a. Moisture budget equations

Following Rasmusson (1968, 1971), Yanai et al. (1973), and Zangvil et al. (1993, 2001, 2004), the traditional atmospheric moisture budget for a region for time period Δt can be expanded to take the following form:

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Here g is the acceleration due to gravity, q is specific humidity, p is atmospheric pressure (S and T indicate the earth’s surface and an appropriate upper integration limit, respectively), V is the horizontal wind vector, and E and P are the surface evapotranspiration and precipitation rates, respectively. All terms are time and space averaged (section 2b below), expressed as water depth equivalents (mm day⁻¹), across the study region. Physically, in Eq. (1), dPW is the time change of atmospheric water vapor [precipitable water (PW)], HA gives the horizontal water vapor advection, HD includes the horizontal velocity divergence and is equal to the vertical water vapor advection (VA), and HA + HD is the total moisture flux divergence (MFD) (Zangvil et al. 2001, 2004).

As explained in Zangvil et al. (2004), standard evaluations of Eq. (1) cannot distinguish the relative contributions of E and imported water vapor to P. Instead, they only can yield information on the relationship between the difference E − P and the total MFD plus the atmospheric storage change (dPW). Zangvil et al. used several steps to overcome this problem. First, the MFD terms in Eq. (1) were expressed as

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where A is the area of the region, V_n is the component of the wind normal to the region’s boundary, dl is a unit length of that boundary, and OF and IF are the total water vapor mass outflow from and inflow to the region, respectively. Next, substitution of Eq. (2) into Eq. (1) yielded

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Although Eq. (3) identified IF/A as the source of externally advected water vapor that supplies the part of the precipitation (P_A) not derived from local evapotranspiration (P_E)—where P = P_A + P_E—it also cannot be used to quantify the relative contributions of E and IF/A to P.

Finally, Zangvil et al. used the processes defined in Eq. (3) and a separately developed conceptual recycling model to derive the following relation for the precipitation fraction supplied by locally evapotranspired moisture:

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Note that Eq. (4) was not derived formally from Eq. (3). Instead, the model’s fundamental assumptions were that water vapor of externally advected (subscripted A above) and locally evapotranspired (subscripted E) origins are fully mixed in the atmospheric “tank” over the study domain (within which all moisture fields vary slowly) and thus make proportionate contributions to P. Because of these assumptions, this tank formulation was considered applicable not only on monthly and seasonal time scales, but also to sets of (not necessarily contiguous) days with similar large-scale moisture characteristics (IF/A, E, P, etc.). Zangvil et al. (2004) provided a comprehensive comparison and reconciliation of Eq. (4) with other recently developed recycling ratios and argued that the Eq. (4) assumptions, derivation, and application were the most straightforward.

The application of Eq. (4) to sets of days was justified by two circumstances. First, in Zangvil et al. (2004, Table 3) the mean P_E/P value for days in the same P category was obtained both by (i) averaging the daily P_E/P ratios and (ii) accumulating the daily P_E and P totals across the days. The generally close agreement between the resulting P_E/P ratios supported the fully mixed tank assumption applying on the daily time scale, and required that only method (i) be used in the present P_E/P computations described in section 2b. The daily applicability of the fully mixed tank assumption also was supported by an estimated regional water vapor replenishment time of ~1.3 days for this study. That estimate is consistent with average daily values of PW (~33 mm, not shown), E (~3.4 mm day⁻¹, Table 3 later), and IF/A (~21.4 mm day⁻¹, Table 3 later).

b. Moisture budget computations

The atmospheric moisture budget components and associated parameters in Eqs. (1)–(4) were evaluated for the extensive SGP region delineated in Fig. 1 for the May–June periods of 2007 (CLASIC, very wet), 2006 (very dry), 2002 (intermediate wetness), and 1998 (very dry especially upstream across Texas). Table 1 and Fig. 2 document the contrasting May–June precipitation patterns involved, and Table 1 also includes statistics for the preceding January–April periods to indicate precursor moisture conditions.

The study domain includes both the SGP ACRF and its upstream (Texas) moisture advection source (Fig. 1). This near-square-shaped region contains 0.83 × 10⁶ km², an area within the 0.6–1.0 × 10⁶ km² minimum size range recommended/used for atmospheric moisture budget studies with monthly and seasonal time scales (Rasmusson 1968, 1971; Yanai et al. 1973; WCRP 1992). Results for smaller areas are considered less reliable, which precluded focusing the present investigation exclusively on the ACRF (Fig. 1). Expanding the study region to the south of the SGP ACRF permitted placement of its southern boundary immediately adjacent and approximately normal to the moisture inflow from the Gulf of Mexico (Rasmusson 1967, Figs. 4 and 6). The final expanded domain thus captures the full advective moisture input to the SGP ACRF. Also, the region’s size and location (i) approximate or exceed the typical scales of most individual May–June weather disturbances [e.g., mesoscale convective systems (MCSs)] and resulting precipitation patterns (e.g., Richman and Lamb 1985; Lamb and Richman 1990), but (ii) encompass only part of propagating larger-scale parent atmospheric systems.

