Recharge on Non-irrigated Land

Mike McVay06/24/2010

Our Process for Estimating Recharge.

Our process for estimating recharge on non-irrigated land is to use ET Idaho data from 45 weather stations to calculate the amount of recharge based on precipitation, root zone moisture and soil type. Then we utilize semi-log kriging to interpolate the recharge data across the model domain.

Interpolation – Data Transformation

Both Willem and I are employing semi-log kriging to interpolate the data. This involves a semi-log transform of the data in which values below a threshold are transformed logarithmically and those values above the threshold are transformed linearly.

•Transformation of data is necessary to avoid negative extrapolated values.•Semi-log transformation employed.

•Prevents extrapolation of “small” numbers to negative values while maintaining linear behavior of “large” numbers. •Threshold (α) of 0.001.

Interpolation - Kriging

•I have employed Geostatistical Analyst in ArcMap to Krige, Willem has written code.

•Ordinary Kriging – No trend in data, so no drift has been incorporated for interpolation.•No nugget has been employed.•Linear Variogram Model – Few data points over a large area precludes fitting a variogram model to data.

•Geostatistical Analyst does not support Linear Variogram, so a Spherical model has been employed with a very large range.

•Sites with no data have been ignored during Kriging.

Interpolation Comparison

I have randomly chosen 30 month/soil-type combinations to compare interpolation results. My comparison of the results indicates that the Kriging methods that Willem and I have

employed are very similar (see table on next slide).

Stress Period/Soil Type McVay Sum (ft)

Schreuder Sum (ft)

Diff (%McVay

Sum)

Abs Diff (%McVay

Sum)Dec 2001 Lava 1455.88 1455.67 0.01% 0.0001Nov 1984 Thin 1149.73 1150.38 -0.06% 0.0006Dec 1998 Thin 459.68 459.99 -0.07% 0.0007May 1980 Thin 1639.82 1638.59 0.08% 0.0008Jan 1982 Lava 781.20 780.42 0.10% 0.0010Dec 2004 Lava 2158.85 2156.18 0.12% 0.0012May 1993 Lava 1271.83 1269.69 0.17% 0.0017Sep 1993 Thick 49.54 49.62 -0.17% 0.0017Sep 1997 Thin 183.48 183.80 -0.17% 0.0017Aug 1999 Thin 76.12 76.26 -0.18% 0.0018Sep 1994 Thick 27.85 27.79 0.21% 0.0021Aug 1989 Thick 38.84 38.76 0.22% 0.0022Jun 2003 Thin 22.65 22.74 -0.36% 0.0036Feb 1990 Lava 311.58 310.33 0.40% 0.0040Oct 2002 Thick 65.36 65.10 0.40% 0.0040Sep 1994 Lava 423.14 421.31 0.43% 0.0043Jul 1995 Thick 43.48 43.29 0.44% 0.0044Oct 2008 Lava 443.84 441.60 0.51% 0.0051Apr 1982 Thin 381.65 379.33 0.61% 0.0061May 2008 Lava 486.53 483.35 0.65% 0.0065Apr 1994 Lava 465.45 462.40 0.66% 0.0066Jan 1995 Thick 74.22 73.73 0.66% 0.0066Oct 1984 Thick 166.46 165.25 0.73% 0.0073Mar 1988 Thick 67.78 67.09 1.02% 0.0102Oct 1999 Lava 60.54 59.89 1.09% 0.0109Jun 1986 Lava 335.28 339.81 -1.35% 0.0135

Mar 1997 Thick 69.00 67.98 1.47% 0.0147Dec 1995 Thick 85.58 84.09 1.74% 0.0174Jan 1992 Thin 34.79 34.10 1.97% 0.0197

