davis three years maximum tempearturesbiomet.ucdavis.edu/evapotranspiration/dwr/pdf_files/2-19...
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Davis Three Years Maximum Tempeartures
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SIMETO A model generates daily weather
variables based on monthly summaries
Model Development ConcernsHow many parameters are needed?
• Overparameterization– Information over-use; inefficient model; unstable
model• Underparameterization
– Information underutilization; potentially large systematic errors
latitudes, longitudes, elevations (m.)
The meteorological variables
(a) fractions of wet days (b) rain per wet day(c) maximum temperature (d) minimum temperature(e) solar radiation (f) vapor pressure(g) maximum relative humidity (h) minimum relative humidity (i) wind speed
Basic Data Inputs
SIMULATION OF ETo
The equations used to simulate reference evapotranspiration (ET0) are taken from R.L. Snyder and W.O. Pruitt (1994) and include the
following:
(1) Original Penman (2) Penman/Monteith (as used in the FAO CROPWAT program)(3) Corrected FAO Penman(4) Priestley/Taylor(5) Jensen/Haise(6) FAO Radiation(7) FAO Blaney/Criddle(8) SCS Blaney Criddle(9) Hargreaves(10) Corrected FAO evaporation pan
Required Meteorological Data For Eto Calculations
Eto Estimate MaxT MinT Solar Humidity Wind
EPEN X X X X XPENM X X X X XCFAO X X X X XFAORD X X X X XFAOBC X X X X XEPT X X X XEJH X X XSCSBC X XHARG X X
– Tow Stage Markov Chain: useful to describe time series events
• to determine the rain or dry day– Gamma function: a skewed distribution ideal for
describe rainfall amount• to determine the amount of rain
YesterdayWet DryToday Today
Wet Dry wet Dry
f11(t) 1f01(t) 1
f10(t) 1
f00(t) 1
P11 = SUM(f11); P01 = 1 - P11; P10 = SUM(f10); P00 = 1 - P10
How many parameters are needed?
A linear relationship existsbetween the transitional probability
and the marginal probability
P(W/D) = 0.006 + 0.75 (fraction of wet days); r2 = 0.96= 0.75 * (fraction of the wet days)
P(W/W) = (1 - b) + b*(Fraction of wet days)= 0.25 + P(W/D)
Thus all transitional probability are estimable form the fraction of wet days!
The Amount of Rainfall: Gamma Function
Alfa = (0.5000876 + 0.16488552Y -0.0544274Y2) / YBata = Arithmetic Mean / Alfawhere Y = In(Arithmetic Mean/Geometric Mean)
Alfa < 1; unit less; most influential to small numbers
Batahas the same unit as the variable and affects extreme numbers, or the tail distribution more than Alfa
Thus Bata related to mean more than Alfa?
A Linear Relationship is Established Between Bata and the Mean Amount of
Rainfall Per wet day
Bata = - 2.16 + 1.83*(amount of rain per wet day) (0.275) (0.036) r2 = 0.965
Alfa = (Amount per Wet Day) / Bata
Thus, given amount rainfall per wet day, we can obtain both Alfa and Bata for the Gamma model to
generate rainfall
Other weather Variables: Temperature and Solar Radiation
Mean Curve = a + b COS [2(Pi)(j - q) /365]where j is Julian day; q is the day with the maximal value
X = Mean* ( 1+ d*CV)
ab
CV is the coefficient of variation.
“d” measures the influence of other correlated weather variables, the serial correlations, and a random component.
di = B0 di-1 + B1 ei
B0 = R1R0-1
B1B1’ = R0 - R1 R0
-1 R1’
R0 is the cross correlation matrix , and R1 is the serial correlation matrix.
1 r12 r13
R0 = r21 1 r23
r31 r32 1
rij is the cross correlation between ith and jth variables.
r(11) r(12) r(13)
R1 = r(21) r(22) r(23)
r(31) r(32) r(33)
r(ij) is the serial correlation between ith and jth variable,with the second vraiable lagged one day.
Temperature Curve
CV Curve
Tmax(CV) = (0.536 - 0.00573 a0 ) - exp(-4.63 + 0.0952 b) *(COS(2(i-q)/365)
Tmin(CV) = exp(-0.0466a) - exp(-4.64 + 0.146b) *COS(2(i-q)/365)
Davis: Raw and Simulated daily Tmin means
Blue -Simulated; R2 = 0.96
Red -Raw; R2 = 0.93
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Davis: Observed versus Simulated Daily Tmin
R2 = 0.82
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Observed Tmin
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min
Davis Tmim Raw Data
CV R2 = 0.71
Mean Curve R2 = 0.93
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Davis Tmin Daily Raw versus Simulated CVs
Blue- Raw ;R2 = 0.71
Red - Simulated ;R2 = 0.69
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Days in Year
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Davis Tmax Raw Data
R2 = 0.96
R2 = 0.49
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C D
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Davis: Observed versus Simulated Daily Tmax
R2 = 0.94
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Observed Tmax
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Davis: Raw and Simulated daily Tmax means
Blue - Raw; R2 = 0.96
Red - Simulated; R2 = 0.96
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Davis Tmax Daily Raw versus Simulated CVs
Red - Simulated; R2 = 0.79
Blue - raw; R2 = 0.49
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Days in Year
Perc
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Davis Raw data of Salor Radiation: Daily means and CVs
Red - CV Curve; R2 = 0.7307
Blue -Means; R2 = 0.9767
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Davis Raw versus Simulated Salor Radiation
R2 = 0.96
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Davis Raw Versus Simualtred Daily CV of Salor Radiation
Blue - Raw; R2 = 0.73
Red - Simulated; R2 = 0.69
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CV
Davis Observed versus Simulated Daily Salor Radiation
Red - Simulated; R2 = 0.98
Blue -Raw; R2 = 0.98
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Dvais ETO Raw Data
R2 = 0.63
R2 = 0.97
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ETO
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Davis: Observed versus Simulated Daily ETo
R2 = 0.93
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ETo Daily CVs: Raw versus Simulated values
Simulated CV; R2 = 0.56
Raw CV; R2 = 0.49
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Davis: Raw and Simulated daily ETo means
Red- Raw; R2 = 0.97
Blue - Simulated; R2 = 0.95
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Davis Real and Simulated Monthly RainfallRed: simulated; Blue: real
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Davis Real and Simulated Rainfall Days per MonthRed: simulated; Blue: real
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Davis Real and Simulated Wind Speed (m/s)Red: Simulated; Blue: Real
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