Computation of all budget components and associated parameters in Eqs. (1)–(4) produced study region averages for 24-h (1200–1200 UTC) periods. Area averages were calculated from gridpoint values within the region, and 24-h time means were obtained by averaging values for 3-h intervals. These procedures were applied to estimates of the following components/parameters: (i) HA and HD (surface to 300 hPa) given by finite difference evaluations of North American Regional Reanalysis (NARR) (Mesinger et al. 2006) wind and specific humidity data with a spatial (vertical) resolution of 32 km (50 hPa), (ii) dPW (surface to 300 hPa) from successive 1200 UTC values of the same NARR specific humidity data, (iii) P from 24-h totals for 0.25° latitude–longitude grid points from the National Centers for Environmental Prediction (NCEP) daily gridded precipitation dataset (Shi et al. 2003; http://www.cpc.noaa.gov/products/precip/realtime/GIS/USMEX/analysis.shtml), and (iv) IF/A (surface to 300 hPa) by line integration of the above NARR data. In addition, 24-h area-averaged estimates of E were obtained as residuals of Eq. (1). The few resulting negative E values (8.3% for all years, 4.4% excluding 1998) were small and set to zero. Because there was no basis to do otherwise, their associated daily budgets were rebalanced simply by compensating for the water added to E equally among the other terms in Eq. (1). For example, if the residual-estimated E was −1 mm day⁻¹, a correction factor of +0.25 mm day⁻¹ was added to each of dPW, HA, HD, and P. Finally, 24-h values of P_E/P and P_E were calculated using Eq. (4) and the above 24-h E, IF/A, and P estimates.

All above 24-h budget component/associated parameter values then were averaged over individual calendar months, May–June periods, and sets of days for five P categories (P ≤ 0.6, 0.6 < P ≤ 2, 2 < P ≤ 4, 4 < P ≤ 8, and P > 8 mm day⁻¹). Results appear in Tables 2 and 3 and Fig. 3 (and Figs. 5 and 6 later).

Table 2.

Linear correlation coefficients between (a) daily, (b) monthly, and (c) monthly anomaly values of atmospheric moisture budget components/parameters for May–June 1998, 2002, 2006, and 2007 combined. Component/parameter abbreviations and sign conventions are as defined in section 2a. Consistent with Eqs. (3) and (4), IF/A is considered positive. See section 2c for explanation of SR. Using the two-tailed t-test procedures described in section 2b, the daily (monthly) correlation magnitude thresholds for 0.1% significance are 0.41 (0.92), for 1% significance 0.33 (0.83), and for 5% significance 0.25 (0.71).

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Table 3.

Mean values of atmospheric moisture budget components and related parameters for 24-h periods (mm day⁻¹, except for SR in MJ m⁻² day⁻¹ and dimensionless P_E/P) when area-averaged precipitation was in one of five categories. Both months are considered together for each May–June period and all four periods combined. Budget component/parameter abbreviations and sign conventions are as defined in section 2a. Consistent with Eqs. (3) and (4), IF/A is considered positive. See section 2c for explanation of SR. The P categories replicated those in Zangvil et al. (2004). Here, intermediate categories B–D have approximately equal total numbers of days (38–49), and the extreme P categories represent excessively dry (A, 84 days) and excessively wet (E, 26 days) conditions.

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Mean values of atmospheric moisture budget components and related parameters for 24-h periods during individual months (thin bars, letter is first letter of month) and combined months (thick bars, number is last number of year) for May–June 1998, 2002, 2006, and 2007 (mm day⁻¹, except for dimensionless P_E/P). CLASIC year (2007) is underlined. Budget component/parameter abbreviations and sign conventions are as defined in section 2a and Table 2, and computational procedures are summarized in section 2b.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Mean values of atmospheric moisture budget components and related parameters for 24-h periods during individual months (thin bars, letter is first letter of month) and combined months (thick bars, number is last number of year) for May–June 1998, 2002, 2006, and 2007 (mm day⁻¹, except for dimensionless P_E/P). CLASIC year (2007) is underlined. Budget component/parameter abbreviations and sign conventions are as defined in section 2a and Table 2, and computational procedures are summarized in section 2b.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Mean values of atmospheric moisture budget components and related parameters for 24-h periods during individual months (thin bars, letter is first letter of month) and combined months (thick bars, number is last number of year) for May–June 1998, 2002, 2006, and 2007 (mm day⁻¹, except for dimensionless P_E/P). CLASIC year (2007) is underlined. Budget component/parameter abbreviations and sign conventions are as defined in section 2a and Table 2, and computational procedures are summarized in section 2b.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Interrelations among the moisture budget components/parameters were investigated using linear correlation and spectral analyses. Correlation coefficients were computed for each component/parameter pair on daily, monthly, and monthly anomaly time scales with their statistical significance being assessed via a two-sided t test (Wilks 2006, 131–135). However, because daily precipitation totals are not independent, the statistical significance levels of the daily correlation coefficients were computed using a reduced number of observations. Based on spectral analysis (not shown) and following Zangvil et al. (2001), we assumed that the precipitation producing disturbances have an approximately 4-day time scale and therefore decreased the number of observations by a factor of 4 (from 240 to 60). This reduction produced limiting significance values that were more conservative than outcomes of more rigorous procedures (Davis 1976; Zangvil et al. 2001).

The two datasets used in the above calculations have key advantages for this investigation. For the NARR data these strengths include the fine spatial (32 km) and temporal (3 h) resolutions, the direct assimilation of precipitation and radiances, and use of an improved land surface model (e.g., Berbery et al. 2003; Ek et al. 2003; Mitchell et al. 2004a,b; Shafran et al. 2004). Inclusion of direct precipitation assimilation in the NARR—which is not part of global reanalysis systems—was intended to increase the reliability of land surface water (especially) and energy budgets. The NCEP daily gridded precipitation dataset has a similarly fine (0.25° latitude–longitude) spatial resolution that is produced by an optimal interpolation (OI) (Xie et al. 2007) objective analysis of totals from ~8000 rain gauge stations nationwide. Those data emanate from multiple independent observing systems and then are subject to several layers of quality control (http://www.cpc.noaa.gov/products/precip/realtime/GIS/USMEX/analysis.shtml).

c. Related environmental data

Interpretation of the above moisture budget estimates required the development of four additional sets of related environmental data for the study region and May–June periods: (i) daily averages of modeled global solar radiation (SR) (Tables 2 and 3; Figs. 4, 6, and 9 later), (ii) instantaneous point measurements and monthly area-averaged model estimates of soil moisture (Figs. 7 and 8 later), (iii) seasonal area-averaged yields for the region’s principal row crops (wheat, grain sorghum) in the context of yield and precipitation variability for 1990–2009 (Table 1, Fig. 8 later), and (iv) May–June and preceding January–April area-averaged precipitation anomalies relative to 1990–2009 variability (Table 1).

