Davis Three Years Maximum Tempeartures 16 31 46 61 76 91 106 - - PDF document

Davis Three Years Maximum Tempeartures

• 5

5 10 15 20 25 30 35 40 45 1 16 31 46 61 76 91 106 121 136 151 166 181 196 211 226 241 256 271 286 301 316 331 346 361

SIMETO

A model generates daily weather variables based on monthly summaries Model Development Concerns

How 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 X PENM X X X X X CFAO X X X X X FAORD X X X X X FAOBC X X X X X EPT X X X X EJH X X X SCSBC X X HARG 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

Yesterday Wet Dry Today Today Wet Dry wet Dry f11(t) 1 f01(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 exists

between 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) / Y Bata = Arithmetic Mean / Alfa where Y = In(Arithmetic Mean/Geometric Mean)

Alfa < 1;

unit less; most influential to small numbers

Bata

has 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

• btain 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)

a b

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; R

2 = 0.96

Red -Raw; R

2 = 0.93

2 4 6 8 10 12 14 16 18

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360

Davis: Observed versus Simulated Daily Tmin

R2 = 0.82 2 4 6 8 10 12 14 16 18 5 10 15 20 Observed Tmin Simulated Tmin

Davis Tmim Raw Data

CV R2 = 0.71 Mean Curve R2 = 0.93 2 4 6 8 10 12 14 16 18 1 31 61 91 121 151 181 211 241 271 301 331 361

C Degree

50 100 150 200 250 300

CV (%)

Davis Tmin Daily Raw versus Simulated CVs Blue- Raw ;R2 = 0.71 Red - Simulated ;R2 = 0.69 50 100 150 200 250 300

30 60 90 120 150 180 210 240 270 300 330 360

Days in Year Percent CV

Davis Tmax Raw Data

R2 = 0.96 R2 = 0.49

5 10 15 20 25 30 35 40 1 31 61 91 121 151 181 211 241 271 301 331 361

C Degree

10 20 30 40 50 60

CV (%) Davis: Observed versus Simulated Daily Tmax

R2 = 0.94 5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 Observed Tmax Simulated Tmax

Davis: Raw and Simulated daily Tmax means

Blue - Raw; R2 = 0.96 Red - Simulated; R2 = 0.96 5 10 15 20 25 30 35 40

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360

Davis Tmax Daily Raw versus Simulated CVs Red - Simulated; R2 = 0.79 Blue - raw; R2 = 0.49 10 20 30 40 50 60

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360

Days in Year Percent CV

Davis Raw data of Salor Radiation: Daily means and CVs

Red - CV Curve; R2 = 0.7307 Blue -Means; R2 = 0.9767 0.0 0.2 0.4 0.6 0.8 1.0 1.2

1 15 29 43 57 71 85 99 113 127 141 155 169 183 197 211 225 239 253 267 281 295 309 323 337 351 365

CV 5 10 15 20 25 30 35 MJ/m2

Davis Raw versus Simulated Salor Radiation R2 = 0.96

5 10 15 20 25 30 35 5 10 15 20 25 30 35 raw simulated Davis Raw Versus Simualtred Daily CV of Salor Radiation

Blue - Raw; R

2 = 0.73

Red - Simulated; R

2 = 0.69

0.0 0.2 0.4 0.6 0.8 1.0 1.2

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321 341 361

CV Davis Observed versus Simulated Daily Salor Radiation

Red - Simulated; R2 = 0.98 Blue -Raw; R2 = 0.98 5 10 15 20 25 30 35 1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321 341 361

Solar

Dvais ETO Raw Data

R2 = 0.63 R2 = 0.97 1 2 3 4 5 6 7 8 1 31 61 91 121 151 181 211 241 271 301 331 361 ETO (mm) 20 40 60 80 100 120 140 CV (%)

Davis: Observed versus Simulated Daily ETo

R2 = 0.93 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 Observed ETo Simulated ETo

ETo Daily CVs: Raw versus Simulated values

Simulated CV; R2 = 0.56 Raw CV; R2 = 0.49

20 40 60 80 100 120 140 30 60 90 120 150 180 210 240 270 300 330 360 Days in Year Percent CV

Davis: Raw and Simulated daily ETo means

Red- Raw; R2 = 0.97 Blue - Simulated; R2 = 0.95 1 2 3 4 5 6 7 8 9 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360

Davis Real and Simulated Monthly Rainfall

Red: simulated; Blue: real 20 40 60 80 100 120 140 1 2 3 4 5 6 7 8 9 10 11 12 Month Rainfall (mm)

Davis Real and Simulated Rainfall Days per Month

Red: simulated; Blue: real 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 10 11 12 Month

Davis Real and Simulated Wind Speed (m/s)

Red: Simulated; Blue: Real 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1 2 3 4 5 6 7 8 9 10 11 12 Month