Absolute Value Average

0.55%

Some figures to assess agreement between Kriging Efforts

McVay381.65

Schreuder379.33

Apr82THIN0.004473 - 0.021840

0.021841 - 0.038428

0.038429 - 0.062001

0.062002 - 0.097196

0.097197 - 0.175000

McVay465.45

Schreuder462.40

Apr94LAVA0.004990 - 0.030746

0.030747 - 0.043898

0.043899 - 0.062672

0.062673 - 0.090261

0.090262 - 0.147525

McVay38.84

Schreuder38.76

Aug89THICK0.000992 - 0.014334

0.014335 - 0.045670

0.045671 - 0.082803

0.082804 - 0.124821

0.124822 - 0.184267

Aug99THIN0.000998 - 0.006010

0.006011 - 0.015079

0.015080 - 0.025996

0.025997 - 0.040262

0.040263 - 0.062212

McVay76.12

Schreuder76.26

Dec95THICK0.000996 - 0.003944

0.003945 - 0.009154

0.009155 - 0.016746

0.016747 - 0.035660

0.035661 - 0.071058

McVay85.58

Schreuder84.09

Dec98THIN0.001000 - 0.024633

0.024634 - 0.045599

0.045600 - 0.073201

0.073202 - 0.117129

0.117130 - 0.188134

McVay459.68

Schreuder459.99

Dec01LAVA0.001322 - 0.052426

0.052427 - 0.094935

0.094936 - 0.135564

0.135565 - 0.184064

0.184065 - 0.286403

McVay1455.88

Schreuder1455.67

Dec05LAVA0.000000 - 0.097000

0.097001 - 0.148000

0.148001 - 0.203000

0.203001 - 0.268000

0.268001 - 0.348063

McVay2158.85

Schreuder2156.18

Feb90LAVA0.001000 - 0.015000

0.015001 - 0.033000

0.033001 - 0.057000

0.057001 - 0.087000

0.087001 - 0.147086

McVay311.58

Schreuder310.33

Jan82LAVA0.000692 - 0.023813

0.023814 - 0.051942

0.051943 - 0.086757

0.086758 - 0.166045

0.166046 - 0.340169

McVay781.20

Schreuder780.42

Jan92THIN0.000994 - 0.004543

0.004544 - 0.010809

0.010810 - 0.030567

0.030568 - 0.066354

0.066355 - 0.125720

McVay34.79

Schreuder34.10

Jan95THICK0.000953 - 0.006299

0.006300 - 0.019629

0.019630 - 0.041309

0.041310 - 0.069145

0.069146 - 0.106479

McVay74.22

Schreuder73.73

Jul95THICK0.000997 - 0.006375

0.006376 - 0.018866

0.018867 - 0.034672

0.034673 - 0.052222

0.052223 - 0.081068

McVay43.48

Schreuder43.29

Jun86LAVA0.000985 - 0.019397

0.019398 - 0.038214

0.038215 - 0.060704

0.060705 - 0.086177

0.086178 - 0.112790

McVay335.28

Schreuder339.81

Jun03THIN0.000999 - 0.002957

0.002958 - 0.007500

0.007501 - 0.013213

0.013214 - 0.019579

0.019580 - 0.030036

McVay22.65

Schreuder22.74

Mar88THICK0.000998 - 0.003129

0.003130 - 0.006745

0.006746 - 0.011762

0.011763 - 0.018741

0.018742 - 0.034005

McVay67.78

Schreuder67.09

Mar97THICK0.000998 - 0.003515

0.003516 - 0.008089

0.008090 - 0.014215

0.014216 - 0.029570

0.029571 - 0.064268

McVay69.00

Schreuder67.98

May80THIN0.009725 - 0.076457

0.076458 - 0.128061

0.128062 - 0.170970

0.170971 - 0.221884

0.221885 - 0.341042

McVay1639.82

Schreuder1638.59

May93LAVA0.001128 - 0.056659

0.056660 - 0.111499

0.111500 - 0.167071

0.167072 - 0.224803

0.224804 - 0.312504

McVay1271.83

Schreuder1269.69

May08LAVA0.003000 - 0.024000

0.024001 - 0.040000

0.040001 - 0.062000

0.062001 - 0.090000

0.090001 - 0.135000

McVay486.53

Schreuder483.35

Nov84THIN0.000000 - 0.026000

0.026001 - 0.070000

0.070001 - 0.112000

0.112001 - 0.158000

0.158001 - 0.341382

McVay1149.73

Schreuder1150.38

Oct84THICK0.000996 - 0.006623

0.006624 - 0.014086

0.014087 - 0.024290

