Soil Science Society of America Journal 65:1065-1074 (2001)
© 2001 Soil Science Society of America
DIVISION S-1—SOIL PHYSICS
State Space Analysis of Soil Water and Salinity Regimes in a Loam Soil Underlain by Shallow Groundwater
L. Wu*,a,
T. H. Skaggsb,
P. J. Shouseb and
J. E. Ayarsc
a Dep. of Environmental Sciences, Univ. of California, Riverside, CA 92507
b George E. Brown, Jr. Salinity Lab., 450 W. Big Springs Rd., Riverside, CA 92507
c USDA-ARS, Water Management Research Lab., Fresno, CA 93727
* Corresponding author (Laowu{at}mail.ucr.edu)
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ABSTRACT
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Improved methods of irrigation scheduling are needed to reduce irrigation and drainage water volumes while not affecting yield. State space models based on mass balance principles and empirical flux laws can be used to estimate and forecast soil water and salinity regimes in the field. In this research, a state space model was developed that describes soil water and salinity dynamics and includes the effects of shallow, saline groundwater. The model was evaluated using daily time domain reflectometry (TDR) measurements of the soil water content (
) and bulk soil electrical conductivity (ECb). Data were collected throughout the 1997 growing season in a field where cotton (Gossypium hirsutum L.) was being grown using an experimental shallow groundwater management technique that was designed to reduce both irrigation and drainage volumes. The model was tested by supposing that either weekly or biweekly profile-averaged measurements of and ECb were available, and then comparing the resulting filtered model forecasts with the full data set. The results show that the measured water content was within the predicted confidence intervals of 1- or 2-wk forecasts of the profile-averaged water content, soil water EC (ECw), and EC of saturated extract (ECe), even though the performance of the model in predicting the resident salt concentration (mass of salt per volume of soil) was less satisfactory.
Abbreviations: EC, electrical conductivity • ET, evapotranspiration • KF, Kalman filter • TDR, time domain reflectometry • , soil water content
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INTRODUCTION
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PRUDENT IRRIGATION SCHEDULING not only saves water, but also reduces the potential for non-point source pollution. Irrigation scheduling is typically based on soil or plant monitoring or evapotranspiration (ET) estimation, both of which have drawbacks. Soil or plant monitoring provides information about the current status of the soil or plant, but does not predict when future irrigation will be needed. Irrigation scheduling based on ET estimation is not site-specific, and does not take into account, for example, the salinity conditions in the field. Therefore, there is a need to develop new techniques that provide flexible irrigation schedules in real time, and that meet irrigation requirements with a minimum amount of water.
Time-series methods have been used more frequently in hydrologic investigations and water quality management during the past a few decades (Hipel et al., 1977). Using the hydrologic budget and soil water transport equations, Parlange et al. (1992) developed a first-order autoregressive Markovian model to estimate the soil water regime in the top 1.05-m soil profile. The predicted water storage in the soil profile was close to that measured by a neutron probe. Wu et al. (1997) found that changes in soil moisture could be modeled as an autoregressive-moving average process.
Aboitiz et al. (1986) used the water balance equation and reference evapotranspiration (ETo) for an irrigated field to develop a state space model capable of estimating and forecasting soil water depletion and crop ET. Their formulation allows for real-time estimation of soil moisture and associated estimation errors. Or and Hanks (1992) developed a state space model of the soil water balance and potential ET and used Kalman filtering to obtain temporal soil water storage estimates and estimation errors. In Kalman filtering, model predictions are updated as new measurements on the system state variables become available. Or and Hanks found that the estimated soil water storage agreed better with measured values when the estimates were based a combination of spatial and temporal data, rather than on either spatial or temporal information independently. Skaggs and Mohanty (1998) developed a state space model that described shallow water table dynamics in a tile-drained field. Their formulation did not include the vadose zone water content.