As in Fig. 3 but for mean values of SR (MJ m⁻² day⁻¹) obtained using computational procedures described in section 2c. Numbers under thick bars are last two numbers of year. CLASIC year 2007 is underlined.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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As in Fig. 3 but for mean values of SR (MJ m⁻² day⁻¹) obtained using computational procedures described in section 2c. Numbers under thick bars are last two numbers of year. CLASIC year 2007 is underlined.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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As in Fig. 3 but for mean values of SR (MJ m⁻² day⁻¹) obtained using computational procedures described in section 2c. Numbers under thick bars are last two numbers of year. CLASIC year 2007 is underlined.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Daily SR averages for all study months were obtained for the entire study region from the above NARR dataset. They were computed from 3-h totals for all NARR grid points in the study region. The NARR SR values were estimated by the Eta model using a precipitation assimilation procedure (Zhao et al. 1997; Schroeder et al. 2009).

Three sources of soil moisture information were analyzed for all study months. Volumetric soil moisture measurements from Campbell 229-L heat dissipation matric potential sensors were used for the SGP ACRF Central Facility (Figs. 1 and 7 later) and 54–91 Oklahoma (OK) Mesonet sites (Fig. 7 later). Instrument and network details are provided in Schneider et al. (2003) and Illston et al. (2008). The Campbell 229-L sensor system gives values of a fractional water index (FWI) that increase from 0 (driest state) to 1 (wettest state) to cover the plant-available soil water range. Campbell 229-L measurements were not available for Texas. This situation necessitated the use of modeled soil moisture estimates for the entire study region (Huang et al. 1996), which were obtained from a NOAA web site (http://ftp.cpc.ncep.noaa.gov/wd51yf/us/). These estimates were monthly averages of vertically integrated water depth (cm) for National Oceanic and Atmospheric Administration climate divisions (30 in the study region), given by a one-layer hydrological model that treats soil moisture through the depth that “it participates in land-surface processes, that is usually in the upper 1–2 m of soil” (Huang et al. 1996, p. 1352). The spatial resolution of these modeled soil moisture estimates was (desirably) very similar to that of the winter wheat yield data with which they later (Fig. 8) are juxtaposed. Also, soil moisture estimates from the same model previously compared favorably with neutron probe measurements for Illinois (Zangvil et al. 2004, their Figs. 6d and 7b). See Huang et al. (1996), Schneider et al. (2003), and Illston et al. (2008) for further information concerning the basis of these soil moisture data.

For nonirrigated winter wheat (February–June growing season) and grain sorghum (May–September), estimates of area [hectares (ha)] and production [megagrams (Mg)] were obtained for 38 U.S. Department of Agriculture crop reporting districts (CRDs) for 1990–2009 from databases maintained by the U.S. National Agriculture Statistics Service, available on its website (http://www.nass.usda.gov). Normalized wheat and sorghum yield anomalies (б) were computed for our study years from detrended (via linear regression) time series for 1990–2009 (N = 20). Anomalies were obtained separately for the entire study region (Table 1) and each CRD (Fig. 8 later). This detrending effected a conventional removal of potential technology-induced (through pesticide and plant hybrid development) yield increases. For the entire study region, the wheat (sorghum) regression line had a slope of +0.011 Mg ha⁻¹ yr⁻¹ (+0.015 Mg ha⁻¹ yr⁻¹) with an explained variance fraction of 3.6% (2.9%) and a significance level of 42% (47%), according to an f test (equivalent of a two-tailed t test) with N − 2 degrees of freedom (Wilks 2006, 131–135). Therefore, there were no statistically significant long-term trends in these crop yield time series.

Normalized May, June, and May–June precipitation anomalies for the entire region, and separately for Oklahoma, were used to rank the 20 years during 1990–2009 and indicate the relative moistness of our four study periods (Table 1). The regional anomalies were computed from actual precipitation totals (not detrended) for 1369 0.25° latitude–longitude grid points in the aforementioned NCEP daily gridded precipitation dataset. The absence of trends in these regional May/June/May–June precipitation anomaly time series is evidenced by their linear regression fits having slopes of only −0.05/+0.03/−0.01 mm yr⁻¹ with explained variances of only 9.09%/2.08%/0.53%, and significance levels of 20%/54%/76% according to the above f test. Similar regression results were obtained for the Oklahoma Mesonet data. The same precipitation analyses were performed for January–April as a whole (Table 1) to document precursor moisture conditions.

a. Traditional moisture budget analysis—Monthly and bimonthly time scales

Results from the traditional moisture budget analysis [Eq. (1)] for the study months and bimonthly periods are included in Table 2 and Fig. 3. This section focuses on the various monthly and bimonthly interrelations between P, E, and the bulk E − P; the total MFD and its HA and HD components; and dPW—but not the moisture sources for P. Quantification of the moisture sources for P appears in section 3c, where the treatment is expanded to include the new parameters IF/A, P_E/P, and P_E. The intermediate section 3b provides an informative bridge by presenting an analysis that stratifies the traditional moisture budget estimates by daily precipitation amount.

