# A Remote-Sensing Driven Tool for Estimating Crop Stress and Yields

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## Abstract

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## 1. Introduction

## 2. Methods and Materials

- (1)
- Estimation of surface and root zone soil moisture proxy values from ALEXI over the period April 2000 to September 2009. Daily values of either surface or root zone soil moisture were obtained on clear days for which ALEXI simulations were available.
- (2)
- Computation of a vertical soil moisture profile from the ALEXI data consistent with the profile depths required by DSSAT.
- (3)
- Comparison of ALEXI soil moisture values with both rainfed DSSAT values and soil moisture estimates from a simulation using Noah land surface model processed from NASA’s Land Information System (LIS) over the same period.
- (4)
- Integration of ALEXI derived soil moisture profiles within the DSSAT model, used in lieu of precipitation data.
- (5)
- Comparison of yield estimates from the ALEXI soil moisture driven model and the DSSAT model driven by the recorded precipitation, and with measured yields.

#### 2.1. Study Site

#### 2.2. ALEXI Modeling Framework

#### 2.2.1. Two-Source Energy Balance Model

_{RAD}(θ

_{L})] is a function of the fraction of vegetation cover apparent at a sensor viewing angle differentiating the soil and canopy temperature (T

_{S}and T

_{C}) and represented by

_{L}, and F is leaf area index [14,23].

^{−2}:

_{p}is the heat capacity of air at constant pressure, T

_{a}is the air temperature at a height above the canopy, and T

_{S}and T

_{C}are the soil and canopy temperatures, respectively, T

_{ac}is an effective temperature within the canopy (similar to an aerodynamic temperature), is transport resistance between the canopy and the reference height, R

_{S}is the soil surface resistance and is the bulk leaf boundary layer resistance. All resistance terms (sm

^{–1}) are discussed in [15], with updates provided by [24–27].

_{C}) is calculated using a modified Priestley-Taylor approximation [28]. The plant transpiration is related to the canopy net radiation divergence RN

_{C}as:

_{c}is the Priestley-Taylor coefficient equivalent to 1.3 which can be down-scaled depending on the vegetative stress [17,14,29] and discussed further below, f

_{c}is the fraction of green vegetation, δ is the slope of saturated vapor pressure curve with respect to temperature; and γ is the psychometric constant (0.066 kPa·°C

^{−1}). The soil latent heat (LE

_{S}) is computed as the residual of the canopy latent heat and latent heat of the system (LE):

_{g}) of the net soil radiation (RN

_{S}):

_{g}is specified using the formulation of Santanello and Friedl [30].

_{S}to become negative in Equation (10). This condition suggests the process of condensation, a situation unlikely during daylight hours. Thus, under canopy stress, LE

_{C}is iteratively reduced from its potential rate until LEs approaches 0 [15].

#### 2.2.2. Regional Implementation

_{a}in the mixed layer to the time-integrated influx of H from the surface [17,34], computing simultaneous energy balances at the surface and in ABL. The TSEB is applied at two times (t

_{1}and t

_{2}) during the morning hours, approximately at 1.5 and 5.5 h after local sun rise, using radiometric surface temperature estimates derived from geostationary satellites (e.g., Geostationary Operational Environmental Satellite (GOES), Meteosat), providing two estimates of instantaneous H flux estimates H

_{1}and H

_{2}. Time changes in surface temperature are known to be correlated with the LE and H fluxes: a wetter land surface warms slowly as compared to the dryer surface, thus requiring more energy for evaporation [35]. ALEXI assumes a rise in H through a linear functional form for H(t). The time integrated heat flux is then:

_{m}) to the time-integrated H from the surface is given as [36]:

_{S}(z) is the early morning potential temperature profile (near time = t

_{1}). At the surface, the mixed layer potential temperature is related to the air temperature by

_{p}) is parameterized as 0.286 [14].