The previous state space formulations of soil moisture dynamics did not consider groundwater recharge–discharge. In an irrigated soil with a shallow groundwater table, a significant amount of groundwater can be used by plants (Wallender et al., 1979; Ayars and Schoneman, 1986; Torres and Hanks, 1989). The salinity level of the root zone is also a concern for crop growth and yield. From an agricultural production standpoint, the concentration of dissolved salts in soil water, commonly quantified by the electrical conductivity of the water (ECw), is a critical parameter. State-space models based on site-specific measurements will be able to estimate and forecast the soil water and salinity regime, which will provide flexible irrigation scheduling for farmers.
The objectives of this research were (i) to develop a state-space model for the root zone water content and salinity that includes the effects of shallow groundwater; (ii) to estimate and forecast the soil water and salinity regimes in an irrigated soil with a shallow groundwater table; (iii) to evaluate the effect of the observation interval on estimation errors associated with the Kalman filter (KF); and (iv) to evaluate the effects of upward groundwater flow on root zone salinity.
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MATERIALS AND METHODS
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Field Experiment
Our research site was Section 13-4 in the Broadview Water District in Firebaugh, CA. The field is a commercial farm and is approximately 60 ha. Ninety percent of the field is a Cerini series (fine-loamy, mixed, superactive, thermic Fluventic Haplocambids). Ten percent, the northwest and southeast corners, are a Tranquillity series (fine, smectitic, thermic Sodic Haploxerert).
The field contains a subsurface drainage system with drain laterals buried 1.5 to 1.8 m deep, running east–west, 123 m apart. The collector drain is located on the east side of the field. At the low end of the collector drain, we installed a device that regulates flow in the drainage system and permits control of the water table depth. The purpose of the modified drainage system is to maintain the water table at a depth that allows crops to obtain water through upward flow of groundwater, with the larger objective being a reduction in both irrigation and drainage volumes. Preliminary studies conducted over two cropping cycles found that irrigation requirements were reduced by 15 to 20% without reduced yields of tomato (Lycopersicon esculentum Mill.) or cotton. The efficiency of this type of shallow groundwater management will depend in part on irrigation scheduling. The long-term sustainability will be determined by the extent to which the induced upward flow of groundwater salinizes the root zone.
This study focuses on a short-term experiment conducted to evaluate plot-scale root-zone soil water and salinity dynamics over a single growing season. The field was planted to cotton during the spring of 1997, and throughout the growing season drain flow was regulated so that the water table on the east side of the field was maintained at a depth about 1.2 m. Irrigation scheduling was based on 60% allowable soil water depletion.
Three-rod TDR probes 20 cm long were installed at 10, 30, 50, 70, 90, and 110 cm below the surface at three sites along a transect perpendicular to the drainage lines in the northeast corner of the field. The three sites were approximately 70 m apart. The TDR instrumentation was used to make daily measurements of the volumetric water content and bulk soil EC (ECb) from Day 141 (21 May) through Day 258 (15 September), 1997 (Herkelrath et al., 1991; Whalley, 1993; Schaap et al., 1996). In this paper we focus mainly on the data from Site 1.
Figures 1A and 1B show the profile-averaged (to depth 120 cm) water content, 
k, and bulk soil EC, 
bk, measured at Site 1 on Days k = 141...258. These two series were constructed by averaging the daily TDR measurements over the six depths.
Furrow irrigation records kept by the farm were not sufficient to determine the timing and volume of water applied to our experimental plots. For modeling purposes, we assumed the water applied during irrigation was equal to the increase in the total water stored in the soil profile, as measured by TDR. The resulting irrigation series Ik, which is an average over the three sites, is shown in Fig. 1C. Although our analyses focus on one experimental plot, we use the averaged irrigation value because in practice irrigation amounts will be known only approximately. There was no measurable precipitation during our study.