Figure 3 shows pronounced interannual P variation on both monthly and bimonthly time scales, with the wetness of the 2007 CLASIC period being extreme relative to the other years. This P variation is related most strongly to E, E − P, and MFD. The monthly correlation of P with E is large (+0.81) and statistically significant (5% level, Table 2b), and was unchanged when the seasonal cycle was removed from each parameter (Table 2c). Only in the extremely wet 2007 CLASIC period did P exceed E on these monthly and bimonthly time scales, with E − P being positive otherwise (Fig. 3). Table 2b shows that monthly E − P varies principally (and inversely) with P rather than E. The monthly correlation between E − P and P is −0.93 (significant at 0.1% level), whereas for E − P versus E it is only −0.54, statistically insignificant and of counterintuitive sign. These correlations were essentially unchanged when the seasonal cycle was removed from each parameter (Table 2c). A monthly correlation of −0.93 (0.1%) also was obtained between P and MFD, including after seasonal cycle removal. Consistent with these results and the budget framework of Eqs. (1)–(3), dPW is poorly related to P, E, and E − P on the monthly time scale (Tables 2b,c).

According to Fig. 3, most of the E − P atmospheric moisture deficit for the very wet 2007 CLASIC period was offset by a net import of water vapor into the region (negative MFD), primarily via moist horizontal water vapor advection (negative HA). While there also were very small May 2007 contributions in this regard from local atmospheric water vapor depletion (negative dPW) and related to horizontal velocity convergence (negative HD), those processes both were positive (albeit extremely weak) during June 2007. Thus, for May–June 2007 as a whole, negative HA provided almost all of the negative MFD that supported the uniquely negative E − P.

The water vapor convergence role of HA also prevailed for most other study months and all bimonthly periods, and in some cases with greater magnitude (Fig. 3). However, these negative HA contributions to the total MFD generally were more than offset by positive HD, especially for the extreme cases of the relatively dry Junes of 2002 and 2006. This opposition of monthly HA and HD is reflected in their moderate-to-strong negative correlations in Tables 2b,c (−0.88, 1%; −0.76, 5%). As a result, the total MFD was slightly positive for all months and bimonthly periods of May–June 1998, 2002, and 2006. For the months when HA and HD did not have similar magnitudes but opposite sign, HD variation produced the maximum positive MFD values (May 1998 and June 2006) or did not weaken the maximum negative MFD values (May and June 2007). Thus, for all four study periods combined, the dominant control on MFD was from HD rather than HA as prevailed for CLASIC 2007 (Fig. 3). This situation is documented statistically by the large difference between the Table 2b monthly correlations of MFD with HD (+0.55, not significant) and HA (−0.07, not significant), which was increased markedly by the seasonal cycle removal (+0.73/5% versus not significant −0.11, Table 2c). The above small atmospheric moisture surpluses for the non-CLASIC years all were enhanced by similarly small atmospheric water vapor storage increases (Fig. 3). This produced the modest positive E − P values for those years that contrast strongly with the larger E − P deficit for the very wet 2007 CLASIC period.

The above traditional budget results complement, on an individual month/bimonthly basis, key findings of earlier multiyear-average investigations for the central United States that extended (not always completely) into the SGP (e.g., Benton et al. 1950; Rasmusson 1968, 1971; Brubaker et al. 1993; Bosilovich and Schubert 2001). Our results are consistent with the overwhelmingly convective origin of the precipitation, the development of which is favored by large-scale horizontal velocity convergence and ascent (hence overall above HD importance) and produces relatively small/transient/short-lived cloud elements that modulate SR only weakly. Concerning the latter, Fig. 4 shows that the interannual variability of the bimonthly mean SR (26.57–30.15 MJ m⁻² day⁻¹) spans only 11.87% of the maximum. The calendar month SR differences between 2007 CLASIC (very wet) and the immediately preceding and much drier 2006 (3.18 and 3.09 MJ m⁻² day⁻¹) vary by only 10%–11% of their drier month maximum. The 1998 versus 2002 calendar month SR differences are even smaller (6.15% and 7.30%), and counterpart values for all four study years (i.e., 2007 versus 1998) differ by only 10.56%–13.21%.

Consistent with the above reasoning and results, on the monthly scale (Table 2b) SR is strongly negatively correlated with P (−0.84, 1%) and has moderate-to-strong positive associations with (i) MFD (+0.78, 5%) primarily via HD (+0.54, not significant) and (ii) E − P (+0.81, 5%). Perhaps counterintuitively, monthly SR is negatively related to E (−0.64, 10%) which suggests that surface moisture availability limits the E response to increased SR. This issue is considered further in section 3c. Note that seasonal cycle removal increased the magnitudes (by 0.05–0.09) and significance levels of all these correlations except for the statistically insignificant SR versus HD (Tables 2b,c).

b. Traditional moisture budget analysis—Daily time scale

Greater insight is obtained into some of the mechanisms of the atmospheric moisture budget—but still not the moisture sources for P—when results from the traditional approach [Eq. (1)] are stratified by daily P amount. The first analysis of this type appeared in Zangvil et al. (2004) for the Midwestern U.S. Corn Belt. Full documentation of the present SGP analysis is presented in Table 3 (except for SR and the last three columns on the right-hand side) and selected results appear in Fig. 5. While a distinctive feature of Table 3 and Fig. 5 is the generally strong within-P-category (i.e., interannual) uniformity and between-P-category separation of the E-P, HA, HD, and MFD results, there are several distinctive interannual differences that involve particularly the very wet CLASIC 2007 and immediately preceding very dry 2006.

