# Presentation: 143345

## Developing Regression Models for Sediment Yield and Nutrient Loss From Biomass Crops 

**1****Department of Plant and Soil Science, Alabama A&M University, P.O. Box 1208, Normal, AL 35762;  ****2****Bioenergy Feedstock Development Programs, Oakridge National Laboratory, Oakridge, TN 37831  **

**Developing Regression Models for Sediment Yield and Nutrient Loss From Biomass Crops **

## Siltation of rivers, dams, and lakes.

Pollution of surface and ground water resources.

**Pollution of surface and ground water resources.**

**INTRODUCTION**

***Soil Erosion***
**An environmental problem.**

## Eutrophication of rivers and lakes.

 NO3- and soluble P (H2PO4-) in runoff water.

 NH4+ and P attached to sediment.

** ****NO****3****-**** and soluble P (H****2****PO****4****-****) in runoff water.**
** ****NH4+ and P attached to sediment.**

## Information needed:

How much runoff occurs.

How much soil is lost as eroded sediment.

Amount of nutrients, esp. N (NO3- and NH4 +) P are lost in runoff water and eroded sediment.

**How much runoff occurs.**
**How much soil is lost as eroded sediment.**
**Amount of nutrients, esp. N (NO****3****-**** and NH****4 ****+****) P are lost in runoff water and eroded sediment.**

***Evaluating the sustainability of growing biomass crops.***

## STUDY

**Co-operation between Tennessee Valley Authority**
**(TVA), DOE’s Bio-energy Feedstock Development**
**Program (BFDP),  Oakridge TN and Alabama**
**A&M University, Huntsville AL.**
***Objective:***
**To assess the environmental impacts of bio-energy**
**crop production on soil and water quality.**

## 
Location

Winfred Thomas Agricultural Research Station (WTARS), Hazel Green AL, from 1995 to 1999.

Soil type
 Decatur silt loam (clayey, kaolinitic thermic, Typic Paleudults).

**Location**
**Winfred Thomas Agricultural Research Station (WTARS), Hazel Green AL, from 1995 to 1999.**
**Soil type**
** ****Decatur silt loam (clayey, kaolinitic thermic, Typic Paleudults).**

## TREATMENT FACTORS

**No-till Corn (NTC)**
**Switchgrass cover crop (SWG)**
**Sweetgum with cover crop (SGC)**
**Sweetgum without cover crop (SWC)**

## FIELD PLAN

**Eight runoff plots (four 0.18 ha and 0.43 ha) established.**
**Treatments randomly assigned to plots with each treatment getting one large and one small plot (see diagram).**

## Plot layout, WTARS

**Plot layout, WTARS**

## FIELD PLAN

**Eight runoff plots (four 0.18 ha and 0.43 ha) established.**
**Treatments randomly assigned to plots with each treatment getting one large and one small plot (see diagram).**
**Earth berm ~ 50 cm high around each plot to isolate them from surrounding fields.**

## DATA COLLECTED

**Rainfall.**
**Runoff volume.**
**Sediment yield.**
**Nutrient loss.**
** ****(nitrate, ammonium, and P).**

## Runoff and sediment collecting point

## Setup for collecting runoff and sediment – V flume

## Housing for data loggers

## Data collection and storage

## Data collection and storage

## Sweet gum plot

## Switchgrass Plot

## Corn plot

## RESULTS AND DISCUSION

## Rainfall and runoff, WTARS 1995-1999

## Runoff NH4 as affected by no-till corn (NTC), switchgrass (SWG), sweetgum wo/cover (SWC), and sweetgum w/cover (SGC) treatments, WTARS, AL

## Runoff NO3 as affected by no-till corn, switchgrass, sweetgum wo/cover, and sweetgum w/cover treatments, WTARS, AL

## Runoff P as affected by no-till corn, switchgrass, sweetgum wo/cover, and sweetgum w/cover treatments, WTARS, AL

## Sediment yield as affected by no-till corn, switchgrass, sweetgum wo/cover, and sweetgum w/cover treatments, WTARS, AL

