40,000 50,000 60,000 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 Other Water Flows in ACF Estimating Other Water Flow. Including 90% Confidence Interval since 2009 Other Model Estimate Low High Since 2009, the Model performance is a lot better. The R Square over this period jumps to 0.71.
Model Performance since 2009 20 (15,000) (10,000) (5,000) - 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 Other Water Flows in ACF Estimating Other Water Flow. since 2009 Other Model Estimate This is just a cleaner look at the Model performance since 2009.
Explaining FY 2021 Other Water Flow (OWF) 21 The average OWF over the entire period is 19,904 ACF In FY 2021, the estimated OWF by our Rain Model is 2,025 ACF The difference calculated below is the difference that is explained by our Rain Model 19,904 – 2,025 = 17,879 ACF The actual OWF in FY 2021 is – 8,319 ACF The difference calculated below is the difference that remains unexplained by our Rain Model 2,025 – (-8,319) = 10,344 ACF The difference between the average OWF and the FY 2021 AWF is: 19,904 ACF –(-8,319) = 28,223. And, 63% of this difference is explained by our Rain Model as calculated below: 17,879/28,223 = 63%
What explains the remaining 37% in Other Water Flow (OWF) in FY 2021 that is not explained by the Rain Model? 22 … It is probably not any of the following: a) Actual water demand and consumed by our 191,000 residents. Such is probably lower than in recent years because of voluntary and mandatory conservation measures; b) Increase in residents served. This number has remained flat or declining since 2013 or so; c) Mandatory water release for fisheries that are locked in at 11,100 ACFs per year. … It could be the following: a) A true model error. An unstable relationship between Rainfall and OWF. The data does suggest the latter; b) Sonoma water imports may have been lower than assumed (at 25% of potable water production). But, they are unlikely to explain more than a 3,000 ACF difference (nowhere close to the 10,344 ACF difference between actual OWF and estimated OWF); c) A confounding factor not captured by the data and the Rain Model.
What is the 10,344 ACF Confounding Factor? 23 Again, it could be just a genuine model error. Otherwise, who knows it could be an opportunity to investigate and figure out what this confounding factor is. If we could figure it out, and resolve it going forward, that could represent an additional water supply of 10,344 ACFs. That probably represents close to 5 months of water demand.

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Marin County Drought Analysis

  • 1.
    Marin Municipal WaterDistrict Marin County Drought Analysis Gaetan Lion, July 28, 2021
  • 2.
    Content • Section 1.Rainfall annual (FY) data • Section 2. Droughts, monthly data • Section 3. Explaining FY 2021 2
  • 3.
    Section 1. RainfallAnnual (FY) data 3
  • 4.
  • 5.
    0 20 40 60 80 100 120 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 Wet Year, annualrainfall in inches FY 1880 - 1916 0 20 40 60 80 100 120 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 Dry Year, annual rainfall in inches FY 1917 - 1950 Very large difference in annual rainfall between the Wet Years and the Dry Years. 5
  • 6.
    0 20 40 60 80 100 120 1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Ranked year from highest to lowest from Left to Right Wet Years vs. Dry Years. Ranked from Highest to Lowest Wet Dry Another look at the very large difference between the Wet Years and the Dry Years. 6
  • 7.
    30 35 40 45 50 55 60 65 70 75 80 1889 1893 1897 1901 1905 1909 1913 1917 1921 1925 1929 1933 1937 1941 1945 1949 1953 1957 1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 2001 2005 2009 2013 2017 2021 10 Year AverageYearlyRainfall in inches Wet Year Dry Year Baseline Year Rainfall inchesper year Percentile Wet Dry Baseline 95% 100.3 68.9 86.7 75% 73.5 46.7 66.3 50% 60.4 39.2 47.4 25% 48.9 29.9 36.8 5% 34.2 22.5 28.7 The Wet Years and Dry Years are most divergent (divergence is somewhat attenuated by the 10 year averaging lagging effect) as shown on the graph. The long Baseline Year period is pretty much in between the two. That is true whether we look at 10 year average yearly rainfall on the graph or various percentiles in annual rainfall in the right hand table. 7
  • 8.