The daily actual evapotranspiration (ETak) was calculated as
 | (1) |
where the reference ETo was obtained from the California Irrigation Management Information System (CIMIS Station 7, Firebaugh/Telles) and the crop coefficient was calculated according to the regression equation reported in Cotton Production Manual (University of California-Division of Agriculture and Natural Resources, 1996):
 | (2) |
where k is day of the year. The resulting ETak time series is shown in Fig. 1D.
We also monitored irrigation water, groundwater, and drainage water quality and crop yield. The irrigation water was from a reservoir and had a total dissolved salt concentration of approximately CI = 288 mg L-1 with little variation over the season, whereas the groundwater had a salt concentration of approximately CGW = 3840 mg L-1. The ET and irrigation time series shown in Fig. 1 are used as forcing functions in our simulation model, which is described next.
State Space Modeling
State space models consist of two parts, a dynamics equation that describes the time evolution of the system state, and a measurement equation that relates system state variables to measurable quantities. The dynamics equation usually consists of a statement of mass balance and empirical flux laws that specify system fluxes in terms of state variables. Model predictions are obtained through a cycle of model forecasting and measurement updating, known as filtering. In this section we develop a state space model for root zone soil water and salinity.
Water Balance Equation
Assuming that there is no runoff and that water flow in the root zone is one dimensional, the water balance equation can be expressed as:
 | (3) |
where P is the precipitation rate, I is the irrigation rate, ETa is the actual evapotranspiration rate, D is the root zone drainage rate to groundwater, R is the root zone recharge rate from groundwater, is the volumetric water content, t is time, z is depth, and L is the depth of the root zone. Although there was no measurable precipitation in our study, we include it here for the sake of generality.
Integrating Eq. [3] with respect to time and dividing both sides by L yields the following expression for the profile-averaged water content on day k + 1 (k+1):
 | (4) |
where
 | (5) |
Salt Balance Equation
Assuming negligible salt uptake by plants and no precipitation or dissolution of salts, the salt balance equation can be formulated similarly to the water balance equation:
 | (6) |
where P, I, R, and D are as defined above, CP is the salt concentration of precipitation, CI is the concentration of irrigation water, CD is the concentration of drainage water, and CGW is the concentration of groundwater water.
Assuming that CP = 0, that CI and CGW are constant over the growing season, and that CD is constant over a given day, integrating Eq. [6] and dividing by L yields:
 | (7) |
where
 | (8) |
is the profile-averaged mass of dissolved salt per unit volume of soil on day k.
State Dynamics Equation
In developing a model for the soil water and salinity dynamics, we make the following assumptions:
1. We assume the water table depth is more or less constant during the growing season, remaining at or very near the root zone depth L. Data from observation wells located near the experimental plots verified that this was a reasonable approximation during our study.
2. Defining Gk = Rk - Dk as the net daily water flux at the bottom of the root zone, we assume that
 | (9) |
where, for our study site,
 | (10) |
and
 | (11) |
Thus we assume the net water flux at the bottom of the root zone on a given day, Gk, is a piece-wise linear function of that day's profile-averaged water content, k. Our rationale for making Gk a function of k is the supposition that when the soil is wet, drainage out of the root zone to groundwater occurs (Gk < 0), and when the soil is dry, upward flow from the shallow groundwater occurs (Gk > 0). The Gk(k) relationship specified by Eq. [9] to [11] is shown as a solid line in Fig. 2. For profile-averaged water contents less than 0.34, Eq. [9] to [11] predict Gk = 0.2 cm of water per day will move from the groundwater to the root zone. For k > 0.34, it is predicted that Gk drops off linearly, crossing over to profile drainage (Gk < 0) at a water content slightly greater than 0.34. We arrived at the specific form of Eq. [9] to [11] by examining the experimental data shown as open circles in Fig. 2. These data are the "observations" of the daily net water flux at the bottom of the root zone, Gk, plotted vs. the daily measured k. The "observed" Gk is calculated according to the water balance equation (Eq. [4]), Gk = Rk - Dk = 
L - Ik - Pk + Etak, using the daily data for Ik, Pk, and ETak that are shown in Fig. 1 and measured water content data for all three experimental plots. It is evident from Fig. 2 that both the functional form and the parameter values used in our Gk
model are based on subjective choices. It is also clear from the scatter of the data that the Gk model is inexact. Below, we account for this imprecision by introducing a random noise term.