0.024291 - 0.038513

0.038514 - 0.065161

McVay166.46

Schreuder165.25

Oct99LAVA0.000999 - 0.003856

0.003857 - 0.006759

0.006760 - 0.010383

0.010384 - 0.017544

0.017545 - 0.031833

McVay60.54

Schreuder59.89

Oct02THICK0.000999 - 0.004149

0.004150 - 0.010469

0.010470 - 0.018581

0.018582 - 0.029108

0.029109 - 0.047011

McVay65.36

Schreuder65.10

Oct08LAVA0.000998 - 0.014497

0.014498 - 0.031277

0.031278 - 0.047166

0.047167 - 0.062931

0.062932 - 0.113931

McVay443.84

Schreuder441.60

Sep93THICK0.000994 - 0.006251

0.006252 - 0.029856

0.029857 - 0.072349

0.072350 - 0.125398

0.125399 - 0.190014

McVay49.54

Schreuder49.62

Sep94THICK0.000997 - 0.006222

0.006223 - 0.018034

0.018035 - 0.033891

0.033892 - 0.055521

0.055522 - 0.095243

McVay27.85

Schreuder27.79

Sep94LAVA0.000997 - 0.017574

0.017575 - 0.034539

0.034540 - 0.051538

0.051539 - 0.073862

0.073863 - 0.100641

McVay423.14

Schreuder421.31

Sep97THIN0.000000 - 0.006000

0.006001 - 0.017000

0.017001 - 0.030000

0.030001 - 0.053000

0.053001 - 0.095176

McVay183.48

Schreuder183.80

Calculating Recharge

Our Process for Calculating Recharge.

We calculate the amount of recharge at each of the 45 weather stations using ET Idaho precipitation (P), root-zone moisture (P_rz) data.

Recharge = P – P_rz

We represent recharge for the three general soil types of Thick Soil, Thin Soil and Lava Rock using the ET Idaho root-zone moisture data for Sage Brush and Dormant Turf covers.

To represent recharge on the various soil types we use:

1. Precipitation – Sage Brush Root-zone Moisture to represent Thick Soil.2. Precipitation – Dormant Turf Root-zone Moisture to represent Thin Soil.3. Precipitation – (2/3*Dormant Turf Root-zone Moisture) to represent Lava Rock.

What is P_rz?

“P_rz – Precipitation residing in the root zone. P_rz is the amount of gross reported precipitation that infiltrates into the soil (i.e. , less any runoff) and that remains in the root zone for consumption by evaporation or transpiration. P_rz is computed as:

P – Runoff – DPercwhere:

P is gross precipitationRunoff is estimated surface runoffDperc is deep percolation of any precipitation below the max root zone for the

land-use condition.”

Note: Definition from “Evaporation and Consumptive Irrigation Water Requirements for Idaho.” Allen and Robinson, 2007.

Note: All values are in units of [L/T] which are multiplied by the number of days in each month.

Our Proxy for Recharge.

Our proxy for recharge is calculated as:

Recharge = P – P_rz P-(P – Runoff – Dperc) Runoff + Dperc

Recharge = Runoff + Dperc

where:Recharge is recharge to the aquiferP is gross precipitationP_rz is precipitation residing in root zoneRunoff is estimated surface runoffDperc is deep percolation of any precipitation below the max root zone for the

land-use condition.

We assume that all runoff will eventually percolate via ponding or stream leakage to become recharge.

Root Zone

Precipitation

Runoff

P_rz

Dperc

Recharge = P – P_rz P-(P – Runoff – Dperc) Runoff + Dperc

Recharge = Runoff + Dperc

Three scenarios are present in the data from ET Idaho that confound our process for estimating recharge.