## Sediment NO3 as affected by no-till corn, switchgrass, sweetgum wo/cover, and sweetgum w/cover treatments, WTARS, AL

## Sediment P as affected by no-till corn, switchgrass, sweetgum wo/cover, and sweetgum w/cover treatments, WTRS, AL

## To relate sediment yield, NH4 and NO3
losses to rainfall and runoff.

Factors affecting sediment yield and
nutrient loss:
Climate
Soil type
Topography (slope)
Land use

***losses to rainfall and runoff.***
**Factors affecting sediment yield and**
**nutrient loss:**
**Climate**
**Soil type**
**Topography (slope)**
**Land use**

***Fitting regression models***

## In this study:

Climate, soil type, and slope are similar for all treatments.

Land use – different as defined by each treatment.

Therefore, interested in models for each treatment to be able to compare land use systems.

**Climate, soil type, and slope are similar for all treatments.**
**Land use – different as defined by each treatment.**
**Therefore, interested in models for each treatment to be able to compare land use systems.**

## Strategy for Developing Regression Models

**Start**

**Exploratory data analysis**

**Develop tentative regression models**

**Is one or more models suitable?**

**Identify most suitable model**

**Make inferences based on model**

**Stop**

**Revise models/new ones?**

**YES**

**NO**

## Statistics for developing regression
models.

Several regression analyses procedures.
Proc Reg, Proc Glm, Proc rsreg, Proc Catmod ...etc
Each procedure has special features for handling similar or different data types.

Choice - largely on applicability of each proc and  degree of complexity of data.

However, individual preference also plays big part.

**models.**
**Several regression analyses procedures.**
**Proc Reg, Proc Glm, Proc rsreg, Proc Catmod ...etc**
**Each procedure has special features for handling similar or different data types.**
**Choice - largely on applicability of each proc and  degree of complexity of data.**
**However, individual preference also plays big part.**

***Fitting the ‘‘BEST’’ model***

## However, no matter how “artistic” model development can be, reality must be kept at manageable proportions !!

Only a limited number of of independent or predictor variables (parameters) should be included in the model.

Considerations in choosing model parameters:
Contribution to reducing variation in dependent variable.
Degree to which parameter can be obtained efficiently (quickness, cost, accuracy).

Importance of parameter to the study.

**Only a limited number of of independent or predictor variables (parameters) should be included in the model.**
**Considerations in choosing model parameters:**
**Contribution to reducing variation in dependent variable.**
**Degree to which parameter can be obtained efficiently (quickness, cost, accuracy).**
**Importance of parameter to the study.**

***Fitting the ‘‘BEST’’ model***

## Scatter plots showing relationships between sediment yield,  rainfall and runoff volume

**No-till corn**

**Switch grass**

**Sweetgum**

**Sweetgum w/cover**

## Scatter plots showing relationships between  NO3 loss,  rainfall and runoff volume

**No-till corn**

**Switch grass**

**Sweetgum**

**Sweetgum w/cover**

## Scatter plots showing relationships between  P loss,  rainfall and runoff volume

**No-till corn**

**Switch grass**

**Sweetgum**

**Sweetgum w/cover**

## Scatter plots showing relationships between runoff volume and rainfall

**No-till corn**

**Switch grass**

**Sweetgum**

**Sweetgum w/cover**

##                      In this study:

Proc REG choice over Proc GLM.

Proc REG – more diagnostic tools and capabilities. 

SAS ver. 6.02 introduced two new model-selection methods for fitting the “best” model.

Adgjusted R2 (ADRSQ) and Mallow’s CP statistic.