#### 2.2.3. ALEXI Input Datasets

#### (i) Surface radiometric temperature and solar insolation data

_{RAD}) data over CONUS used in the ALEXI runs described here were generated using the GOES–East/West sounder instruments. The GOES sounder at channel 4 (10.7 μm) has a spatial resolution of ∼10 km and thermal radiances were regridded to the ALEXI grid [14,37]. Atmospheric and emissivity corrections used to retrieve surface radiometric temperature are described in [14].

_{S}and T

_{C}and parameterized values of surface albedo and emissivity.

#### (ii) Surface and upper air meteorological data

#### (iii) Land surface and canopy data

#### 2.3. Available Water Derived from ALEXI

_{s}) and canopy transpiration (LE

_{c}) sub-components. These fluxes in turn are largely controlled by soil moisture in the surface layer and the root-zone layer, respectively, and by energy available to each component. In general, wet soil moisture conditions lead to increased LE (decreased H) and a depressed morning surface temperature amplitude, while dry soil moisture conditions lead to decreased LE (increased H) and an increased morning surface temperature amplitude. Anderson et al. [14] and Hain et al. [37,41] outline a technique for simulating the effects of soil moisture on LE estimates from ALEXI using a soil moisture stress function, relating the value of the fraction of actual to potential evapotranspiration (f

_{PET}):

_{AW}) in the soil profile:

_{fc}and θ

_{wp}are the volumetric soil moisture contents at field capacity and permanent wilting point, respectively (Table 1). Normalization by PET reduces sensitivity to available energy, better isolating variations in evaporative flux due to soil moisture [16]. In many prognostic modeling frameworks, a semi-empirical linear or non-linear relationship is defined between f

_{PET}and f

_{AW}to account for effects of soil moisture depletion on the surface evaporative fluxes [14,37,41]. Assuming a linear relationship,

_{fc}and approaches saturation. While Equation (17) requires specification of soil texture-specific values of θ

_{fc}and θ

_{wp}, these local constants fall out in the computation of standardized temporal anomalies. Standardized anomalies in θ

_{ALEXI}can be therefore computed directly from f

_{PET}without requiring soil texture information. It is assumed that the relative contributions to ET from the surface and root-zone SM are related to the observed vegetation cover fraction as viewed from nadir (f

_{c}). Over sparsely vegetated surfaces (0 ≤ f

_{c}≤ 0.3), ALEXI LE is dominated by direct soil evaporation and reflects soil moisture conditions in only the first 1-2 centimeters of the profile, similar to an effective sensing depth of microwave sensors [42]. However, over dense to full vegetation cover (f

_{c}> 75%) and under well-watered conditions, ALEXI LE is predominantly partitioned to canopy transpiration, and soil evaporation becomes negligible in comparison. In this case, f

_{PET}is governed by moisture conditions in the plant root zone. Between these two extremes (sparse to full vegetation cover), ALEXI provides a composite of both surface and root-zone soil moisture information, with relative influence related to f

_{c.}Therefore, θ

_{ALEXI}values represent a composite of surface and root-zone soil moisture conditions depending on surface vegetation conditions, which can be expressed conceptually as:

_{ALEXIsfc}and θ

_{ALEXIrz}are not retrieved independently; however, Equation (6) provides a conceptual framework for comparison with microwave and land surface model (LSM) soil moisture estimates. In a previous study, Hain, et al. [41] evaluated ALEXI f

_{AW}retrievals in comparison with ground-based soil moisture observations over a multi-year period (2002–2004) from the Oklahoma Mesonet and found reasonable temporal and spatial agreement (RMSE values around 20% of mean observed soil moisture).