Recharge = P – P_rz Runoff + Dperc

There are three scenarios in the ET Idaho data that we need to address.1. Precipitation residing in root zone is negative.

i. Typically occurs during dry periods.ii. P – (-P_rz) results in abnormally large amount of recharge.

2. Precipitation residing in root zone is greater than gross precipitation.i. Typically occurs during non-summer months (one in July) – only 15 occurrences.ii. Difference is always 0.01 mm/day.iii. P – P_rz results in negative recharge value.

3. Dormant Turf precipitation residing in root zone is greater than that of Sage Brush.i. Occurs in 31% of data.ii. Does not appear to be seasonal.iii. P – P_rz results in more recharge on Thick Soils than on Thin Soils and Lava.

Scenario 1 – Root Zone Moisture is negative

Our work-around for moving forward is to consider this a soil moisture “deficit” and set recharge to be zero.

P_rz = P – Runoff – Dperc Negative values should not occur, based on mass balance.

American Falls August 1981: P – P_rzSage = 0.07 – (-2.06) = 2.13

Our work-around for moving forward is to compute recharge as the absolute difference .

P_rz = P – Runoff – Dperc P_rz > P should not occur, based on mass balance.

Scenario 2 – Root Zone Moisture is greater than precipitation

Swan Valley March 1985: P – PrzSage = 0.80 – 0.81 = -0.01

No work-around for moving forward has been employed.

Performing the P – P_rz calculation results in more recharge from Thick Soil than from Thin Soil and Lava.

Previous work has demonstrated that recharge from precipitation is partly a function of soil texture and depth, and the general relationships between the soil types represented on the ESPA are that recharge from Lava > Thin Soil > Thick Soil (Contor, 2004; Garabedian, 1992).

Scenario 3 – Dormant Turf P_rz is greater than Sage Brush P_rz

Blackfoot

ESPAM SoilsTHIN_CELLS

THICK_CELLS

LAVA_CELLS

May 1980 Recharge (ft)0.000 - 0.016

0.017 - 0.034

0.035 - 0.045

0.046 - 0.055

0.056 - 0.066

0.067 - 0.076

0.077 - 0.087

0.088 - 0.098

0.099 - 0.109

0.110 - 0.120

0.121 - 0.131

0.132 - 0.143

0.144 - 0.156

0.157 - 0.171

0.172 - 0.188

0.189 - 0.208

0.209 - 0.229

0.230 - 0.251

0.252 - 0.293

0.294 - 0.381

Sep 1997 Recharge (ft)0.000 - 0.002

0.003 - 0.004

0.005 - 0.007

0.008 - 0.010

0.011 - 0.013

0.014 - 0.016

0.017 - 0.020

0.021 - 0.023

0.024 - 0.027

0.028 - 0.030

0.031 - 0.035

0.036 - 0.040

0.041 - 0.046

0.047 - 0.053

0.054 - 0.062

0.063 - 0.073

0.074 - 0.088

0.089 - 0.104

0.105 - 0.123

0.124 - 0.143

ESPAM SoilsTHIN_CELLS

THICK_CELLS

LAVA_CELLS

Recharge Calculation Summary

•Both Willem and I are using the same methodology in calculating recharge. •There are three scenarios that confound our recharge proxy process.

•Precipitation residing in root zone is negative.•Precipitation residing in root zone is greater than gross precipitation.•Dormant Turf precipitation residing in root zone is greater than that of Sage Brush.

•We have employed two temporary work-around solutions to move forward with interpolation.

•Precipitation residing in root zone is negative. Work-around: Recharge = Zero.•Precipitation residing in root zone is greater than gross precipitation. Work-around: Recharge = 0.01 mm/day.•Dormant Turf precipitation residing in root zone is greater than that of Sage Brush. Work-around: None.

•Formal solutions should be pursued by the committee once Dr. Allen has had a chance to look at the data.

Any Questions?