Mean values of traditional atmospheric moisture budget components for 24-h periods (mm day⁻¹) when area-averaged precipitation (P) was in one of five categories. Both months are considered together for each May–June period and all periods combined. Budget component and sign conventions are as defined in section 2a and Tables 2 and 3. Bars are color coded: wet periods are in green (deepest green for very wet CLASIC 2007; Table 1, Figs. 2 and 3), and dry periods are in brown (deepest brown for very dry 1998; Table 1, Figs. 2 and 3). Same scale is used in all panels with numerical value at end of each bar. Numbers at start of each E − P bar give number of days in that P category for each year.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Mean values of traditional atmospheric moisture budget components for 24-h periods (mm day⁻¹) when area-averaged precipitation (P) was in one of five categories. Both months are considered together for each May–June period and all periods combined. Budget component and sign conventions are as defined in section 2a and Tables 2 and 3. Bars are color coded: wet periods are in green (deepest green for very wet CLASIC 2007; Table 1, Figs. 2 and 3), and dry periods are in brown (deepest brown for very dry 1998; Table 1, Figs. 2 and 3). Same scale is used in all panels with numerical value at end of each bar. Numbers at start of each E − P bar give number of days in that P category for each year.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Mean values of traditional atmospheric moisture budget components for 24-h periods (mm day⁻¹) when area-averaged precipitation (P) was in one of five categories. Both months are considered together for each May–June period and all periods combined. Budget component and sign conventions are as defined in section 2a and Tables 2 and 3. Bars are color coded: wet periods are in green (deepest green for very wet CLASIC 2007; Table 1, Figs. 2 and 3), and dry periods are in brown (deepest brown for very dry 1998; Table 1, Figs. 2 and 3). Same scale is used in all panels with numerical value at end of each bar. Numbers at start of each E − P bar give number of days in that P category for each year.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Days with P ≤ 0.6 mm were characterized by moderate E − P atmospheric moisture surpluses that either were exported from the region (positive MFD) or stored locally (positive dPW), generally with similar magnitude (Table 3, Fig. 5). These processes characterized especially the very wet 2007 CLASIC period, when E was large (Table 3, Fig. 6). However, the most striking result for this lowest daily P category is that the modest positive MFD values for all years were relatively small differences between much larger HD and HA values of opposite sign. The water vapor convergence role of HA consistently was more than offset by divergent HD. This difference was largest for the 2007 CLASIC period. These SGP May–June results are in strong contrast to those obtained for the Midwestern U.S. Corn Belt by Zangvil et al. (2004). There, for P < 0.6 mm day⁻¹ during May–August, very small divergent HA consistently supplemented modest divergent HD.

As in Fig. 5 but for mean values of atmospheric moisture budget recycling and related parameters (mm day⁻¹, except for dimensionless P_E/P and SR in MJ m⁻² day⁻¹). Scale varies between parameters except for P_E and E. Numbers at start of each P_E/P bar give number of days in that P category for each year.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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As in Fig. 5 but for mean values of atmospheric moisture budget recycling and related parameters (mm day⁻¹, except for dimensionless P_E/P and SR in MJ m⁻² day⁻¹). Scale varies between parameters except for P_E and E. Numbers at start of each P_E/P bar give number of days in that P category for each year.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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As in Fig. 5 but for mean values of atmospheric moisture budget recycling and related parameters (mm day⁻¹, except for dimensionless P_E/P and SR in MJ m⁻² day⁻¹). Scale varies between parameters except for P_E and E. Numbers at start of each P_E/P bar give number of days in that P category for each year.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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When daily P increased to 0.6 < P ≤ 2 mm day⁻¹ (Table 3, Fig. 5), E − P remained positive but generally was somewhat reduced and the MFD atmospheric export drew on most or all of this diminished surplus and sometimes (1998 and 2006 dry years) also small local storage depletions. For this enhanced P category, the positive MFD tended to be increased and continued to result from divergent HD exceeding convergent HA, but the magnitudes of both these components generally were reduced and especially for the 2007 CLASIC year. These changes became more pronounced as daily P increased further to 2 < P ≤ 4 mm day⁻¹ (Table 3, Fig. 5). When daily P was in this range, the E − P atmospheric moisture surpluses generally were very small (except for CLASIC 2007) and, along with local storage depletion in most years, continued to support modest positive MFD that again resulted from divergent HD exceeding convergent HA. The exception is the 2002 period of intermediate regional wetness (Table 1), when convergent HA sufficiently exceeded divergent HD to support both a small negative MFD and increased local storage despite the E − P surplus being minute.

The above water vapor budget changes are accentuated considerably when daily P increases further to 4 < P ≤ 8 mm (Table 3, Fig. 5). Most importantly, E − P now is moderately negative and balanced primarily by convergent MFD that reflects a strong tendency for HD to be negative. These changes occurred completely or predominantly in three of the four years—with the notable partial exception of CLASIC 2007—and so characterized fully all four years combined. However, considerable interannual variability was involved. During 2007, the convergent MFD was the product of HA remaining moderately negative to offset substantially a still positive (but very small) HD and contribute also to a minute local storage increase. Note that this HA dominance for 2007 occurred on 20 of the 61 days, and those days produced 34% of the total May–June P (Table 3). The other pronounced exception to the above general pattern involved the year of intermediate wetness (2002), when local storage depletion and large E (Table 3, Fig. 6) were major moisture sources. The latter budget balancing contributions were necessitated by the moderately convergent HD only half compensating for surprisingly strong divergent HA. The results for the dry years of 2006 (especially) and 1998 conformed more closely to those for all four years combined.

The above general pattern for 4 < P ≤ 8 mm day⁻¹ was more pronounced and more consistent interannually when daily P exceeded 8 mm (Table 3, Fig. 5). In particular, the P > 8 mm day⁻¹ results for CLASIC 2007 (for 16 days that produced 55% of total P, Table 3) replicated closely those for all four years combined (26 total days that averaged 40% of total P)—large E − P deficits essentially were completely supplied by strongly convergent MFD that was forced totally by negative HD, with dPW and HA both being near zero. This pattern also characterized the very dry pre-CLASIC year (2006) when daily P exceeded 8 mm, despite its much smaller sample size (one-third of 2007), with the addition of an approximate balance between modest values of convergent HA and positive dPW. Both of the remaining study periods (intermediate 2002 and dry Texas 1998) experienced strongly convergent HD when P > 8 mm day⁻¹, which forced moderately-to-strongly convergent MFD and also contributed to the largest positive dPW values in Table 3 and Fig. 5.

