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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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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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Davis Tmax Raw Data

R2 = 0.96

R2 = 0.49

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Davis: Observed versus Simulated Daily Tmax

R2 = 0.94

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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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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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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

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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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