Using provided long term data, generated a quantitative and visual data analysis to better understand the current drought and water supply crisis affecting Marin County in 2021

1. Marin Municipal Water District
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. Rainfall Annual (FY) data
3

4. 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

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, 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

6. 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

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 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

8. 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. 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.

10. Section 2. Droughts, monthly data
10

11. 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

12. 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

13. Section 3. Explaining FY 2021
13

14. 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.

15. 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. 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. 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 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

19. 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.

20. 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.

21. 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%

22. 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.

23. 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.