Although several of the underlying 1998 moisture budget component results for P > 8 mm ⁻¹ are interestingly extreme, they are for a single day and likely have low representativeness. The especially small negative E − P and large positive HA values for the otherwise dry 1998 were associated with extremely large local (E) and external (IF/A) moisture supplies (Fig. 6). While this large E computationally was required by the divergent HA reducing the total MFD convergence, it also physically could reflect widespread surface water availability due to abundant precipitation on dry, hardened soil. Interestingly, very low E characterized the larger number of 1998 days (8) when daily P was in the lower and less flood-inducing 4–8 mm category, which likely also is consistent with the seasonal dryness of that year (Tables 1 and 3, Fig. 6).

Several of the daily moisture budget associations suggested in the above discussion of Table 3 and Fig. 5 are confirmed quantitatively by the daily correlation results in Table 2a. Some key daily correlations reaffirm those identified earlier for the monthly time scale (Tables 2b,c), while other daily correlations are profoundly and revealingly different. Daily E − P varies principally and inversely with daily P (−0.84, 0.1%) rather than E, similar to the monthly time scales (both 0.93, 0.1%). Most importantly, the daily association between P and HD (−0.71, 0.1%) is enhanced slightly from its monthly anomaly counterpart (−0.66, 10%) and substantially so over the monthly value (−0.46, not significant). In contrast, Table 2 indicates that the daily correlation between P and the total MFD (−0.52, 0.1%) is reduced substantially from its monthly counterparts (both −0.93, 0.1%). This reduction coincides with a slight strengthening of the opposing (positive) correlation of P with HA (+0.24 daily, 6%, versus near zero for monthly and monthly anomaly).

Consistent with this situation, the daily negative HA versus HD correlation (−0.60, 0.1%) is weaker than its monthly (−0.88, 1%) and monthly anomaly (−0.76, 5%) counterparts, and the daily correlations of HD and HA with MFD (both +0.45, 0.1%) are changed differently from the monthly time scale. The daily HD versus MFD correlation is weaker than its monthly anomaly (+0.73, 5%) and monthly (+0.55, not significant) counterparts. In contrast, for the daily association of HA with MFD the correlation magnitude is increased substantially from the near-zero monthly values, and the positive sign reflects the variability when daily P < 4 mm and not higher (Fig. 5).

While P is unrelated to dPW on the daily (−0.10, not significant) as well as monthly time scales (−0.18, −0.19, not significant), the daily dependence of dPW on HA (−0.66, 0.1%) and MFD (−0.71, 0.1%) is striking given the near-zero monthly associations of these processes (Table 2). Clearly, moist (dry) HA enhances (decreases) PW on a daily basis by controlling the total MFD—much more than HD and E, which have near-zero daily associations with dPW. The daily correlations of SR with P, E − P, MFD, HD, and E are of the same sign but smaller than their monthly counterparts discussed above (Table 2). Most pronounced is the weakening of the SR associations with MFD (+0.78/+0.84 to +0.18), E − P (+0.81/+0.86 to +0.55), and E (−0.64/−0.73 to −0.24).

c. Moisture recycling, soil moisture, and wheat and sorghum crops

Important new insight into SGP growing season land–atmosphere interactions is added to the above results of traditional analyses through stratification of the new atmospheric moisture budget recycling parameters [IF/A, P_E/P, P_E; Eqs. (3)–(4)] by daily P amount (Table 3, Fig. 6). In particular, the recycling ratio (P_E/P) quantifies the contribution of local E (versus imported atmospheric moisture) to P. For the parameters treated in the previous section, Table 3 and Fig. 6 contained generally strong within-P-category (i.e., interannual) uniformity and between-P-category separation. These features are less characteristic of the IF/A, P_E/P, and P_E results considered here, which include some distinctive interannual features, especially the uniqueness of the very dry 1998 and further similarities between the very wet 2007 CLASIC period versus the immediately preceding very dry 2006 (Table 3, Fig. 6). To facilitate interpretation of these recycling results, Fig. 6 also includes the related parameters E and SR.

Here, P_E/P tends to increase modestly from relatively low values as daily P increases from 0–4 mm (Table 3, categories A–C; Fig. 6), and then returns to the same low values as daily P exceeds that threshold (Table 3, categories D–E; Fig. 6). Specifically, the mean P_E/P generally is similar for P ≤ 0.6 (0.12–0.21 range for individual May–June periods and 0.15 for all periods combined) and 0.6 < P ≤ 2 (0.09–0.22, 0.15), then increases somewhat for 2 < P ≤ 4 mm day⁻¹ (0.12–0.28, 0.19), after which it decreases for 4 < P ≤ 8 (0.07–0.22, 0.16) and P > 8 mm day⁻¹ (0.11–0.16, 0.15). The range of 4-yr-average P_E/P ratios across all P categories (0.15–0.19) is 27% of the minimum, while the individual year values that contribute to those averages span a fourfold increase (0.07–0.28). A zero daily correlation between P_E/P and P (Table 2a) certifies their nonrelationship. In contrast to this relative P_E/P constancy for all daily P categories except the intermediate 2 < P ≤ 4 mm, both E and IF/A moisture sources tend to increase progressively with daily P elevation (Table 3, Fig. 6). For the 4-yr average, E increases from 2.84 to 4.16 mm day⁻¹ (46%) and IF/A is raised from 19.12 to 24.85 mm day⁻¹ (30%). Such dependencies on P are reflected in small (not significant) positive correlations in Table 2a. These SGP May–June results are in pronounced contrast to those obtained by Zangvil et al. (2004) for the Midwestern U.S. Corn Belt. There, for the full May–August growing season, P_E/P and E decreased when P increased from 0 to 8 mm day⁻¹ and increased with higher daily P, while the progressive IF/A elevation across the same P categories was much larger (averaging 130%), albeit from a much lower average for P ≤ 0.6 mm day⁻¹ (11.94 mm day⁻¹).