    Count ofDrought Years Percentile20% 10% 5% Inch per year 35 30 25 1880 -1916 3 0 0 1917 -1950 12 9 5 1951 -2021 14 6 3 % ofDrought Years Percentile 20% 10% 5% Inch per year 35 30 25 1880 -1916 8% 0% 0% 1917 -1950 35% 26% 15% 1951 -2021 20% 8% 4% The green area defines different Drought thresholds ranging from the 20th percentile at 35 inches per year down to the 5th percentile at 25 inches per year. These percentiles are based on the entire data set from 1880 – 2021. This table simply counts the number of Drought years falling within each category thresholds from 35 inches down to 25 inches per year. This table is actually much more informative because it discloses the percentage of years that fell into the respective Drought categories. And, if a period disclosed percentages are close to the overall percentile levels defining the Drought thresholds (20%/10%/5%), then this period’s Drought frequency is similar to the entire history of the data. And, we can see that this is the case for our Baseline period from 1951 – 2021 (20%/8%/4%). 8
  • 9.
    9 This table showsthe number of times a Drought has lasted at least two consecutive years or more. Keep in mind that the Dry Period (1917 – 1950) is less than half as long as the current Baseline Period (1951 – 2021). Given that, the Dry Period distinguishes itself as having more frequent long Droughts. This table is similar to the above, but identifies the periods when at least 50% of the years were in Drought conditions.
  • 10.
    Section 2. Droughts,monthly data 10
  • 11.
    These are the15 driest years in our historical data going back to 1880. Notice that 8 of the 15 did occur during the Dry Year period (1917 – 1950). None occurred during the Wet Year Period (1880 – 1916). Within the 15th driest years, 2021 was in the mid of the pack early on. But, it was unusually dry during the mid-Winter and early Spring. 11 Cumulative rainfall in inchesduring respective Fiscal Year Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun 1 1924 0.30 0.30 1.08 1.50 2.37 5.22 11.90 16.24 19.08 19.08 19.08 19.08 2 1918 0.00 0.00 0.12 0.12 1.90 4.12 4.83 13.00 19.25 20.65 20.65 20.65 3 2021 0.00 0.35 0.35 0.35 3.40 8.31 14.57 16.85 20.26 20.62 20.62 20.66 4 1976 0.36 0.41 0.41 8.33 9.68 11.17 11.48 14.71 18.06 22.13 22.13 22.13 5 1920 0.00 0.00 1.30 1.56 2.02 9.18 10.37 12.61 18.19 22.91 22.91 23.45 6 1931 0.00 0.00 0.61 1.71 4.20 5.54 15.65 17.60 21.37 21.82 23.17 23.65 7 1939 0.00 0.00 0.17 2.40 4.82 8.58 15.54 18.95 23.15 23.44 24.45 24.49 8 1977 0.00 1.73 3.06 3.85 6.20 10.38 14.94 17.69 22.65 23.16 24.95 24.97 9 1929 0.00 0.00 0.04 0.09 5.47 13.64 15.29 19.92 21.76 24.69 24.69 26.96 10 1959 0.00 0.00 0.10 0.25 1.23 4.12 14.61 25.49 27.25 28.25 28.25 28.25 11 1947 0.05 0.05 0.27 0.56 6.54 10.78 12.31 16.64 24.02 25.17 26.24 28.48 12 1934 0.00 0.00 0.08 3.23 3.23 13.62 16.21 25.56 25.96 26.76 28.08 29.10 13 1987 0.00 0.00 1.24 1.68 1.81 4.65 12.91 21.69 28.72 29.15 29.18 29.18 14 1933 0.05 0.05 0.05 0.05 2.09 7.40 17.57 19.86 26.63 26.78 29.74 29.74 15 1972 0.00 0.00 0.40 0.61 4.71 15.65 18.62 23.99 25.28 29.51 29.55 29.92 2021 ranking. Monthsreflect cumulative rainfall up to that month Nov Dec Jan Feb Mar Apr May June 8th 7th 7th 6th 5th 2nd 2nd 3d
  • 12.
    Same data ason the previous slide, but in graphical form. Same graph, but eliminating 1918 and 1976. Notice now how the 13 Droughts look remarkably similar with most of the rain hitting in December through March. 12
  • 13.
  • 14.