**Proc REG choice over Proc GLM.**
**Proc REG – more diagnostic tools and capabilities. **
**SAS ver. 6.02 introduced two new model-selection methods for fitting the “best” model.**
**Adgjusted R****2**** (ADRSQ) and Mallow’s C****P**** statistic.**

## Proc rsquare cp mse adjrsq; 	by trt; by season trt; 

rsquare = regression SS/corrected total sum of squares
this finds a no.of models with the highest R square.

cp = Mallow’s Cp 
= (Residual SSp)/ (Res MS from full model) + 2p-n 
this finds a no.of models with the lowest Cp.

adjusted R2 (ADRSQ) 
= 1 – Error Mean Square/Total MS =  1 – (1- R2)(n-1)/(n-p)
this finds a no.of models with the highest adjusted R square

MSE = mean square error. 

**rsquare = regression SS/corrected total sum of squares**
**this finds a no.of models with the highest R square.**
**cp = Mallow’s Cp **
**= (Residual SSp)/ (Res MS from full model) + 2p-n **
**this finds a no.of models with the lowest Cp.**
**adjusted R****2**** (ADRSQ)**** **
**= 1 – Error Mean Square/Total MS =  1 – (1- ****R****2****)(n-1)/(n-p)**
**this finds a no.of models with the highest adjusted R square**
**MSE = mean square error. **

**SAS Procedure**

## Model sediment NH4 NO3 = X1 X2 X3 Y1 Y2                     		                                    Y3 Z1; 
Where
X1 = rainfall
X2 = rainfall*rainfall
X3 = rainfall*rainfall*rainfall

Y1 = runoff
Y2 = runoff*runoff
Y3 = runoff*runoff*runoff
 Z1 = rainfall*runoff. 

**Where**
**X1 = rainfall**
**X2 = rainfall*rainfall**
**X3 = rainfall*rainfall*rainfall**
**Y1 = runoff**
**Y2 = runoff*runoff**
**Y3 = runoff*runoff*runoff**
** ****Z1 = rainfall*runoff.**** **

**SAS Model Statement**

## Regression Models for Dependent Variable: SEDIMENT

**Number  R-square  Adjusted    C(p)        MSE          Variables in Model**
**Model                        R-square**
-          1     0.06656206   0.05018596     1.11168    349275.40   X1
-           .      ...............   ...............     ..........    .............   ...
-           1     0.01977926   0.00258240      1.58914    366780.67   Y1
- -------------------------------------------------------------------------------------------------------
-           2     0.08346260   0.05072912     0.08737    349075.66   X2 X3
-           .     ................   ..............     ..........    .............   ..........
- --------------------------------------------------------------------------------------------------------
-           3     0.09370310   0.04426873      1.32144    351451.34   X1 X2 X3
-           .     . ................   ..............     ..........    .............   ...............
- ---------------------------------------------------------------------------------------------------------
-           4     0.10033782   0.03369618      2.93841    355339.19   X1 Y1 Y2 Y3
-           .     . . ................   ..............     ..........    .............   ...............
- ---------------------------------------------------------------------------------------------------------
-           5     0.11168467   0.02788134      4.28335    357477.48   X2 X3 Y1 Y2 Y3
-           .   . . ................   ..............     ..........    .............   ...............
- --------------------------------------------------------------------------------------------------------
-          6     0.11506849   0.01296101      6.08799    362964.14   X2 X3 Y1 Y2 Y3 Z1
- --------------------------------------------------------------------------------------------------------
-          7     0.11659270   -.00465929      8.00000    369443.65   X1 X2 X3 Y1 Y2 Y3 Z1
-       ---------------------------------------------------------------------------------------------------

## ---------------------------TRT = NTC WINTER-----------------------------

|  | “Best”  Model | Adj. R2 | Remark |
| --- | --- | --- | --- |
| Sediment | Y = X1, X2, X3 | 0.0443  | Very poor (only 4%)  |
| NH4 | Y = X1, Y1, Y2, Y3 | 0.0510 | Very poor (only 5%)  |
| NO3 | Y = X2, X3 | 0.0245 | Very poor (only 2%)  |