#### 2.4. Agricultural Simulation Model

#### 2.5. Development of Soil Moisture Profiles from ALEXI AW

_{PET}estimates. The method is based on the principle of maximum entropy (POME) expounded by Jaynes [62,63]. The principle states that if inferences are to be made from incomplete data, they should be based on the probability distribution that possesses maximum entropy permitted by the prior information [59]. Using an approach originally employed by Chiu [64] to compute vertical velocity distributions in open channels, Al-Hamdan and Cruise [59] assumed a uniform distribution of soil moisture through the soil column to develop a set of profiles corresponding to all possible cases. In the situation considered here, only two cases are required—the case of a wet surface layer with drier soil underneath, and the reverse case, e.g., a dry surface with wetter conditions underneath. The application of POME to develop a one-dimensional soil moisture profile requires two constraints: the total probability constraint:

_{r}is the irreducible water content of the soil; whereas Θ

_{0}and Θ

_{L}are the surface and bottom effective saturations. The second constraint serves to connect the first moment in probability space to the mean water content of the soil column in physical space. The Shannon entropy is given by [65]:

_{0}and mean effective saturation value of the soil column Θ̄), z is calculation depth, and L is total depth of the column.

## 3. Integration of ALEXI SM within DSSAT

#### 3.1. Gap-Filling ALEXI SM Time Series

_{AW}was gap-filled using data from pixels within this 3 × 3 grid increasing temporal coverage to 678 days (41%). Of this total, 591 values were recovered from either the target pixel or one of the three pixels immediately adjacent to it so that ultimately about 87% the ALEXI retrievals utilized came from the pixel containing the Belle Mina station or one of the three adjacent pixels. More importantly, 75.6% of the retrievals utilized came from the Belle Mina pixel itself. A consequence of note relevant to the expansion of the ALEXI footprint (however modest) would be that moisture conditions in the adjacent irrigated land in Limestone and Madison Counties would be included in the ALEXI signal.

#### 3.2. Intercomparison of Soil Moisture Time Series

_{i}− x̄)/σ. Where x

_{i}is composite soil moisture estimates whereas x̄ and σ are the multi-year 29 days centered (−14:+14 days) mean and standard deviation, respectively.

#### 3.3. Updating DSSAT with ALEXI Soil Moisture

_{PET}data were separated into surface values and root zone values according to the observed MODIS fraction of vegetation cover as previously discussed: f

_{c}≤ 0.4 surface; f

_{c}≥ 0.75 root zone; 0.4 ≤ f

_{c}≤ 0.75 combination of surface and root zone. For purposes of this analysis, values where 0.4 ≤ f

_{c}≤ 0.75 were also utilized to get the total water available in the soil column in order to compute the mean effective soil moisture.

_{PET}readings associated with cover fractions greater than 0.4 since it is unlikely that root zone soil moisture would demonstrate such rapid fluctuations.

## 4. Results and Discussion

_{PET}anomalies with Noah SM anomalies are shown in Figure 1, while the similar comparison of ALEXI to DSSAT is shown in Figure 2. These figures demonstrate that ALEXI does appear to offer a fair representation of the high frequency soil moisture fluctuations for the study area despite the ∼10 day update frequency, and that it correlates well with the soil moisture dynamics in the rainfed DSSAT model. In fact, the correlation is slightly better with DSSAT as compared to LIS (r = 0.74 vs. 0.58). In this regard, even though the ALEXI retrieved signal is undoubtedly sensing both rainfed and irrigated farmland, the anomalies should be comparable since they are being standardized by the mean in each case.

## 5. Errors and Uncertainties in the Study

## 6. Conclusions

## Acknowledgments

## Conflict of Interest

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**Figure 1.**(

**a**) Anomaly time series plot between LIS (yellow) and ALEXI (blue) 14-day soil moisture composite at Belle Mina, Alabama for the period of 2000–2010; (

**b**) Scatter plot of the anomalies between LIS and ALEXI again at the Belle Mina, Alabama.

**Figure 2.**(

**a**) Anomaly time series between DSSAT rainfed (green) and ALEXI (blue) 14-day soil moisture composite at Belle Mina, Alabama for the period of 2000–2010; (