    A Simple WaterFlow Model Based on the data provided by the MMWD, we can construct a simple water flow model to disclose the reservoir capacity and disaggregate it in several components described below: 14 Beginning Reservoir level (July 1st, at beginning of fiscal year) - Potable water generation + Sonoma water imports (estimated at 25% of Potable water generation) + Other items Ending Reservoir level (June 30th, at end of fiscal year) The Sonoma water imports are just an estimate representing 25% of Potable water generation. “Other items” capture all other net water flows that make the sum of the mentioned flows generate the correct Ending Reservoir level. We suspect a good part of the “Other Items” are associated with rainfall that replenish the reservoirs.
  • 15.
    Here is therelevant data from 1987 to 2021 FY. The data provided included: • Beginning reservoir level • Ending reservoir level • Potable water production The reason the Ending reservoir level was at a record low as of June 30, 2021 was due to the record negative Other Water Flow of – 8,319 acre feet. This figure is in good part due to the near record low rainfall during FY 2021. 15 Reservoir Flows in acre foot Beginning Reservoir level Potable Water Production Sonoma Water Imports (25%) Other Water Flow Ending Reservoir level Begin to end change Rainfall in inches 1987 69,179 -33,056 8,264 9,003 53,390 -15,789 29.18 1988 53,227 -32,845 8,211 20,120 48,713 -4,514 30.55 1989 48,580 -28,555 7,139 33,178 60,342 11,762 36.44 1990 60,197 -29,392 7,348 6,174 44,327 -15,870 31.01 1991 44,274 -25,210 6,303 25,038 50,404 6,130 35.38 1992 50,393 -23,078 5,770 33,250 66,334 15,941 39.41 1993 66,299 -23,459 5,865 26,398 75,103 8,804 61.09 1994 74,988 -26,951 6,738 5,955 60,730 -14,258 33.02 1995 60,590 -26,288 6,572 35,766 76,640 16,050 87.44 1996 76,548 -28,039 7,010 20,138 75,657 -891 66.53 1997 75,822 -29,423 7,356 12,765 66,520 -9,302 51.65 1998 66,414 -27,111 6,778 31,272 77,353 10,939 91.71 1999 77,262 -29,405 7,351 18,038 73,247 -4,015 53.10 2000 73,102 -30,125 7,531 22,599 73,107 5 49.17 2001 72,930 -31,343 7,836 10,429 59,852 -13,078 34.26 2002 59,742 -30,452 7,613 33,695 70,598 10,856 54.98 2003 70,439 -30,310 7,578 27,233 74,939 4,500 56.71 2004 74,753 -31,406 7,852 16,958 68,156 -6,597 47.39 2005 67,910 -28,636 7,159 31,110 77,543 9,633 66.05 2006 77,394 -28,963 7,241 18,570 74,242 -3,152 73.03 2007 74,080 -29,775 7,444 8,307 60,056 -14,024 36.31 2008 59,899 -29,365 7,341 25,676 63,551 3,652 41.24 2009 63,256 -27,474 6,869 17,430 60,080 -3,176 42.94 2010 59,944 -25,231 6,308 34,118 75,139 15,195 58.24 2011 74,992 -25,372 6,343 20,379 76,342 1,350 70.16 2012 76,250 -26,070 6,518 16,796 73,493 -2,757 40.51 2013 73,372 -27,060 6,765 11,384 64,461 -8,911 40.20 2014 64,319 -26,709 6,677 15,619 59,906 -4,413 33.40 2015 59,661 -22,454 5,613 24,391 67,212 7,551 39.82 2016 67,094 -29,007 7,252 27,646 72,985 5,891 49.74 2017 72,823 -23,006 5,752 19,825 75,393 2,570 95.95 2018 75,278 -25,175 6,294 16,258 72,655 -2,623 38.89 2019 72,539 -24,590 6,147 23,253 77,350 4,811 74.03 2020 77,243 -26,828 6,707 6,177 63,299 -13,944 34.99 2021 63,175 -26,196 6,549 -8,319 35,209 -27,966 20.66
  • 16.