***---------------------------TRT = NTC WINTER-----------------------------***

***-----------------------------TRT = NTC------------------------------***

***----------------------------TRT = NTC SPRING -----------------------------***

***--------------------------TRT = NTC SUMMER ----------------------------***

| Sediment | Y = X1 | 0.2493  | Better (<25 vs 4%)  |
| --- | --- | --- | --- |
| NH4 | Y  = X2, X3, Y1, Y2, Y3 | 0.7969 | Very good (80 vs 5%)  |
| NO3 | Y =  X3, Y2, Y3, Z1  | 0.2891 | Better (29 vs 2%)  |

| Sediment | Y = X1, X3, Y1, Y2, Z1 | 0.9716  | Very good (97 vs 4%)  |
| --- | --- | --- | --- |
| NH4 | ............... | ......... | Worse (<1 vs 5%)  |
| NO3 | Y = X2, Y1, Y2 | 0.6220 | Good (62 vs 2%)  |

| Sediment | Y = X1, Y1, Y2, Z1 | 0.1129  | Better (only 11 vs 4%)  |
| --- | --- | --- | --- |
| NH4 | ............... | ......... | Worse (<1 vs 5%)  |
| NO3 | Y = X2, Y2, Y3, Z1 | 0.6018 | Good (60 vs 2%)  |

## -------------------------- TRT = SGC WINTER -----------------------------

|  | “Best”  Model | Adj. R2 | Remark |
| --- | --- | --- | --- |
| Sediment | Y = X1, X2, Y1, Y3 | 0.0978  | Very poor (only 10%)  |
| NH4 | Y = X1, Y1, Y2 | 0.0458 | Very poor (only 5%)  |
| NO3 | Y = Z1 | 0.0148 | Very poor (only 1%)  |

***-------------------------- TRT = SGC WINTER -----------------------------***

***-------------------------------- TRT = SGC -------------------------------***

***------------------------- TRT = SGC SPRING -----------------------------***

***------------------------ TRT = SGC SUMMER ----------------------------***

| Sediment | Y = X2, X3, Y1, Y2 | 0.6494  | Good (65 vs 10%)  |
| --- | --- | --- | --- |
| NH4 | Y = X3, Y1, Y2, Z1 | 0.4356 | Better  (44 vs 5%)  |
| NO3 | Y = X1, X2, X3, Y1 | 0.4546 | Better (45 vs 1%)  |

| Sediment | Y = X1, X2, X3 | 0.6710  | Good (67 vs 10%)  |
| --- | --- | --- | --- |
| NH4 | Y = X2, X3, Y1, Y2, Y3, Z1  | 0.8669 | Very good (87 vs 5%)  |
| NO3 | Y = X2, X3, Y1, Y2, Z1 | 0.5326 | Better (53 vs 1%)  |

| Sediment | Y = X2, X3, Y3 | 0.3900  | Better (39 vs 10%)  |  |
| --- | --- | --- | --- | --- |
| NH4 | Y = X1, X2, X3 | 0.3553 | Better (35 vs 5%)  |  |
| NO3 | Y = X3, Y3, Z3 | 0.1770 | Better (17 vs 1%)  |  |

## -------------------------- TRT = SWC WINTER -----------------------------

|  | “Best”  Model | Adj. R2 | Remark |
| --- | --- | --- | --- |
| Sediment | Y = X1, X2, Z1 | 0.0654  | Very poor (only 6%)  |
| NH4 | Y = X1, Y1, Y3,  | 0.0793 | Very poor (only 8%)  |
| NO3 | Y = X1 | 0.0905 | Very poor (only 9%)  |