Note that the above relative constancy of P_E/P with increasing P is accompanied by a striking progressive inflation of the P_E magnitude involved (Table 3, Fig. 6). There is a 60-fold enhancement of the 4-yr-average P_E from the lowest to highest P categories (0.03 to 1.78 mm day⁻¹), which have identical average P_E/P ratios (0.15). Even when P_E/P tends to be largest (for 2 < P ≤ 4 mm day⁻¹, 0.19 mean), the average amount of water recycled is only 30% of that for P > 8 mm day⁻¹. Table 2a shows that this strong positive dependence of daily P_E on P has a linear correlation of +0.79 (0.1%), whereas the daily P_E versus P_E/P correlation is only +0.41 (0.1%). The monthly correlations between P_E and P in Tables 2b,c are even higher (+0.96, +0.97, both 0.1%), whereas those for P_E versus P_E/P are increased to only +0.61 and +0.59 (both not significant). This very strong SGP May–June daily and monthly dependence of P_E on P essentially duplicates that Zangvil et al. (2004) identified for the Midwestern U.S. Corn Belt for May–August.

The recycling and related results for the very wet 2007 CLASIC period are not especially distinctive in Fig. 6. Most prominent for 2007 are the substantially above-average P_E/P and E values for daily P ≤ 4 mm, when the IF/A moisture source was below the 4-yr average. When P > 4 mm day⁻¹, the 2007 P_E/P, E, and IF/A values generally were near average and reasonably similar to counterparts for the immediately preceding and very dry 2006. This similarity is reflected in the near-identical May–June average P_E/P ratios for 2007 and 2006 (Fig. 3), for which the contributing E and IF/A moisture sources both were proportionally larger in the wet 2007. Interestingly, the most anomalous results in Fig. 6 are for 1998, which had the driest May–June of 1990–2009 (Table 1, Fig. 2). The 1998 P_E/P ratios were the lowest for all P categories, and offset by IF/A always being largest. Except for daily P > 8 mm (only one observation), E was below average for 1998. For 4 < P ≤ 8 mm day⁻¹, especially large 1998 IF/A was associated with strongly convergent HD and MFD (Fig. 5). These extreme daily 1998 results are reflected in the Table 3 May–June averages for P_E/P (lowest), IF/A (largest), and E (lowest).

Figures 7–9 develop the roles of soil moisture availability and solar radiation amount for the above E and recycling results and associated crop yields. The 1998 sequence of abundant January–April P (Table 1), resulting soil near saturation through mid-May (Fig. 7, bottom left), and an excessively dry May–June (Table 1; Fig. 2) produced the highest winter wheat yield for 1990–2009 (Table 1, Fig. 8). The El Niño–induced January–April 1998 wetness (Montroy et al. 1998) permitted the early maturation and harvesting of that wheat crop (Fig. 8, right panel insets), which, coupled with the extreme May–June dryness (Table 1, Fig. 2) and associated progressive soil moisture depletion (Figs. 7 and 8), resulted in very low absolute (P_E) and aforementioned relative (P_E/P) May–June moisture recycling values (Figs. 3 and 6). To offset this very low recycling, May–June 1998 daily P > 4 mm was fed by abnormally large IF/A and resulting strongly convergent HD and (for 4 < P ≤ 8 mm day⁻¹) MFD (Figs. 5 and 6). When P ≤ 4 mm day⁻¹ in those 1998 months, the very large IF/A was associated with substantially reduced divergent HD. The continuation of these 1998 drought conditions later into the summer—which has been attributed to positive regional feedback from the above earlier reduced recycling (Hong and Kalnay 2000, 2002)—produced the lowest Oklahoma–Texas (summer) grain sorghum yield for 1990–2009 (Table 1).