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Fig. 2. Observed and regression lines of groundwater recharge (+) and discharge (-) as a function of profile-averaged soil water content.
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3. The profile-averaged salt concentration of water is approximated to be 
k = 
k/k (see Eq. [8]).
4. The salt concentration of water draining out of the soil profile is assumed to be equal to the profile-averaged concentration, CDk = k.
5. For purposes of calculating the salt flux at the bottom of the root zone, we assume that either profile drainage or recharge occurs on a given day, but not some combination of the two. Thus, the daily salt flux at the bottom of the root zone can be approximated as CGWGk when Gk > 0, and as CDkGk = 
Gk when Gk < 0.
These assumptions and definitions for the various water and salt fluxes can be substituted into the water and salt balance equations to obtain the following (nonlinear) state equation that describes the time evolution of the state variables k and k:
 | (12) |
where 
k 
, ßk ß,
 | (13) |
and wk = 
T is a random noise sequence with covariance Mk. The first term on the right-hand side of Eq. [12] represents the internal system dynamics. The second term represents the external forcing of the system. The noise term accounts for errors introduced by the various simplifying assumptions, as well as our inability to specify exactly the forcing terms Pk, Ik, and ETak. The noise covariance is quantified below in the parameter estimation section.
State Forecasting
Equation [12] can be written more compactly as
 | (14) |
where xk 
T is the system state variable, and where lower case letters are vectors and upper case letters are matrices. The noise term in Eq. [14] makes xk a random variable, and consequently forecasts of the state dynamics must be in terms of some estimate of xk, such as the mean value. Additionally, it is desirable to quantify the distribution of xk about that estimate, so that some type of confidence interval can be assigned.
Specifically, we seek an estimate 
k 
T of xk at future times, as well as the covariance of the estimation error, Pk = E[(xk - k)(xk - k)T]. Given an estimate of system state on day k = 0, 0 = x0, and the error covariance, P0, it can be shown that the minimum mean square error estimate of xk is given by (Gelb, 1974; Lewis, 1986)
 | (15) |
The corresponding equation for the error covariance is (to first-order)
 | (16) |
where
 | (17) |
In these projection equations, it is assumed that E[x0] = 0, E[x0 - 0)(x0 - 0)T] = P0, and wk = 
T is uncorrelated in time, zero mean Gaussian noise sequence with covariance Mk.
Updating Forecasts When Measurements Are Available
Given daily measurements of the system forcing uk, Eq. [15] and [16] can be used to calculate k and Pk in real time. Suppose at some time k we make a field measurement that provides information about system state xk. We would like to use this information to update our estimates of xk and Pk. To implement the filtering, we must specify the relationship between the measurements and the system state.
Measurement Equation
Rhoades et al. (1976) assumed that ECb is comprised of a liquid phase conductivity and a solid phase conductivity (ECs), and that the two conductivities can be modeled as parallel resistors. Noting that the liquid phase conductivity depends on the EC of the soil water (ECw) as well as the transmission coefficient (T, a water content-dependent tortuosity factor), Rhoades et al. (1976) arrived at the following expression for the bulk soil EC:
 | (18) |
where T is defined as
 | (19) |
with empirical parameters a and b. Additionally, a common approximation is that ECw is proportional to the total dissolved salt concentration (Marion and Babcock, 1976; U.S. Salinity Laboratory Staff, 1954),
 | (20) |
where the value of K is approximately 0.64 when EC is in dS m-1 and C is in mg mL-1 (Rhoades, 1986).