***-------------------------- TRT = SWC WINTER -----------------------------***

***-------------------------------- TRT = SWC -------------------------------***

***------------------------- TRT = SWC SPRING -----------------------------***

***------------------------ TRT = SWC SUMMER ----------------------------***

| Sediment | Y = X1, X2, Y1, Y2, Y3, Z1 | 0.9962  | Very good (99 vs 10%)  |
| --- | --- | --- | --- |
| NH4 | Y = X1, X2, X3, Y1, Y2, Z1 | 0.9999 | Very good (99 vs 5%)  |
| NO3 | Y = X1, X2, X3, Y1, Y2, Y3 | 0.9998 | Very good (99 vs 1%)  |

| Sediment | Y = X1, X2, X3 | 0.0857  | Worse (8 vs 10%)  |
| --- | --- | --- | --- |
| NH4 | Y = Y1, Y2, Y3  | 0.5558 | Good (55 vs 5%)  |
| NO3 | Y = X2, X3, Y1, Y2, Y3 | 0.5806 | Better (58 vs 1%)  |

| Sediment | Y =X1, Y2, Y3, Z1 | 0.0393  | Worse (4 vs 10%)  |  |
| --- | --- | --- | --- | --- |
| NH4 | Y = X1, X2 | 0.3320 | Better (33 vs 5%)  |  |
| NO3 | Y = X1, Y2, Y3, Z1 | 0.4964 | Better (49 vs 1%)  |  |

## -------------------------- TRT = SWG WINTER -----------------------------

|  | “Best”  Model | Adj. R2 | Remark |
| --- | --- | --- | --- |
| Sediment | Y = X1, X2, Y1, Y2, Y3 | 0.0742  | Very poor (only 7%)  |
| NH4 | Y = X1, X2, Y1, Y2 | 0.1556 | Very poor (only 16%)  |
| NO3 | Y = X1, X2, Y1, Y3 | 0.1234 | Very poor (only 12%)  |

***-------------------------- TRT = SWG WINTER -----------------------------***

***-------------------------------- TRT = SWG -------------------------------***

***------------------------- TRT = SWG SPRING -----------------------------***

***------------------------ TRT = SWG SUMMER -----------------------------***

| Sediment | Y = X1, Y1, Y2, Y3 | 0.4040  | Better (40 vs 10%)  |
| --- | --- | --- | --- |
| NH4 | Y = X2, X3, Y3, Z1 | 0.8398 | Very good (84 vs 5%)  |
| NO3 | Y = X1 | 0.0261 | Very poor (only 2%)  |

| Sediment | Y = X1, X2 | 0.1890  | Better (18 vs 10%)  |
| --- | --- | --- | --- |
| NH4 | Y = X1, X2, Y1, Y2, Z1  | 0.7335 | Good (73 vs 5%)  |
| NO3 | Y = X1, X2  | 0.5718 | Better (57 vs 1%)  |

| Sediment | Y =X1, Y1, Y2  | 0.0086  | Worse (1 vs 10%)  |  |
| --- | --- | --- | --- | --- |
| NH4 | Y = X2, X3, Y2, Y3, Z1 | 0.5988 | Better (60 vs 5%)  |  |
| NO3 | Y = X2, X3, Y1, Y3, Z1 | 0.1429 | Better (14 vs 1%)  |  |

## For each treatment and dependent variable, “best” model varies with season (most likely reflecting rainfall variation).

Seasonal changes also affect nutrient chemistry hence behavior (minerilization, immobilization, microbial activity)

Therefore, have to develop models separately for each season.....these can be called in succession during a simulation.

Within treatments and seasons, model parameters seem to change depending on amount rainfall and initial soil moisture content (affects runoff, and behavior of soil particles) . 

**Seasonal changes also affect nutrient chemistry hence behavior ****(minerilization, immobilization, microbial activity)**
**Therefore, have to develop models separately for each season.....****these can be called in succession during a simulation.**
**Within treatments and seasons, model parameters seem to change depending on amount rainfall and initial soil moisture content ****(affects runoff, and behavior of soil particles) . **

**SUMMARY**