**b**) Scatter plot of the anomalies between DSSAT and ALEXI again at the Belle Mina, Alabama.

**Figure 6.**Irrigated and ALEXI forced DSSAT Yields compared to NASS County Yields for Limestone and Madison Counties, AL

DSSAT Input Soil Parameters | ALEXI Soil Parameters | ||||||
---|---|---|---|---|---|---|---|

Depth (cm) | Clay % | Silt % | Sand % | pH | Cation Exchange Capacity (cmol/Kg) | WP (cm^{3}/cm^{3}) | FC (cm^{3}/cm^{3}) |

0–10 | 21.0 | 52.7 | 26.3 | 5.3 | 5.0 | 0.084 | 0.360 |

10–40 | 34.4 | 47.8 | 11.6 | 5.3 | 6.2 | 0.103 | 0.382 |

40–100 | 45.9 | 29.2 | 23.3 | 5.3 | 5.9 | 0.138 | 0.412 |

100–200 | 47.5 | 29.2 | 23.3 | 5.3 | 5.9 | 0.138 | 0.412 |

Year | Planting Day | Rainfed Yields (kg/ha) | Irrigated Yields (kg/ha) | ALEXI Yields (kg/ha) | Number of Updates |
---|---|---|---|---|---|

2000 | 07-Mar | 3,512 | 15,234 | 6,078 | 7 |

2001 | 27-Apr | 7,711 | 16,095 | 7,501 | 8 |

2002 | 17-Apr | 5,516 | 13,781 | 9,272 | 8 |

2003 | 30-Apr | 11,856 | 14,844 | 11,332 | 11 |

2004 | 23-Mar | 11,173 | 12,839 | 11,211 | 11 |

2005 | 20-Apr | 9,761 | 11,661 | 9,112 | 10 |

2006 | 17-Apr | 2,797 | 15,033 | 8,269 | 12 |

2007 | 04-May | 3,223 | 11,013 | 3,741 | 9 |

2008 | 24-Apr | 6,011 | 14,729 | 8,449 | 12 |

2009 | 23-Mar | 3,967 | 18,443 | 4,159 | 9 |

Mean | 6,552.7 | 14,367.2 | 7,912.4 |

Year | Rainfed S.M. (mm) | ALEXI S.M. (mm) | % Diff |
---|---|---|---|

2000 | 530.40 | 556.16 | 4.64 |

2001 | 568.70 | 557.18 | −2.08 |

2002 | 514.81 | 554.82 | 7.21 |

2003 | 544.94 | 574.74 | 5.19 |

2004 | 523.43 | 559.30 | 6.42 |

2005 | 529.51 | 565.12 | 6.32 |

2006 | 522.86 | 560.30 | 6.69 |

2007 | 511.29 | 556.67 | 8.15 |

2008 | 502.21 | 555.55 | 9.95 |

2009 | 545.46 | 573.43 | 4.88 |

© 2013 by the authors; licensee MDPI, Basel, Switzerland This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Mishra, V.; Cruise, J.F.; Mecikalski, J.R.; Hain, C.R.; Anderson, M.C.
A Remote-Sensing Driven Tool for Estimating Crop Stress and Yields. *Remote Sens.* **2013**, *5*, 3331-3356.
https://doi.org/10.3390/rs5073331

**AMA Style**

Mishra V, Cruise JF, Mecikalski JR, Hain CR, Anderson MC.
A Remote-Sensing Driven Tool for Estimating Crop Stress and Yields. *Remote Sensing*. 2013; 5(7):3331-3356.
https://doi.org/10.3390/rs5073331

**Chicago/Turabian Style**

Mishra, Vikalp, James F. Cruise, John R. Mecikalski, Christopher R. Hain, and Martha C. Anderson.
2013. "A Remote-Sensing Driven Tool for Estimating Crop Stress and Yields" *Remote Sensing* 5, no. 7: 3331-3356.
https://doi.org/10.3390/rs5073331