    16 -15,000 -10,000 -5,000 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 1987 1989 19911993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021 Other Water Flow in Acre Feet 0 20 40 60 80 100 120 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 Rainfall in Inches There is definitely a correspondence between Other Water Flow and Rainfall. The correlation coefficient between the two is 0.54, which is statistically significant given the number of data points. This corresponds to an R Square of close to 0.29 when using a linear regression to explain Other Water Flow, as the dependent variable Y, using Rainfall (as the causal X variable). However, on the next slide we present a polynomial regression that can dramatically increase the R Square of the model up to 0.42. In plain English, this second model using Rainfall as the X variable can explain 42% of the variance in Other Wate Flow, the Y variable.
  • 17.
    17 y = -9.6299x2+ 1403.3x - 22858 R² = 0.424 -15,000 -10,000 -5,000 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 0 20 40 60 80 100 120 Other Water Flows in ACF Rainfall in Inches Rainfall vs. Other Water Flow Polynomial Model explaining Other Water flows with Rainfall As shown, there is close to a linear relationship between Rainfall and Other Water Flow when Rainfall ranges between 20 and 60 inches. Beyond that point, this relationship somewhat evaporates. This is probably due because when Rainfall exceeds 60 inches, depending on the beginning Reservoir Level, a portion of the Rainfall just overflows. Focusing on 2021, the actual Other Water Flow is negative – 8,319 ACF. Meanwhile, the model estimate comes in at + 2,025 ACF. Thus, in this case the model overestimates 2021 Other Water Flow by 10,344 ACFs. This represents the 2nd largest overestimation out of 35 data points.
  • 18.
    Model Performance 18 That iswhat a model with an R Square of 0.42 looks like. It is far from perfect. But, it does capture some overall trends. (30,000) (20,000) (10,000) - 10,000 20,000 30,000 40,000 50,000 60,000 Other Water Flows in ACF Estimating Other Water Flow. Including 90% Confidence Interval Other Model Estimate Low High
  • 19.
    Model Performance since2009 with 90% C.I. 19 (30,000) (20,000) (10,000) - 10,000 20,000 30,000 40,000 50,000 60,000 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 Other Water Flows in ACF Estimating Other Water Flow. Including 90% Confidence Interval since 2009 Other Model Estimate Low High Since 2009, the Model performance is a lot better. The R Square over this period jumps to 0.71.
  • 20.
    Model Performance since2009 20 (15,000) (10,000) (5,000) - 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 Other Water Flows in ACF Estimating Other Water Flow. since 2009 Other Model Estimate This is just a cleaner look at the Model performance since 2009.
  • 21.
    Explaining FY 2021Other Water Flow (OWF) 21 The average OWF over the entire period is 19,904 ACF In FY 2021, the estimated OWF by our Rain Model is 2,025 ACF The difference calculated below is the difference that is explained by our Rain Model 19,904 – 2,025 = 17,879 ACF The actual OWF in FY 2021 is – 8,319 ACF The difference calculated below is the difference that remains unexplained by our Rain Model 2,025 – (-8,319) = 10,344 ACF The difference between the average OWF and the FY 2021 AWF is: 19,904 ACF –(-8,319) = 28,223. And, 63% of this difference is explained by our Rain Model as calculated below: 17,879/28,223 = 63%
  • 22.
    What explains theremaining 37% in Other Water Flow (OWF) in FY 2021 that is not explained by the Rain Model? 22 … It is probably not any of the following: a) Actual water demand and consumed by our 191,000 residents. Such is probably lower than in recent years because of voluntary and mandatory conservation measures; b) Increase in residents served. This number has remained flat or declining since 2013 or so; c) Mandatory water release for fisheries that are locked in at 11,100 ACFs per year. … It could be the following: a) A true model error. An unstable relationship between Rainfall and OWF. The data does suggest the latter; b) Sonoma water imports may have been lower than assumed (at 25% of potable water production). But, they are unlikely to explain more than a 3,000 ACF difference (nowhere close to the 10,344 ACF difference between actual OWF and estimated OWF); c) A confounding factor not captured by the data and the Rain Model.
  • 23.
    What is the10,344 ACF Confounding Factor? 23 Again, it could be just a genuine model error. Otherwise, who knows it could be an opportunity to investigate and figure out what this confounding factor is. If we could figure it out, and resolve it going forward, that could represent an additional water supply of 10,344 ACFs. That probably represents close to 5 months of water demand.