These relationships, along with the previously assumed k = k/k, allow us to write an equation that relates the measurable quantities k and bk to the state variables k and k:
 | (21) |
where vk = 
T is an error sequence (with variance Nk) that accounts for errors in the measurement of k and bk, as well as uncertainties in the specified relationship between bk, k, and k.
Updating Forecasts with the Kalman Filter
The measurement Eq. [21] can be written more compactly as
 | (22) |
where zk 
T. If a measurement zk is available and assuming E[wj(vk)T] = 0, the projected state and error estimates are updated according to the extended KF (Gelb, 1974; Lewis, 1986)
 | (23) |
 | (24) |
where superscripted pluses and minuses indicate updated and projected quantities, respectively, I is an identity matrix, and
 | (25) |
 | (26) |
 | (27) |
Parameter Estimation
The unknown parameters that need to be quantified are the noise covariances,
 | (28) |
and
 | (29) |
as well as the Rhoades et al. (1976) model parameters, a, b, and ECs.
First, we assume that Nk and NSk are zero, implying that the measurements of k and bk are exact. This seems to be a reasonable first approximation given that our measurements are likely to be much more accurate than our simulation equations, which contain numerous simplifications and approximations. Specifying zero measurement error means that the state update Eq. [23] sets the estimate of the current system state to be equal to the value indicated by the measurement, and the error update Eq. [24] sets the estimation error to zero. Of interest, then, is how long we can forecast the system state without the estimation error becoming unacceptably large. In other words, how far into the future can we project the system state before we need a new measurement to reset the simulation model?
Next we assume that Mk is constant 
. The value of M was set equal to the variance of the residuals in Fig. 2, divided by L2. The result was M =7.7 x 10-5. An examination of the residuals in Fig. 2 as a function of time indicated some short-range temporal correlation in the residuals from Site 1 but not for Sites 2 and 3. The KF equations require wk to be uncorrelated in time. We assume the small temporal correlations in the Site 1 data are insignificant when combined with data from all three sites (as we did in Fig. 2). MS was subsequently determined by maximizing the likelihood function (Bras and Rodríquez-Iturbe, 1985):
 | (30) |
where m = 2 is the number of state variables and n is the number of measurements used in the fitting. We used the first n = 60 d of measurements from Site 1 for the fitting, and the fitted value was MS = 6 x 10-4 mg2 cm-2.
Lastly, we use transmission coefficient parameters a = 1.38 and b = -0.09 (Rhoades et al., 1976) and assume the conductivity of the solid phase is negligibly small (ECs = 0).
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RESULTS AND DISCUSSION
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We now consider the measured data in Fig. 1 more carefully. The profile-averaged water content increased during irrigation and decreased between irrigations due to drainage and ET. The apparent rate of water depletion from the soil profile decreased as time progressed in an irrigation cycle, presumably due to increased resistance to root water uptake and surface evapotranspiration from dry soil. Records maintained by the water district indicate that the field was irrigated during Days 208 through 216, with the irrigation volume being roughly two-thirds that applied during the previous irrigation (which encompassed Days 196–197). However, our three sites, which were located at the tail end of the field, apparently received only minimal amounts of water, if any, because the only increase in the total profile stored during this time was a slight increase of about 1 cm near Day 215. However, the water content in the surface layers (10 and 30 cm) did not increase on this day. Rather, the small increase was due to increasing water contents at the 90- and 110-cm depths. Because the surface layers did not show an increased water content, we decided for modeling purposes to assume that no irrigation occurred during this time (recall we calculated Ik based on measured changes in total water storage, Fig. 1C). As will be seen, this will have implications for our modeling results.
The ECb data (Fig. 1B) mirrored the water content data, increasing during irrigation and decreasing during soil drying, indicating that ECb is affected by the water content of the soil as well as the salinity of the soil. Equation [18] assumes that the water content component of ECb can be separated from the salinity component giving us a measurement of soil solution electrical conductivity (ECw).