Patterns of observed Oklahoma soil moisture fractional water index (FWI) for study years. (left) May–June time series (daily resolution, left ordinate) for five depths at Central Facility (CF, white dot in right panels) of SGP ACRF. Blue bars at bottom of (left) indicate CF/SGP/ACRF daily P totals (mm, right ordinate); asterisks on baseline (2002 and 2006) indicate P data were missing for at least half of a day’s 30-min periods, with no P recorded when data were available; asterisk above bar (2007) denotes P was missing for 16 30-min periods but totaled 8.64 mm during rest of day; asterisk on baseline (2007) indicates data were missing for entire day. (right) Average June Oklahoma FWI fields for 25-cm depth, obtained from Oklahoma Mesonet measurements for locations where FWI values are given.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Patterns of observed Oklahoma soil moisture fractional water index (FWI) for study years. (left) May–June time series (daily resolution, left ordinate) for five depths at Central Facility (CF, white dot in right panels) of SGP ACRF. Blue bars at bottom of (left) indicate CF/SGP/ACRF daily P totals (mm, right ordinate); asterisks on baseline (2002 and 2006) indicate P data were missing for at least half of a day’s 30-min periods, with no P recorded when data were available; asterisk above bar (2007) denotes P was missing for 16 30-min periods but totaled 8.64 mm during rest of day; asterisk on baseline (2007) indicates data were missing for entire day. (right) Average June Oklahoma FWI fields for 25-cm depth, obtained from Oklahoma Mesonet measurements for locations where FWI values are given.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Patterns of observed Oklahoma soil moisture fractional water index (FWI) for study years. (left) May–June time series (daily resolution, left ordinate) for five depths at Central Facility (CF, white dot in right panels) of SGP ACRF. Blue bars at bottom of (left) indicate CF/SGP/ACRF daily P totals (mm, right ordinate); asterisks on baseline (2002 and 2006) indicate P data were missing for at least half of a day’s 30-min periods, with no P recorded when data were available; asterisk above bar (2007) denotes P was missing for 16 30-min periods but totaled 8.64 mm during rest of day; asterisk on baseline (2007) indicates data were missing for entire day. (right) Average June Oklahoma FWI fields for 25-cm depth, obtained from Oklahoma Mesonet measurements for locations where FWI values are given.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Patterns of modeled (left) May and (center) June soil moisture and (right) harvested winter wheat yield anomalies for study years across the SGP. Rectangular boxes enclose study region. Modeled soil moisture (SM, cm) is from model by Huang et al. (1996) with NOAA Climate Division resolution. Winter wheat anomalies (σ) are from detrended 1990–2009 means, with USDA crop reporting district resolution (NA is not available). Stars locate soil moisture monitoring station used in Fig. 7, left panels. Percentages in bottom corners of right panels are for statewide winter wheat harvest completions by (left) 31 May–4 June and (right) 28 June–2 July, obtained from NOAA/USDA Weekly Weather and Crop Bulletin. See section 2c for further details.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Patterns of modeled (left) May and (center) June soil moisture and (right) harvested winter wheat yield anomalies for study years across the SGP. Rectangular boxes enclose study region. Modeled soil moisture (SM, cm) is from model by Huang et al. (1996) with NOAA Climate Division resolution. Winter wheat anomalies (σ) are from detrended 1990–2009 means, with USDA crop reporting district resolution (NA is not available). Stars locate soil moisture monitoring station used in Fig. 7, left panels. Percentages in bottom corners of right panels are for statewide winter wheat harvest completions by (left) 31 May–4 June and (right) 28 June–2 July, obtained from NOAA/USDA Weekly Weather and Crop Bulletin. See section 2c for further details.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Patterns of modeled (left) May and (center) June soil moisture and (right) harvested winter wheat yield anomalies for study years across the SGP. Rectangular boxes enclose study region. Modeled soil moisture (SM, cm) is from model by Huang et al. (1996) with NOAA Climate Division resolution. Winter wheat anomalies (σ) are from detrended 1990–2009 means, with USDA crop reporting district resolution (NA is not available). Stars locate soil moisture monitoring station used in Fig. 7, left panels. Percentages in bottom corners of right panels are for statewide winter wheat harvest completions by (left) 31 May–4 June and (right) 28 June–2 July, obtained from NOAA/USDA Weekly Weather and Crop Bulletin. See section 2c for further details.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Dependence of daily E (mm day⁻¹) on daily SR (MJ m⁻² day ⁻¹) for each May–June study period and all periods combined. May–June daily means are from Figs. 3 (E) and 4 (SR). Numbers at top of bars give number of days in that SR category. Arrows in upper right table indicate direction of parameter increase.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Dependence of daily E (mm day⁻¹) on daily SR (MJ m⁻² day ⁻¹) for each May–June study period and all periods combined. May–June daily means are from Figs. 3 (E) and 4 (SR). Numbers at top of bars give number of days in that SR category. Arrows in upper right table indicate direction of parameter increase.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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Dependence of daily E (mm day⁻¹) on daily SR (MJ m⁻² day ⁻¹) for each May–June study period and all periods combined. May–June daily means are from Figs. 3 (E) and 4 (SR). Numbers at top of bars give number of days in that SR category. Arrows in upper right table indicate direction of parameter increase.

Citation: Journal of Hydrometeorology 13, 6; 10.1175/JHM-D-12-01.1

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At the other extreme, the soil moisture abundance throughout the very wet May–June 2007 CLASIC period (Figs. 7 and 8) resulted from not only that period being the wettest of 1990–2009 (Table 1), but also the preceding January–April ranking fourth wettest during 1990–2009 (Table 1). The resulting extreme soil wetness during June 2007 delayed or prevented the final maturation and harvesting of the crop (Fig. 8, right panel insets). This situation produced a yield that was the fourth lowest for 1990–2009, despite the maximum P, and which was only one rank higher than for the very dry immediately preceding May–June (and January–April) 2006 (Table 1; Fig. 8). Interestingly, this 2007-versus-2006 wheat yield similarity is consistent with the aforementioned near-identical May–June average P_E/P ratios in those years (Fig. 3), and which characterized especially their days when P > 4 mm (Fig. 6).

Concerning the role of SR for E and recycling, SR was higher in all P categories for one or both of the very dry May–June periods than in the two wet periods (Fig. 6), and thus did not suppress E in the dry periods. Accordingly, the daily SR versus E correlation in Table 2a (−0.24, not significant) suggests the same negative relation as surprisingly characterized the monthly time scales (Tables 2b,c; −0.64 and −0.73, 10% and 5%), albeit much weaker. This implication that soil moisture availability limits the E response to increased SR is assessed further in Fig. 9. Such control is confirmed for all four years combined, the 2002 May–June of intermediate wetness, and (to a lesser extent) the very dry 2006. Only during the very wet CLASIC May–June 2007 did E increase strongly with SR (for SR > 27 MJ m⁻² day⁻¹), consistent with the soil moisture abundance. While E also increased with SR for the May–June days during the very dry 1998 when 25 < SR < 31 MJ m⁻², this involved much lower E rates because of the aforementioned ongoing soil moisture depletion (Figs. 7 and 8) and associated low recycling (Fig. 6). This limitation of E by soil moisture rather than SR previously was noted by Dirmeyer et al. (2009).