Figure 3A compares the measured profile-averaged water content with k, as calculated by Eq. [15] and [23] (the KF). The calculations were done assuming that a water content measurement was made every 7 d (weekly). These measurements are shown as open diamonds in Fig. 3A. Because we updated the forecast at these points (using Eq. [23]), the modeled and measured water contents coincide on these days and the error bars are zero (recall we have assumed zero measurement error). The other water content data shown in the figure are not used in the calculations and are shown only for comparison purposes. The error bars on the predicted water contents are equal to ± 
, where
 | (31) |
and Pk is calculated by Eq. [16] and [24]. As expected, the estimation error increases as the forecast gets further away from a measurement update.
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Fig. 3. (A) Time domain reflectometry measured and Kalman filter estimated profile-averaged soil water content (WC) and its estimation error and (B) Kalman filter estimated salt concentration (mg cm-3 soil) and its estimation error with weekly measurement update. The diamond symbol indicates the weekly water content measurement used to update the filter.
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In general, the predicted values are close to the measured values, with the measured values falling within the predicted confidence intervals. The poorest results are found on Days 215 through 225, where relatively large differences between measured and predicted values are observed. The poor performance during this time period is partly, but not entirely, due to the ambiguous irrigation data that were discussed above. Poor performance is also seen after approximately Day 219, where the forecast water content decreases more rapidly than the measured water content. This discrepancy may be due to an overestimation of ETa and/or an underestimation of the rate of upward groundwater flow by Eq. [9]. Nevertheless, the maximum difference between the forecast and measured water content during the period of relatively poor performance is only 0.023 (m3 m-3), comparing the water content range of 0.24 to 0.41 in the field.
Figure 3B shows the profile-averaged resident salt concentration, k (mg cm-3 soil), as calculated by the KF equations. The timing of the measurement updating is the same as in Fig. 3A. The concentration changes in response to the loss of salt by leaching and the addition of salt by irrigation and upward groundwater flow. Although there are no measurements shown on the Fig. 3B, we can infer that the model is not tracking the data very well. Note that over much of the figure the model forecast between measurements shows an increasing salt concentration, whereas the trend of the measurement updates is decreasing or constant, leading to the sawtooth appearance of portions of the plot. The higher salt loading predicted by the model may be due to an overestimation of either the groundwater salt concentration or the rate of upward groundwater flow. Figure 4A shows the daily water flux, Gk at the bottom of the root zone, as computed in the KF calculations. Figure 4B shows the corresponding computed daily salt flux, GkC*k.
Simultaneous with our forecasting and updating of k and k, we can estimate ECw as
 | (32) |
This estimate of ECw is shown in Fig. 5, where k and k are the KF calculations shown in Fig. 3 (weekly measurement updates). Also shown is the measured value of ECw, which is given by (see Eq. [18])
 | (33) |
where k and bk are the daily TDR measurements. As expected, the general trend is that ECw increases as water is extracted by plant roots (increasing the soil water salt concentration) and decreases during irrigation (the salt concentration is diluted). Overall, there is good agreement between the daily measured values and the weekly forecast values, with the maximum difference being less than 1 dS m-1.
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Fig. 5. Time domain reflectometry measured and Kalman filter (KF) estimated soil water electrical conductivity (ECw) and electrical conductivity of saturated extract (ECe) with weekly measurement update.
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Similarly, an estimate of ECe is given by (see Rhoades, 1986, Eq. [10])
 | (34) |
where SP = 62 is the soil saturation percentage and 
b = 1.29 g cm-3 is the soil bulk density. Figure 5 shows wk, where k is again the KF calculation from Fig. 3 that is based on weekly measurement updates. Figure 5 also shows the daily measured values (see Rhoades, 1986, Eq. [10]),
 | (35) |
where wk is given by Eq. [33] and k is the daily TDR measurement. The modeled and measured ek are in good agreement. ECe is the measure of root zone salinity that is used by agronomists, extension experts, and farmers to quantify the effects of salt on crop growth. Figure 5 shows that ECe was essentially constant, indicating that the irrigation and shallow groundwater management practices used at the experimental site did not increase soil salinity during the 1997 growing season. No reductions in cotton yield would be expected with an average root-zone ECe of 3.6 to 4 dS m-1, and none were observed. The measured EC of a saturation extract made from a soil sample taken near Site 1 was ECe = 3.6 dS m-1, which is in good agreement with values shown in Fig. 5.
Figure 6 is directly analogous to Fig. 3 except the model forecasts now span 2 wk and the measurement updates are biweekly. The 2-wk interval coincides roughly with the irrigation cycle used by the farmer. The error bars continue to grow over the course of the 2-wk forecasts. The measured water contents fall within the prediction error bars, except for Days 215 through 225. Following the measurement update at Day 225, the modeled water content tracks the measured water content fairly well. The modeled resident salt concentrations in Fig. 3 and 6 show the same general trend, with the plot again exhibiting something of a sawtooth appearance. The computed water and salt fluxes were very similar to those in Fig. 4 and are not shown. Figure 7 shows the estimated and measured ECw and ECe using the biweekly measurement updates. The results are similar to those seen in Fig 5. Overall, the modeled water and salinity dynamics were not substantially different for the 1- or 2-wk update interval.
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Fig. 6. (A) Time domain reflectometry measured and Kalman filter estimated profile-averaged soil water content (WC) and its estimation error and (B) Kalman filter estimated salt concentration (mg cm-3 soil) and its estimation error with biweekly measurement update. The diamond symbol indicates the biweekly water content measurement used to update the filter.
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Fig. 7. Time domain reflectometry measured and Kalman filter (KF) estimated soil water electrical conductivity (ECw) and electrical conductivity of saturated extract (ECe) with biweekly measurement update.
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SUMMARY AND CONCLUSIONS
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In this study, a state-space model for profile-averaged water content and salt concentration were developed based on mass balance and an empirical relationship that specifies the water flux at the bottom of the root zone as a function of the profile-averaged water content. The water balance equation considers irrigation, precipitation, evapotranspiration, and root-zone drainage to and recharge from shallow groundwater. The salt balance equation considers dissolved salts in irrigation water, soil water, and groundwater. Based on our model, forecasts of state variables (profile-averaged water and salt contents) and the estimation error covariances at future times were obtained using daily ET and irrigation data as inputs. The forecasts were updated by Kalman filtering when measurements of soil water content and electrical conductivity were made available. We found that weekly and biweekly measurement updating could predict profile-averaged water content and ECw reasonably well for the 1997 cotton growing season. A biweekly scheme is more in line with current irrigation practices for cotton on the west side of the San Joaquin Valley, California. A discrepancy between observed and forecast salt and water regimes during Days 215 to 225 was attributed to the net groundwater recharge–discharge not being accurately described by our assumed empirical relationship, and due to inaccurate irrigation data. The ECe did not vary substantially during our study, so further testing of the proposed salinity dynamics model is warranted.
The forecast increases in ECw seem to be realistic especially when ECe is relatively constant throughout the season. Under our field conditions ECe changed very slowly and ECw could be estimated from Eq. [35] by the use of water content information. Thus, forecasting of both soil water content and ECw could be done with periodic measurements of soil water content, and one single measurement of soil ECe. In situations where soil water salinity above some threshold is detrimental to crop production, ECw forecasts could be used to schedule irrigation timing and/or amount to alleviate salinity stress. Such an approach could be especially beneficial for high cash value crops that exhibit a high sensitivity to soil water salinity. Forecast of field soil water and salinity regimes can provide irrigation managers flexibility in irrigation scheduling and help prevent yield decline due to water and/or salinity stresses.
Received for publication June 17, 2000.
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